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EUR 25193 EN - 2012
Bridge Design to Eurocodes Worked examples
Worked examples presented at the Workshop ldquoBridge Design to Eurocodesrdquo Vienna 4-6 October 2010
Support to the implementation harmonization and further development of the Eurocodes
Y Bouassida E Bouchon P Crespo P Croce L Davaine S Denton M Feldmann R Frank G Hanswille W Hensen B Kolias N Malakatas G Mancini M Ortega G Sedlacek G Tsionis
Editors A Athanasopoulou M Poljansek A Pinto
G Tsionis S Denton
The mission of the JRC is to provide customer-driven scientific and technical support for the conception development implementation and monitoring of EU policies As a service of the European Commission the JRC functions as a reference centre of science and technology for the Union Close to the policy-making process it serves the common interest of the Member States while being independent of special interests whether private or national European Commission Joint Research Centre Contact information Address JRC ELSA Unit TP 480 I-21027 Ispra (VA) Italy E-mail eurocodesjrceceuropaeu Tel +39-0332-789989 Fax +39-0332-789049 httpwwwjrceceuropaeu Legal Notice Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of this publication
Europe Direct is a service to help you find answers to your questions about the European Union
Freephone number ()
00 800 6 7 8 9 10 11
() Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed
A great deal of additional information on the European Union is available on the Internet It can be accessed through the Europa server httpeuropaeu JRC 68415 EUR 25193 EN ISBN 978-92-79-22823-0 ISSN 1831-9424 doi 10278882360 Luxembourg Publications Office of the European Union 2012 copy European Union 2012 Reproduction is authorised provided the source is acknowledged Printed in Italy
i
Acknowledgements
The work presented in this report is a deliverable within the framework of the Administrative
Arrangement SI2558935 under the Memorandum of Understanding between the Directorate-General
for Enterprise and Industry of the European Commission (DG ENTR) and the Joint Research Centre
(JRC) on the support to the implementation harmonisation and further development of the
Eurocodes
ii
iii
Table of Contents
Acknowledgements i
Table of contents iii
List of authors and editors xi
Foreword xiii
Introduction xv
Chapter 1
Introduction to the design example
11 Introduction 3
12 Geometry of the deck 3
121 LONGITUDINAL ELEVATION 3
122 TRANSVERSE CROSS-SECTION 3
123 ALTERNATIVE DECKS 4
13 Geometry of the substructure 5
131 PIERS 5
132 ABUTMENTS 7
133 BEARINGS 7
14 Design specifications 8
141 DESIGN WORKING LIFE 8
142 NON-STRUCTURAL ELEMENTS 8
143 TRAFFIC DATA 9
144 ENVIRONMENTAL CONDITIONS 10
145 SOIL CONDITIONS 11
146 SEISMIC DATA 11
147 OTHER SPECIFICATIONS 11
15 Materials 11
16 Details on structural steel and slab reinforcement 12
161 STRUCTURAL STEEL DISTRIBUTION 12
162 DESCRIPTION OF THE SLAB REINFORCEMENT 15
iv
17 Construction process 16
171 LAUNCHING OF THE STEEL GIRDERS 16
172 SLAB CONCRETING 16
Chapter 2
Basis of design (EN 1990)
21 Introduction 21
22 EN 1990 Section 1 ndash General 21
23 EN 1990 Section 2 - Requirements 21
24 EN 1990 Section 3 ndash Principles of limit state design 22
241 DESIGN SITUATIONS 22
242 ULTIMATE LIMIT STATES 23
243 SERVICEABILITY LIMIT STATES 23
25 EN 1990 Section 4 ndash Basic variables 24
251 ACTIONS 24
252 MATERIAL AND PRODUCTS PROPERTIES 25
26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26
27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26
271 DESIGN VALUES 26
272 ULTIMATE LIMIT STATES 27
273 SINGLE SOURCE PRINCIPLE 27
274 SPECIAL CASES IN THE APPLICATION OF EQU 28
275 COMBINATIONS OF ACTIONS 29
276 LIMIT STATE VERIFICATIONS 31
28 Conclusions 32
29 Summary of key concepts 33
CHAPTER 3
Actions on bridge deck and piers (EN 1991)
Part A Wind and thermal action on bridge deck and piers
31 Introduction 37
32 Brief description of the procedure 37
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 CHS ltFEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002gt13 CHT ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt13 CZE 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 DAN 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 DEU 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 ESP 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 ETI 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 FRA ltFEFF005500740069006c006900730065007a00200063006500730020006f007000740069006f006e00730020006100660069006e00200064006500200063007200e900650072002000640065007300200064006f00630075006d0065006e00740073002000410064006f00620065002000500044004600200070006f0075007200200075006e00650020007100750061006c0069007400e90020006400270069006d007000720065007300730069006f006e00200070007200e9007000720065007300730065002e0020004c0065007300200064006f00630075006d0065006e00740073002000500044004600200063007200e900e90073002000700065007500760065006e0074002000ea0074007200650020006f007500760065007200740073002000640061006e00730020004100630072006f006200610074002c002000610069006e00730069002000710075002700410064006f00620065002000520065006100640065007200200035002e0030002000650074002000760065007200730069006f006e007300200075006c007400e90072006900650075007200650073002egt13 GRE 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 HEB ltFEFF05D405E905EA05DE05E905D5002005D105D405D205D305E805D505EA002005D005DC05D4002005DB05D305D9002005DC05D905E605D505E8002005DE05E105DE05DB05D9002000410064006F006200650020005000440046002005D405DE05D505EA05D005DE05D905DD002005DC05D405D305E405E105EA002005E705D305DD002D05D305E405D505E1002005D005D905DB05D505EA05D905EA002E002005DE05E105DE05DB05D90020005000440046002005E905E005D505E605E805D5002005E005D905EA05E005D905DD002005DC05E405EA05D905D705D4002005D105D005DE05E605E205D505EA0020004100630072006F006200610074002005D5002D00410064006F00620065002000520065006100640065007200200035002E0030002005D505D205E805E105D005D505EA002005DE05EA05E705D305DE05D505EA002005D905D505EA05E8002E05D005DE05D905DD002005DC002D005000440046002F0058002D0033002C002005E205D905D905E005D5002005D105DE05D305E805D905DA002005DC05DE05E905EA05DE05E9002005E905DC0020004100630072006F006200610074002E002005DE05E105DE05DB05D90020005000440046002005E905E005D505E605E805D5002005E005D905EA05E005D905DD002005DC05E405EA05D905D705D4002005D105D005DE05E605E205D505EA0020004100630072006F006200610074002005D5002D00410064006F00620065002000520065006100640065007200200035002E0030002005D505D205E805E105D005D505EA002005DE05EA05E705D305DE05D505EA002005D905D505EA05E8002Egt13 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 ITA ltFEFF005500740069006c0069007a007a006100720065002000710075006500730074006500200069006d0070006f007300740061007a0069006f006e00690020007000650072002000630072006500610072006500200064006f00630075006d0065006e00740069002000410064006f00620065002000500044004600200070006900f900200061006400610074007400690020006100200075006e00610020007000720065007300740061006d0070006100200064006900200061006c007400610020007100750061006c0069007400e0002e0020004900200064006f00630075006d0065006e007400690020005000440046002000630072006500610074006900200070006f00730073006f006e006f0020006500730073006500720065002000610070006500720074006900200063006f006e0020004100630072006f00620061007400200065002000410064006f00620065002000520065006100640065007200200035002e003000200065002000760065007200730069006f006e006900200073007500630063006500730073006900760065002egt13 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH 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 LVI 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 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR ltFEFF004200720075006b00200064006900730073006500200069006e006e007300740069006c006c0069006e00670065006e0065002000740069006c002000e50020006f0070007000720065007400740065002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e00740065007200200073006f006d00200065007200200062006500730074002000650067006e0065007400200066006f00720020006600f80072007400720079006b006b0073007500740073006b00720069006600740020006100760020006800f800790020006b00760061006c0069007400650074002e0020005000440046002d0064006f006b0075006d0065006e00740065006e00650020006b0061006e002000e50070006e00650073002000690020004100630072006f00620061007400200065006c006c00650072002000410064006f00620065002000520065006100640065007200200035002e003000200065006c006c00650072002000730065006e006500720065002egt13 POL 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 PTB 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 RUM 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 RUS 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 SKY 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 SLV 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 SUO 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 SVE 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 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
The mission of the JRC is to provide customer-driven scientific and technical support for the conception development implementation and monitoring of EU policies As a service of the European Commission the JRC functions as a reference centre of science and technology for the Union Close to the policy-making process it serves the common interest of the Member States while being independent of special interests whether private or national European Commission Joint Research Centre Contact information Address JRC ELSA Unit TP 480 I-21027 Ispra (VA) Italy E-mail eurocodesjrceceuropaeu Tel +39-0332-789989 Fax +39-0332-789049 httpwwwjrceceuropaeu Legal Notice Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of this publication
Europe Direct is a service to help you find answers to your questions about the European Union
Freephone number ()
00 800 6 7 8 9 10 11
() Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed
A great deal of additional information on the European Union is available on the Internet It can be accessed through the Europa server httpeuropaeu JRC 68415 EUR 25193 EN ISBN 978-92-79-22823-0 ISSN 1831-9424 doi 10278882360 Luxembourg Publications Office of the European Union 2012 copy European Union 2012 Reproduction is authorised provided the source is acknowledged Printed in Italy
i
Acknowledgements
The work presented in this report is a deliverable within the framework of the Administrative
Arrangement SI2558935 under the Memorandum of Understanding between the Directorate-General
for Enterprise and Industry of the European Commission (DG ENTR) and the Joint Research Centre
(JRC) on the support to the implementation harmonisation and further development of the
Eurocodes
ii
iii
Table of Contents
Acknowledgements i
Table of contents iii
List of authors and editors xi
Foreword xiii
Introduction xv
Chapter 1
Introduction to the design example
11 Introduction 3
12 Geometry of the deck 3
121 LONGITUDINAL ELEVATION 3
122 TRANSVERSE CROSS-SECTION 3
123 ALTERNATIVE DECKS 4
13 Geometry of the substructure 5
131 PIERS 5
132 ABUTMENTS 7
133 BEARINGS 7
14 Design specifications 8
141 DESIGN WORKING LIFE 8
142 NON-STRUCTURAL ELEMENTS 8
143 TRAFFIC DATA 9
144 ENVIRONMENTAL CONDITIONS 10
145 SOIL CONDITIONS 11
146 SEISMIC DATA 11
147 OTHER SPECIFICATIONS 11
15 Materials 11
16 Details on structural steel and slab reinforcement 12
161 STRUCTURAL STEEL DISTRIBUTION 12
162 DESCRIPTION OF THE SLAB REINFORCEMENT 15
iv
17 Construction process 16
171 LAUNCHING OF THE STEEL GIRDERS 16
172 SLAB CONCRETING 16
Chapter 2
Basis of design (EN 1990)
21 Introduction 21
22 EN 1990 Section 1 ndash General 21
23 EN 1990 Section 2 - Requirements 21
24 EN 1990 Section 3 ndash Principles of limit state design 22
241 DESIGN SITUATIONS 22
242 ULTIMATE LIMIT STATES 23
243 SERVICEABILITY LIMIT STATES 23
25 EN 1990 Section 4 ndash Basic variables 24
251 ACTIONS 24
252 MATERIAL AND PRODUCTS PROPERTIES 25
26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26
27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26
271 DESIGN VALUES 26
272 ULTIMATE LIMIT STATES 27
273 SINGLE SOURCE PRINCIPLE 27
274 SPECIAL CASES IN THE APPLICATION OF EQU 28
275 COMBINATIONS OF ACTIONS 29
276 LIMIT STATE VERIFICATIONS 31
28 Conclusions 32
29 Summary of key concepts 33
CHAPTER 3
Actions on bridge deck and piers (EN 1991)
Part A Wind and thermal action on bridge deck and piers
31 Introduction 37
32 Brief description of the procedure 37
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
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156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
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159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
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160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
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167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
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168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
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169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
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170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
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171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
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172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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HEB 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 PTB 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 RUM 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 SUO ltFEFF004b00e40079007400e40020006e00e40069007400e4002000610073006500740075006b007300690061002c0020006b0075006e0020006c0075006f00740020006c00e400680069006e006e00e4002000760061006100740069007600610061006e0020007000610069006e006100740075006b00730065006e002000760061006c006d0069007300740065006c00750074007900f6006800f6006e00200073006f00700069007600690061002000410064006f0062006500200050004400460020002d0064006f006b0075006d0065006e007400740065006a0061002e0020004c0075006f0064007500740020005000440046002d0064006f006b0075006d0065006e00740069007400200076006f0069006400610061006e0020006100760061007400610020004100630072006f0062006100740069006c006c00610020006a0061002000410064006f00620065002000520065006100640065007200200035002e0030003a006c006c00610020006a006100200075007500640065006d006d0069006c006c0061002egt13 SVE 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 TUR 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 UKR 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documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
i
Acknowledgements
The work presented in this report is a deliverable within the framework of the Administrative
Arrangement SI2558935 under the Memorandum of Understanding between the Directorate-General
for Enterprise and Industry of the European Commission (DG ENTR) and the Joint Research Centre
(JRC) on the support to the implementation harmonisation and further development of the
Eurocodes
ii
iii
Table of Contents
Acknowledgements i
Table of contents iii
List of authors and editors xi
Foreword xiii
Introduction xv
Chapter 1
Introduction to the design example
11 Introduction 3
12 Geometry of the deck 3
121 LONGITUDINAL ELEVATION 3
122 TRANSVERSE CROSS-SECTION 3
123 ALTERNATIVE DECKS 4
13 Geometry of the substructure 5
131 PIERS 5
132 ABUTMENTS 7
133 BEARINGS 7
14 Design specifications 8
141 DESIGN WORKING LIFE 8
142 NON-STRUCTURAL ELEMENTS 8
143 TRAFFIC DATA 9
144 ENVIRONMENTAL CONDITIONS 10
145 SOIL CONDITIONS 11
146 SEISMIC DATA 11
147 OTHER SPECIFICATIONS 11
15 Materials 11
16 Details on structural steel and slab reinforcement 12
161 STRUCTURAL STEEL DISTRIBUTION 12
162 DESCRIPTION OF THE SLAB REINFORCEMENT 15
iv
17 Construction process 16
171 LAUNCHING OF THE STEEL GIRDERS 16
172 SLAB CONCRETING 16
Chapter 2
Basis of design (EN 1990)
21 Introduction 21
22 EN 1990 Section 1 ndash General 21
23 EN 1990 Section 2 - Requirements 21
24 EN 1990 Section 3 ndash Principles of limit state design 22
241 DESIGN SITUATIONS 22
242 ULTIMATE LIMIT STATES 23
243 SERVICEABILITY LIMIT STATES 23
25 EN 1990 Section 4 ndash Basic variables 24
251 ACTIONS 24
252 MATERIAL AND PRODUCTS PROPERTIES 25
26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26
27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26
271 DESIGN VALUES 26
272 ULTIMATE LIMIT STATES 27
273 SINGLE SOURCE PRINCIPLE 27
274 SPECIAL CASES IN THE APPLICATION OF EQU 28
275 COMBINATIONS OF ACTIONS 29
276 LIMIT STATE VERIFICATIONS 31
28 Conclusions 32
29 Summary of key concepts 33
CHAPTER 3
Actions on bridge deck and piers (EN 1991)
Part A Wind and thermal action on bridge deck and piers
31 Introduction 37
32 Brief description of the procedure 37
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
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154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 DAN 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 DEU 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 ETI 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 HEB 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ii
iii
Table of Contents
Acknowledgements i
Table of contents iii
List of authors and editors xi
Foreword xiii
Introduction xv
Chapter 1
Introduction to the design example
11 Introduction 3
12 Geometry of the deck 3
121 LONGITUDINAL ELEVATION 3
122 TRANSVERSE CROSS-SECTION 3
123 ALTERNATIVE DECKS 4
13 Geometry of the substructure 5
131 PIERS 5
132 ABUTMENTS 7
133 BEARINGS 7
14 Design specifications 8
141 DESIGN WORKING LIFE 8
142 NON-STRUCTURAL ELEMENTS 8
143 TRAFFIC DATA 9
144 ENVIRONMENTAL CONDITIONS 10
145 SOIL CONDITIONS 11
146 SEISMIC DATA 11
147 OTHER SPECIFICATIONS 11
15 Materials 11
16 Details on structural steel and slab reinforcement 12
161 STRUCTURAL STEEL DISTRIBUTION 12
162 DESCRIPTION OF THE SLAB REINFORCEMENT 15
iv
17 Construction process 16
171 LAUNCHING OF THE STEEL GIRDERS 16
172 SLAB CONCRETING 16
Chapter 2
Basis of design (EN 1990)
21 Introduction 21
22 EN 1990 Section 1 ndash General 21
23 EN 1990 Section 2 - Requirements 21
24 EN 1990 Section 3 ndash Principles of limit state design 22
241 DESIGN SITUATIONS 22
242 ULTIMATE LIMIT STATES 23
243 SERVICEABILITY LIMIT STATES 23
25 EN 1990 Section 4 ndash Basic variables 24
251 ACTIONS 24
252 MATERIAL AND PRODUCTS PROPERTIES 25
26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26
27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26
271 DESIGN VALUES 26
272 ULTIMATE LIMIT STATES 27
273 SINGLE SOURCE PRINCIPLE 27
274 SPECIAL CASES IN THE APPLICATION OF EQU 28
275 COMBINATIONS OF ACTIONS 29
276 LIMIT STATE VERIFICATIONS 31
28 Conclusions 32
29 Summary of key concepts 33
CHAPTER 3
Actions on bridge deck and piers (EN 1991)
Part A Wind and thermal action on bridge deck and piers
31 Introduction 37
32 Brief description of the procedure 37
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
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148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
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149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
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150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
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152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
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154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
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159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
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160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 CHS 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ltFEFF005400610074006f0020006e006100730074006100760065006e00ed00200070006f0075017e0069006a007400650020006b0020007600790074007600e101590065006e00ed00200064006f006b0075006d0065006e0074016f002000410064006f006200650020005000440046002c0020006b00740065007200e90020007300650020006e0065006a006c00e90070006500200068006f006400ed002000700072006f0020006b00760061006c00690074006e00ed0020007400690073006b00200061002000700072006500700072006500730073002e002000200056007900740076006f01590065006e00e900200064006f006b0075006d0065006e007400790020005000440046002000620075006400650020006d006f017e006e00e90020006f007400650076015900ed007400200076002000700072006f006700720061006d0065006300680020004100630072006f00620061007400200061002000410064006f00620065002000520065006100640065007200200035002e0030002000610020006e006f0076011b006a016100ed00630068002egt13 DAN 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 DEU ltFEFF00560065007200770065006e00640065006e0020005300690065002000640069006500730065002000450069006e007300740065006c006c0075006e00670065006e0020007a0075006d002000450072007300740065006c006c0065006e00200076006f006e002000410064006f006200650020005000440046002d0044006f006b0075006d0065006e00740065006e002c00200076006f006e002000640065006e0065006e002000530069006500200068006f006300680077006500720074006900670065002000500072006500700072006500730073002d0044007200750063006b0065002000650072007a0065007500670065006e0020006d00f60063006800740065006e002e002000450072007300740065006c006c007400650020005000440046002d0044006f006b0075006d0065006e007400650020006b00f6006e006e0065006e0020006d006900740020004100630072006f00620061007400200075006e0064002000410064006f00620065002000520065006100640065007200200035002e00300020006f0064006500720020006800f600680065007200200067006500f600660066006e00650074002000770065007200640065006e002egt13 ESP 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 ETI 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 FRA 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 GRE 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 HEB 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 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH ltFEFF004e006100750064006f006b0069007400650020016100690075006f007300200070006100720061006d006500740072007500730020006e006f0072011700640061006d00690020006b0075007200740069002000410064006f00620065002000500044004600200064006f006b0075006d0065006e007400750073002c0020006b00750072006900650020006c0061006200690061007500730069006100690020007000720069007400610069006b007900740069002000610075006b01610074006f00730020006b006f006b007900620117007300200070006100720065006e006700740069006e00690061006d00200073007000610075007300640069006e0069006d00750069002e0020002000530075006b0075007200740069002000500044004600200064006f006b0075006d0065006e007400610069002000670061006c006900200062016b007400690020006100740069006400610072006f006d00690020004100630072006f006200610074002000690072002000410064006f00620065002000520065006100640065007200200035002e0030002000610072002000760117006c00650073006e0117006d00690073002000760065007200730069006a006f006d00690073002egt13 LVI 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 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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 RUM 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 RUS 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 SKY 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 SLV 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 SUO 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 SVE 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 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
iii
Table of Contents
Acknowledgements i
Table of contents iii
List of authors and editors xi
Foreword xiii
Introduction xv
Chapter 1
Introduction to the design example
11 Introduction 3
12 Geometry of the deck 3
121 LONGITUDINAL ELEVATION 3
122 TRANSVERSE CROSS-SECTION 3
123 ALTERNATIVE DECKS 4
13 Geometry of the substructure 5
131 PIERS 5
132 ABUTMENTS 7
133 BEARINGS 7
14 Design specifications 8
141 DESIGN WORKING LIFE 8
142 NON-STRUCTURAL ELEMENTS 8
143 TRAFFIC DATA 9
144 ENVIRONMENTAL CONDITIONS 10
145 SOIL CONDITIONS 11
146 SEISMIC DATA 11
147 OTHER SPECIFICATIONS 11
15 Materials 11
16 Details on structural steel and slab reinforcement 12
161 STRUCTURAL STEEL DISTRIBUTION 12
162 DESCRIPTION OF THE SLAB REINFORCEMENT 15
iv
17 Construction process 16
171 LAUNCHING OF THE STEEL GIRDERS 16
172 SLAB CONCRETING 16
Chapter 2
Basis of design (EN 1990)
21 Introduction 21
22 EN 1990 Section 1 ndash General 21
23 EN 1990 Section 2 - Requirements 21
24 EN 1990 Section 3 ndash Principles of limit state design 22
241 DESIGN SITUATIONS 22
242 ULTIMATE LIMIT STATES 23
243 SERVICEABILITY LIMIT STATES 23
25 EN 1990 Section 4 ndash Basic variables 24
251 ACTIONS 24
252 MATERIAL AND PRODUCTS PROPERTIES 25
26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26
27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26
271 DESIGN VALUES 26
272 ULTIMATE LIMIT STATES 27
273 SINGLE SOURCE PRINCIPLE 27
274 SPECIAL CASES IN THE APPLICATION OF EQU 28
275 COMBINATIONS OF ACTIONS 29
276 LIMIT STATE VERIFICATIONS 31
28 Conclusions 32
29 Summary of key concepts 33
CHAPTER 3
Actions on bridge deck and piers (EN 1991)
Part A Wind and thermal action on bridge deck and piers
31 Introduction 37
32 Brief description of the procedure 37
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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ltFEFF04180437043f043e043b043704320430043904420435002004420435043704380020043d0430044104420440043e0439043a0438002c00200437043000200434043000200441044a0437043404300432043004420435002000410064006f00620065002000500044004600200434043e043a0443043c0435043d04420438002c0020043c0430043a04410438043c0430043b043d043e0020043f044004380433043e04340435043d04380020043704300020043204380441043e043a043e043a0430044704350441044204320435043d0020043f04350447043004420020043704300020043f044004350434043f0435044704300442043d04300020043f043e04340433043e0442043e0432043a0430002e002000200421044a04370434043004340435043d043804420435002000500044004600200434043e043a0443043c0435043d044204380020043c043e0433043004420020043404300020044104350020043e0442043204300440044f0442002004410020004100630072006f00620061007400200438002000410064006f00620065002000520065006100640065007200200035002e00300020043800200441043b0435043404320430044904380020043204350440044104380438002egt13 CHS ltFEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002gt13 CHT ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt13 CZE 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 DAN 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 DEU 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 ESP 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 ETI 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 FRA 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 GRE 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HEB 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 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH ltFEFF004e006100750064006f006b0069007400650020016100690075006f007300200070006100720061006d006500740072007500730020006e006f0072011700640061006d00690020006b0075007200740069002000410064006f00620065002000500044004600200064006f006b0075006d0065006e007400750073002c0020006b00750072006900650020006c0061006200690061007500730069006100690020007000720069007400610069006b007900740069002000610075006b01610074006f00730020006b006f006b007900620117007300200070006100720065006e006700740069006e00690061006d00200073007000610075007300640069006e0069006d00750069002e0020002000530075006b0075007200740069002000500044004600200064006f006b0075006d0065006e007400610069002000670061006c006900200062016b007400690020006100740069006400610072006f006d00690020004100630072006f006200610074002000690072002000410064006f00620065002000520065006100640065007200200035002e0030002000610072002000760117006c00650073006e0117006d00690073002000760065007200730069006a006f006d00690073002egt13 LVI 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 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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 RUM 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 RUS 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 SKY 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 SLV 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 SUO 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 SVE ltFEFF0041006e007600e4006e00640020006400650020006800e4007200200069006e0073007400e4006c006c006e0069006e006700610072006e00610020006f006d002000640075002000760069006c006c00200073006b006100700061002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e007400200073006f006d002000e400720020006c00e4006d0070006c0069006700610020006600f60072002000700072006500700072006500730073002d007500740073006b00720069006600740020006d006500640020006800f600670020006b00760061006c0069007400650074002e002000200053006b006100700061006400650020005000440046002d0064006f006b0075006d0065006e00740020006b0061006e002000f600700070006e00610073002000690020004100630072006f0062006100740020006f00630068002000410064006f00620065002000520065006100640065007200200035002e00300020006f00630068002000730065006e006100720065002egt13 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
iv
17 Construction process 16
171 LAUNCHING OF THE STEEL GIRDERS 16
172 SLAB CONCRETING 16
Chapter 2
Basis of design (EN 1990)
21 Introduction 21
22 EN 1990 Section 1 ndash General 21
23 EN 1990 Section 2 - Requirements 21
24 EN 1990 Section 3 ndash Principles of limit state design 22
241 DESIGN SITUATIONS 22
242 ULTIMATE LIMIT STATES 23
243 SERVICEABILITY LIMIT STATES 23
25 EN 1990 Section 4 ndash Basic variables 24
251 ACTIONS 24
252 MATERIAL AND PRODUCTS PROPERTIES 25
26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26
27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26
271 DESIGN VALUES 26
272 ULTIMATE LIMIT STATES 27
273 SINGLE SOURCE PRINCIPLE 27
274 SPECIAL CASES IN THE APPLICATION OF EQU 28
275 COMBINATIONS OF ACTIONS 29
276 LIMIT STATE VERIFICATIONS 31
28 Conclusions 32
29 Summary of key concepts 33
CHAPTER 3
Actions on bridge deck and piers (EN 1991)
Part A Wind and thermal action on bridge deck and piers
31 Introduction 37
32 Brief description of the procedure 37
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
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156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
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159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
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160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
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167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
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168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
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169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
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170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
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171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
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172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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HEB 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 UKR 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documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
v
33 Wind actions on the deck 40
331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40
332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43
333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)
43
334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)
45
335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46
34 Wind actions on the piers 46
341 SQUAT RECTANGULAR PIER 250x500x1000 46
342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47
35 Thermal actions 48
Part B Action during execution accidental actions and traffic loads
36 Introduction 50
37 Actions during execution 50
371 LAUNCHING PHASE 52
38 Accidental actions 55
381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56
382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56
39 Traffic loads 57
391 STATIC LOAD MODELS 58
392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60
393 LOAD COMBINATIONS FOR THE CASE STUDY 61
394 FATIGUE LOAD MODELS 65
395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67
CHAPTER 4
Bridge deck modelling and structural analysis
41 Introduction 79
42 Shear lag effect 79
421 GLOBAL ANALYSIS 79
422 SECTION ANALYSIS 80
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
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156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
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159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
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160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
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169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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ltFEFF004200720075006700200069006e0064007300740069006c006c0069006e006700650072006e0065002000740069006c0020006100740020006f007000720065007400740065002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e007400650072002c0020006400650072002000620065006400730074002000650067006e006500720020007300690067002000740069006c002000700072006500700072006500730073002d007500640073006b007200690076006e0069006e00670020006100660020006800f8006a0020006b00760061006c0069007400650074002e0020004400650020006f007000720065007400740065006400650020005000440046002d0064006f006b0075006d0065006e0074006500720020006b0061006e002000e50062006e00650073002000690020004100630072006f00620061007400200065006c006c006500720020004100630072006f006200610074002000520065006100640065007200200035002e00300020006f00670020006e0079006500720065002egt13 DEU 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 ETI 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 HEB 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 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
vi
43 Concrete creep effect (modular ratios) 81
431 SHORT TERM MODULA RATIO 81
432 LONG TERM MODULAR RATIO 81
44 Elastic mechanical properties of the cross sections 83
441 UN-CRACKED COMPOSITE BEHAVIOR 83
442 CKRACKED COMPOSITE BEHAVIOR 84
45 Actions modelling 85
451 SELF-WEIGHT 85
452 NON-STRUCTURAL EQUIPMENTS 85
453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86
454 ROAD TRAFFIC 87
46 Global analysis 90
47 Main results 91
471 VERTICAL SUPPORT REACTIONS 92
472 INTERNAL FORCES AND MOMENTS 92
473 STRESSES AT ULS 92
CHAPTER 5 93
Concrete bridge design (EN 1992-2)
51 Introduction 97
52 Local verifications in the concrete slab 97
521 DURABILITY ndash CPVER TO REINFORCEMENT 97
522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99
523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116
524 PUNCHING SHEAR (ULS) 118
53 Second order effects in the high piers 121
531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS
121
532 FORCES AND MOMENTS ON TOP OF THE PIERS 122
533 SECOND ORDER EFFECTS 122
vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 DAN 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 DEU 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 ETI 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ltFEFF03a703c103b703c303b903bc03bf03c003bf03b903ae03c303c403b5002003b103c503c403ad03c2002003c403b903c2002003c103c503b803bc03af03c303b503b903c2002003b303b903b1002003bd03b1002003b403b703bc03b903bf03c503c103b303ae03c303b503c403b5002003ad03b303b303c103b103c603b1002000410064006f006200650020005000440046002003c003bf03c5002003b503af03bd03b103b9002003ba03b103c42019002003b503be03bf03c703ae03bd002003ba03b103c403ac03bb03bb03b703bb03b1002003b303b903b1002003c003c103bf002d03b503ba03c403c503c003c903c403b903ba03ad03c2002003b503c103b303b103c303af03b503c2002003c503c803b703bb03ae03c2002003c003bf03b903cc03c403b703c403b103c2002e0020002003a403b10020005000440046002003ad03b303b303c103b103c603b1002003c003bf03c5002003ad03c703b503c403b5002003b403b703bc03b903bf03c503c103b303ae03c303b503b9002003bc03c003bf03c103bf03cd03bd002003bd03b1002003b103bd03bf03b903c703c403bf03cd03bd002003bc03b5002003c403bf0020004100630072006f006200610074002c002003c403bf002000410064006f00620065002000520065006100640065007200200035002e0030002003ba03b103b9002003bc03b503c403b103b303b503bd03ad03c303c403b503c103b503c2002003b503ba03b403cc03c303b503b903c2002egt13 HEB 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vii
CHAPTER 6
Composite bridge design (EN 1994-2)
61 Verification of cross-section at mid-span P1-P2 127
611 GEOMETRY AND STRESSES 127
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
127
613 PLASTIC SECTION ANALYSIS 130
62 Verification of cross-section at internal support P1 132
621 GEOMETRY AND STRESSES 132
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
132
623 SECTION ANALYSIS 134
63 Alternative double composite cross-section at internal support P-1 139
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
142
632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK
144
633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
144
64 Verification of the Serviceability Limit Sates (SLS) 145
65 Stresses control at Serviceability Limit States 145
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145
652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146
653 STRESS LIMITATION IN STRUCTURAL STEEL 147
654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES
150
655 LIMITATION OF WEB BREATHING 151
66 Control of cracking for longitudinal global bending 151
661 MAXIMUM VALUE OF CRACK WIDTH 151
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152
663 CONTROL OF CRACKING UNDER DIRECT LOADING 153
664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155
67 Shear connection at steel-concrete interface 156
671 RESISTANCE OF HEADED STUDS 156
672 DETAILING OF SHEAR CONNECTION 157
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
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154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
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155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
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156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
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159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
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160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 DAN 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 DEU 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 ETI 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 GRE 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 HEB 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UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
viii
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
160
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
163
675 SYNOPSIS OF THE DESIGN EXAMPLE 165
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
166
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
171
CHAPTER 7
Geotechnical aspects of bridge design (EN 1997)
71 Introduction 177
72 Geotechnical data 177
73 Ultimate limit states 183
731 SUPPORT REACTIONS 183
732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185
74 Abutment C0 189
741 BEARING CAPACITY (ULS) 189
742 SLIDING (ULS) 192
75 Pier P1 (Squat Pier) 193
751 BEARING CAPACITY (ULS) 193
752 SETTLEMENT (SLS) 195
76 Seismic design situations 196
CHAPTER 8
Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
81 Introduction 201
82 Example of ductile pier 201
821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201
822 SEISMIC STRUCTURAL SYSTEM 203
823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION
205
824 MULTIMODE RESPONSE ANALYSIS 206
825 DESIGN ACTION EFFECTS AND VERIFICATION 209
826 BEARINGS AND ROADWAY JOINTS 219
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
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154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 DAN 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 DEU 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 ETI 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 HEB 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documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
ix
827 CONCLUSION FOR DESIGN CONCEPT 224
83 Example of limited ductile piers 224
831 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 224
832 DESIGN SEISMIC ACTION 225
833 SEISIC ANALYSIS 226
834 VERIFICATIONS OF PIERS 237
835 BEARINGS AND JOINTS 239
84 Example of seismic isolation 241
841 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 241
842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247
843 DESIGN SEISMI ACTION 249
844 SEISMIC STRUCTURAL SYSTEM 253
845 FUNDAMENTAL MODE METHOD 257
846 NON-LINERTIME HISTORY ANALYSIS 262
847 VERIFICATION OF THE ISOLATION SYSTEM 269
848 VERIFICATION OF SUBSTRUCTURE 271
849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278
8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279
APPENDICES 283
APPENDIX A A-1
Design of steel bridges Overview of key contents of EN 1993
APPENDIX B B-1
A sample analytical method for bearing resistance calculation
APPENDIX C C-1
Examples of a method to calculate settlements for spread foundations
APPENDIX D D-1
Generation of semi-artificial accelerograms for time-history analysis through modification of natural records
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
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169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 DAN 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 DEU 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 ETI 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 HEB 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 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 RUM ltFEFF005500740069006c0069007a00610163006900200061006300650073007400650020007300650074010300720069002000700065006e007400720075002000610020006300720065006100200064006f00630075006d0065006e00740065002000410064006f006200650020005000440046002000610064006500630076006100740065002000700065006e0074007200750020007400690070010300720069007200650061002000700072006500700072006500730073002000640065002000630061006c006900740061007400650020007300750070006500720069006f006100720103002e002000200044006f00630075006d0065006e00740065006c00650020005000440046002000630072006500610074006500200070006f00740020006600690020006400650073006300680069007300650020006300750020004100630072006f006200610074002c002000410064006f00620065002000520065006100640065007200200035002e00300020015f00690020007600650072007300690075006e0069006c006500200075006c0074006500720069006f006100720065002egt13 RUS 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ltFEFF005900fc006b00730065006b0020006b0061006c006900740065006c0069002000f6006e002000790061007a006401310072006d00610020006200610073006b013100730131006e006100200065006e0020006900790069002000750079006100620069006c006500630065006b002000410064006f006200650020005000440046002000620065006c00670065006c0065007200690020006f006c0075015f007400750072006d0061006b0020006900e70069006e00200062007500200061007900610072006c0061007201310020006b0075006c006c0061006e0131006e002e00200020004f006c0075015f0074007500720075006c0061006e0020005000440046002000620065006c00670065006c0065007200690020004100630072006f006200610074002000760065002000410064006f00620065002000520065006100640065007200200035002e003000200076006500200073006f006e0072006100730131006e00640061006b00690020007300fc007200fc006d006c00650072006c00650020006100e70131006c006100620069006c00690072002egt13 UKR 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UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
x
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
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156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
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157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
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158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
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159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
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160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
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161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
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162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
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163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
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164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
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165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
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166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
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167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
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168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
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169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
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170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
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171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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HEB 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maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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 RUM 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 RUS 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 SLV 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 SUO 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 SVE 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 TUR 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 UKR ltFEFF04120438043a043e0440043804410442043e043204430439044204350020044604560020043f043004400430043c043504420440043800200434043b044f0020044104420432043e04400435043d043d044f00200434043e043a0443043c0435043d044204560432002000410064006f006200650020005000440046002c0020044f043a04560020043d04300439043a04400430044904350020043f045604340445043e0434044f0442044c00200434043b044f0020043204380441043e043a043e044f043a04560441043d043e0433043e0020043f0435044004350434043404400443043a043e0432043e0433043e0020043404400443043a0443002e00200020042104420432043e04400435043d045600200434043e043a0443043c0435043d0442043800200050004400460020043c043e0436043d04300020043204560434043a0440043804420438002004430020004100630072006f006200610074002004420430002000410064006f00620065002000520065006100640065007200200035002e0030002004300431043e0020043f04560437043d04560448043e04570020043204350440044104560457002egt13 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
xi
List of authors and editors
Authors
Introduction
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges
Chapter 1 ndash Introduction to the design example
Pilar Crespo Ministry of Public Works (Spain)
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 2 ndash Basis of design (EN 1990)
Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges
Chapter 3 ndash Actions on bridge decks and piers (EN 1991)
Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)
Pietro Croce Department of Civil Engineering University of Pisa Italy
Chapter 4 ndash Bridge deck modeling and design
Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)
Chapter 5 ndash Concrete bridge design (EN 1992)
Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France
Giuseppe Mancini Politecnico di Torino Italy
Chapter 6 ndash Composite bridge design (EN 1994-2)
Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain
Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France
Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)
Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES
Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)
Basil Kolias DENCO SA Athens
Appendix A ndash Design of steel bridges Overview of key content of EN 1993
Gerhard Hanswille Bergische Universitat
Wolfang Hensen PSP - Consulting Engineers
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 DAN 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 DEU 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 ESP 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 ETI 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 FRA 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 GRE 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HEB 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HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH 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maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 RUM 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 RUS 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 SKY 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 SLV 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 SUO 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 SVE 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 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13
xii
Markus Feldmann RWTH Aachen University
Gerhard Sedlacek RWTH Aachen University
Editors
Adamantia Athanasopoulou Martin Poljansek Artur Pinto
European Laboratory for Structural Assessment
Institute for the Protection and Security of the Citizen
Joint Research Centre European Commission
Georgios Tsionis Steve Denton
CENTC250 Horizontal Group Bridges
xiii
Foreword
The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy
In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire
With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level
In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports
1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector
2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)
3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications
4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee
5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group
Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group
The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes
xiv
This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users
The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode
The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it
We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop
It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators
All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)
Ispra November 2011
Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)
Institute for the Protection and Security of the Citizen (IPSC)
Joint Research Centre (JRC) - European Commission
Steve Denton George Tsionis CENTC250 Horizontal Group Bridges
xv
Introduction
The Eurocodes are currently in the process of national implementation towards becoming the Europe-
wide means for structural design of civil engineering works
As part of the strategy and general programme for promotion and training on the Eurocodes a
workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main
objective of this workshop was to transfer background knowledge and expertise The workshop aimed
to provide state-of-the-art training material and background information on Eurocodes with an
emphasis on practical worked examples
This report collects together the material that was prepared and presented at the workshop by a
group of experts who have been actively involved in the development of the Eurocodes It
summarises important points of the Eurocodes for the design of concrete steel and composite road
bridges including foundations and seismic design The worked examples utilise a common bridge
project as a basis although inevitably they are not exhaustive
THE EUROCODES FOR THE DESIGN OF BRIDGES
The Eurocodes
The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of
civil engineering works and construction products They were produced by the European Committee
for Standardization (CEN) and embody national experience and research output together with the
expertise of international technical and scientific organisations The Eurocodes suite covers all
principal construction materials all major fields of structural engineering and a wide range of types of
structures and products
Table I Eurocode parts
EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures
From March 2010 the Eurocodes were intended to be the only Standards for the design of structures
in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The
Member States of the EU and EFTA recognise that the Eurocodes serve as
a means to prove compliance of buildings and civil engineering works with the essential
requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential
Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case
of firerdquo
a basis for specifying contracts for construction works and related engineering services
xvi
a framework for drawing up harmonised technical specifications for construction products (ENs
and ETAs)
The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural
Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the
Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within
CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to
support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group
Bridges embraces the following work streams maintenance and evolution of Eurocodes development
of National Annexes and harmonisation promotion (trainingguidance and international) future
developments and promotion of research needs
Bridge Parts of the Eurocodes
Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The
Eurocodes for concrete steel composite and timber structures and for seismic design comprise a
Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be
used for the design of new bridges including piers abutments upstand walls wing walls and flank
walls etc and their foundations The materials covered are i) plain reinforced and prestressed
concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)
timber or other wood-based materials either singly or compositely with concrete steel or other
materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and
masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of
Eurocode 8
A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN
1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for
geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for
the design of concrete steel and composite bridges are given in Table II
The ten Eurocodes are part of the broader family of European standards which also include material
product and execution standards The Eurocodes are intended to be used together with such
normative documents and through reference to them adopt some of their provisions Fig I
schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product
(eg bearings barriers and parapets) and execution standards for the design and construction of a
bridge
xvii
Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements
EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic
Figure I Use of Eurocodes with product material and execution standards for a bridge
xviii
THE DESIGN EXAMPLE
The worked examples in this report refer to the same structure However some modifications andor
extensions are introduced to cover some specific issues that would not otherwise be addressed
details are given in the pertinent chapters Timber bridges are not treated in this report although their
design is covered by the Eurocodes
The following assumptions have been made
the bridge is not spanning a river and therefore no hydraulic actions are considered
the climatic conditions are such that snow actions are not considered
the soil properties allow for the use of shallow foundations
the recommended values for the Nationally Determined Parameters are used throughout
The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)
The continuous composite deck is made up of two steel girders with I cross-section and a concrete
slab with total width 120 m Alternative configurations namely transverse connection at the bottom of
the steel girders and use of external tendons are also studied Two solutions are considered for the
piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a
50times25 m rectangular cross-section while the slender piers have a circular cross-section with external
diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the
piers and free to move on the abutments For the case of squat piers the deck is connected to each
pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow
footings The abutments are made up of gravity walls that rest on rectangular footings
The configuration of the example bridge was chosen for the purpose of this workshop It is not
proposed as the optimum solution and it is understood that other possibilities exist It is also noted
that the example is not fully comprehensive and there are aspects that are not covered
Figure II Geometry of the example bridge
OUTLINE OF THE REPORT
Following the introduction Chapter 1 describes the geometry and materials of the example bridge as
well as the main assumptions and the detailed structural calculations Each of the subsequent
chapters presents the main principles and rules of a specific Eurocode and their application on the
example bridge The key concepts of basis of design namely design situations limit states the single
source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with
the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM
analysis and the design of the deck and the piers for the ULS and the SLS including the second-
order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of
xix
composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep
and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three
design approaches for the abutment and the verification of the foundation for the seismic design
situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance
considering the alternative solutions of slender or squat piers the latter case involves seismic
isolation and design for ductile behaviour
Steve Denton Chairman of Horizontal Group Bridges
Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges
CHAPTER 6
Composite bridge design (EN1994-2)
Miguel ORTEGA CORNEJO
Project Manager IDEAM SA
Prof at University ldquoEuropea de Madridrdquo Spain
Joeumll RAOUL
Assistant to the Director of Large Bridge Division SeacutetraCTOA
Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France
Convenor EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
126
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
127
61 Verification of cross-section at mid-span P1-P2
611 GEOMETRY AND STRESSES
At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases
The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN
Fig 61 Stresses at ULS in cross-section at mid-span P1-P2
Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression
612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1
To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows
o Design plastic resistance of the concrete in compression
γ= = times =ck
c cc
fF A MN
085 085middot3519484 38643
150 (force of frac12 slab)
Note that the design compressive strength of concrete is γ
= ckcd
c
ff (EN-1994-2 2412)
EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
128
applied α
γ= cc ck
cdc
ff
middot αcc takes account of the long term effects on the compressive
strength and of unfavourable effects resulting from the way the loads are applied
The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1
- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63
Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)
Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)
- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges
- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab
- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100
o The reinforcing steel bars in compression are neglected
o Design plastic resistance of the structural steel upper flange (1 flange)
1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
129
γ= = times times =y uf
s uf s ufM
fF A MN
0
345(10 004) 1380
10
Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(272 0018) 16891
10
o Design plastic resistance of the structural steel lower flange (1 flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
345(120 004) 1656
10
Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2
As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is
concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange
The internal axial forces equilibrium of the cross section leads to the location of the PNA
minusminus minus + + + =c s uf s uf s w s lf
xF F x F F F
(004 )middot middot 0
004
minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm
As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)
Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
130
This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web
613 PLASTIC SECTION ANALYSIS
6131 Bending resistance check
The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)
MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)
MplRd = 7959 MNmiddotm
MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified
The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))
6132 Shear resistance check
As τ
εη
= = ge =w
w
hk
t272 31
15111 51360018
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times= + = =le times
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2720middot1810 1063
3middot 3 110 (EN 1993-1-5 52)
Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN
As the vertical frame posts are assumed to be rigid
τ = + = + times =
whk
a
2 2272534 4 534 4 5802
8 is the shear buckling coefficient according to EN-
1993-1-5 Annex A3
( ) ( )π π
σν
times= = =
times
times times timestimes
wE
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 188312
12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)
ττ σ= = times =cr Ek MPa5802 8312 4822
(EN-1993-1-5 53)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
131
λττ
= = = =y w y ww
crcr
f f 345
076 076 20324822middot 3
is the slenderness of the panel according to EN-1993-
1-5 53 As wλ is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370501
07 203207(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γ
times times times= = =
timestimesw y w w
bw Rd
M
f h tV MN -6
1
0501 345 2720 184441
3 3middot1 1010
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b Rd
V V V MN V MN
444 0 1063 444
And η
γ
times times times= = =
timesy w w
pl a Rd
M
f h tV E MN -6
0
12 345 2720 181170
3 3 10 (EN 1993-1-1 626)
So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified
6133 Bending and vertical shear interaction
According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)
In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V
Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and
without shear buckling (b) (Figure 66 of 1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
132
62 Verification of cross-section at internal support P1
621 GEOMETRY AND STRESSES
At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases
Fig 66 Stresses at ULS in cross-section at internal support P1
Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression
The internal forces and moments in this cross-section are
MEd = -10935 MNmiddotm
VEd = 812 MN
622 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =lf wb t
c mm1200 26
587 2 2
ε= = le = times =lf
ct
587 2354891 9 9 8033
120 295
(Lower flange tlf=120 mm fylf=295 MPa)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
133
Then the lower flange is in Class 1
The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows
o The slab is cracked and its contribution is neglected
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
1 1
500144996 10 6304
115 (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γ= = times times =sk
s ss
fF A m MN-4 2
2 2
50092797 10 4034
115 (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =y uf
s uf s ufM
fF A MN
0
295(12 012) 354
10
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =y w
s w s wM
fF A MN
0
345(256 0026) 22963
10
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =y lf
s lf s lfM
fF A MN
0
295(120 012) 4248
10
As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)
the PNA is deduced to be located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA
minus+ + + minus minus =s s s uf s w s w s w s lf
x xF F F F F F F1 2 (256 ) 0
256 256
6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m
Over half of the steel web is in compression (the lower part) 256-1098=1462 m
α = = = gtw
w
h xh
- 256 - 10980571 050
256
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then
The limiting slenderness between Class 2 and Class 3 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
134
εα
= = gtgt = =minus minus
ct
235456middot
256 456 3459846 58590026 13 1 13middot0571 1
The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)
( ) ( )ε ψ ψ= = le times = times + =times timesct
256 2359846 62 1- (- ) 62 1 1059 1059 10849
0026 345
It is concluded that the steel web is in Class 3
Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis
623 SECTION ANALYSIS
6231 Elastic bending verification
In the elastic bending verification the maximum stresses in the structural steel must be below the
yield strength σγ
le0
ys
M
f
As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified
This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))
6232 Alternative Plastic bending verification (Effective Class 2 cross-section)
EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
135
Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA
εγ γ
+ + + times minus times times times times minus =
y w y ws s s uf w w s lf
M M
f fF F F X t t F
1 2 0 0
2 20 0
6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m
And the hogging bending moment resistance of the effective class 2 cross-section is
MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm
As = lt =10935 12253Ed pl RdM M the bending resistance is verified
6233 Shear resistance check
As τ
εη
= = ge =w
w
hk
t256 31
9846 51360026
the web (stiffened by the vertical stiffeners) should be
checked in terms of shear buckling according to EN-1993-1-5 51
The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626
η
γ
times times times= + le = times =
timesy w w
b Rd bw Rd bf Rd
M
f h tV V V MN -6
1
12 345 2560 2610 1446
3 3middot1 10 (EN 1993-1-5 52)
Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN
The vertical frame posts are assumed to be rigid This yields
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
136
τ = + = + =
whk
a
2 2256534 4 534 4 575
8 is the shear buckling coefficient according to EN-1993-
1-5 Annex A3
( ) ( )π π
σν
times times times= = =
minus times minus timesw
E
w
EtMPa
h
2 2 2 5 2
2 2 2 2
21 10 261958
12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)
ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)
λττ
= = = =y w y ww
crcr
f f 345076 076 133
11258middot 3 is the slenderness of the panel according to EN-
1993-1-5 53 As λw is ge108 then
The factor for the contribution of the web to the shear buckling resistance χw is
( ) ( )χ
λ= = =
++w
w
137 1370675
07 13307(Table 51 of EN-1993-1-5 53)
Finally the contribution of the web to the shear buckling resistance is
χ
γminustimes times times
= = times =times
w y w wbw Rd
M
f h tV MN 6
1
0675 345 2560 2610 814
3 3 110
If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814
And η
γminustimes times times
= = times =times
y w wpl a Rd
M
f h tV MN 6
0
12 345 2560 2610 1591
3 3 10 (EN 1993-1-1 626)
As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance
6234 Flange contribution to the shear buckling resistance
When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1
Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way
Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web
MfRd is the plastic bending resistance of the cross-section neglecting the web area
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
137
Fig 68 Design plastic bending resistance neglecting the web area
If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA
( )minus+ + minus minus =s s s uf s uf s lf
xxF F F F F1 2
0120
012 012
( )minus+ + sdot minus sdot minus =
xx 0126304 4034 354 354 4248 0
012 012
Then x =01145 m
And the hogging bending moment resistance of the effective cross-section neglecting the web area is
MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm
As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the
influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example
Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as
γ
= minus
f f yf Edbf Rd
M f Rd
b t f MV
c M
22
1
1middot
As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance
According to EN-1993-1-5 54 (1)
times times times= + = + =
times times
f f yf
w yw
b t fc a m
th f
2 2
2 2
16 16 1200 120 295025 8 025 3110
26 256 345
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
138
Then minus times = minus = times
timesbf RdV
226
1200 120 295 10935middot 1 0197 MN
3110 11 1174010
The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained
before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is
= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0197 1446 8337
The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before
According to EN-1993-1-5 55 the shear verification is
η = le3
10Ed
b Rd
VV
and in this case η = =3
81209975
814 without considering the contribution of the
flanges to the shear buckling resistance
6235 Bending and shear interaction
The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified
η η
+ minus minus le
f Rd
pl Rd
MM
21 3
1 2 1 10
Where
η = Ed
pl Rd
MM1
and η = Ed
bw Rd
VV3
Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
139
This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener
If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side
Then we will verify the interaction for the design internal forces and moments
VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN
That leads to η = =1
1006050818
12297 η = =3
788509686
814 and
[ ]η η+ minus minus = + minus times minus = le
f Rd
pl Rd
M
M
2 21 3
117401 2 1 0818 1 2 09686 1 0858 1
12297
So the interaction M-V is verified
Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section
63 Alternative double composite cross-section at internal support P-1
As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them
The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange
Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion
The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state
As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives
Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
140
Fig 610 Two examples of road composite bridges with double composite action in hogging
areas
Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m
In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion
The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending
Fig 611 Example of a High Speed Railway Viaduct with double composite action
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
141
Fig 612 Cross-section at support P-1 with double composite action Design plastic bending
resistance
Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange
Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction
Fig 613 Alternative steel distribution of the double composite main girder and bottom
concrete slab thickness
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
142
For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action
EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable
EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods
Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression
631 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)
The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)
The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)
minus minus= = =
1000 26487 mm
2 2lf wb t
c
ε= = le = =487 235
8116 10middot 10middot 837560 335lf
ct
(Lower flange tlf=60 mm fylf=335 MPa)
Then the lower flange is in Class 2
The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows
o The tensioned upper slab is cracked and we neglect its contribution
o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)
γminus= = times =times4 2
1 1
500144996 10 6304 MN
115sk
s ss
fF A m (force of frac12 slab)
o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)
γminus= = times =times4 2
2 2
50092797 10 4034 MN
115sk
s ss
fF A m (force of frac12 slab)
o Design plastic resistance of the structural steel upper flange (1 flange)
γ= = times times =
0
295(12 012) 354 MN
10y uf
s uf s ufM
fF A
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
143
o Design plastic resistance of the total structural steel web (1 web)
γ= = times times =
0
345(262 0026) 2350 MN
10y w
s w s wM
fF A
o Design plastic resistance of the structural steel lower flange (1 lower flange)
γ= = times times =
0
335(100 006) 201 MN
10y lf
s lf s lfM
fF A
o Design plastic resistance of the bottom concrete slab in compression
γtimes
= = times times =inf
085 085 3535 05 347 MN
150ck
c cc
fF A
As + + le + +1 2 infs s s uf s w s lf cF F F F F F
(4573le783) and
+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web
If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA
minus+ + + minus minus minus =1 2 inf
(262 )0
262 262s s s uf s w s w s w s lf c
x xF F F F F F F F
6304+4034+354+897middotX-235+897middotX-548=0 X=1815 m
Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m
αminus minus
= = = le262 1815
0307 050262
w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then
Therefore the limiting slenderness between Class 2 and Class 3 is given by
εα
times= = lt = =
235415
262 415 34510076 111560026 0307
ct
According to this the steel web is in Class 2
However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before
With this new values αminus minus
= = = le
212 18150144 050
212w
w
h xh
Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then
Therefore the limiting slenderness between Class 1 and Class 2 is given by
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
144
εα
times= = lt = =
23536
212 36 3458154 206330026 0144
ct
The steel web could be in fact classified as Class 1
Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section
632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK
If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is
MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm
In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders
For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case
633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE
EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40
Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete
In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance
Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance
In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm
In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
145
64 Verification of the Serviceability Limit States (SLS)
EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are
o The functioning of the structure or structural members under normal use
o The comfort of people
o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics
At SLS under global longitudinal bending the following should be verified
o Stress limitation and web breathing according to EN-1994 72
o Deformations deflections and vibrations according to EN-1994 73
o Cracking of concrete according to EN-1994 74
In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73
65 Stresses control at Serviceability Limit States
651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE
EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation
EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption
Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
146
Fig 614 Concrete slab stress under the characteristic SLS combination
652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS
Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)
Fig 615 Upper reinforcement layer stress under the characteristic SLS combination
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
147
Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)
Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa
Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)
When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)
653 STRESS LIMITATION IN STRUCTURAL STEEL
EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS
For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)
σγ
le
yEd ser
M ser
f
τγ
lesdot
3y
Ed ser
M ser
f
σ τγ
+ sdot le2 2
3 yEd ser Ed ser
M ser
f
The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)
Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values
For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))
Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked
The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)
σγ
le
yEd ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
148
Fig 616 Upper steel flange stress under the characteristic SLS combination
Fig 617 Lower steel flange stress under the characteristic SLS combination
These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
149
Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit
τγ
le = =times
35520496
3 3 10y
Ed ser
M ser
fMPa
Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination
To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)
Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit
σ τγ
+ le2 2
3 yEd ser Ed ser
M ser
f
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
150
Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination
Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination
654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES
According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
151
σγ
∆ le
15 yfre
M ser
f
This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided
655 LIMITATION OF WEB BREATHING
Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener
According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if
le + le30 40 300w
w
hL
t
Where L is the span length in m but not less than 20 m
For the design example
o in end-span hwtw = 1511 le 30+4middot60=270
o in central span hwtw = 1511 le 300
Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on
o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)
σcr = kσmiddotσE and τcr = kτmiddotσE
o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)
σ τ
σ τ+ le
2 2
1111x Ed ser x Ed ser
cr cr
66 Control of cracking for longitudinal global bending
661 MAXIMUM VALUE OF CRACK WIDTH
The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)
For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
152
According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination
We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions
662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA
The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by
σ= s s c ct eff ct sA k k kf A
Where
fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)
k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))
ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))
kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by
( )= + le
+ 0
103 10
1 2cc
kh z
hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m
z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m
σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa
Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
Then
( )= + = le
+ times
103 113 10
1 0307 2 0764ck for the support P-1 cross-section hence kc=10
( )= + = le
+ times
103 102 10
1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10
= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
153
As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified
663 CONTROL OF CRACKING UNDER DIRECT LOADING
According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width
Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360 400 450
40 32 20 16 12 10 8 6
32 25 16 12 10 8 6 5
25 16 12 8 6 5 4 -
The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)
φ φ=
0
ct eff
ct
ff
Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa
Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)
Steel Stresses σs (Nmm2)
Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm
160 200 240 280 320 360
300 300 250 200 150 100
300 250 200 150 100 50
200 150 100 50 - -
The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
154
In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete
The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)
σ σ σ= + ∆0s s s
With σα ρ
∆ =04 ctm
sst s
f and α =st
a a
AIA I
Where
σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension
fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa
ρs is the reinforcement ratio given by ρ = ss
ct
AA
Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2
As is the area of all layers of longitudinal reinforcement within the effective concrete area
A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension
Aa Ia are area and second moment of area respectively of the structural steel section
Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2
At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence
ρminustimes
= =423779 10
001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ
16130 in 6 m) hence ρminustimes
= =418559 10
000952195s
The value of αst at the P-1cross-section isαtimes
= =times
03543 058321232
03305 05076st while in the mid-span P-1P-2
cross-section αtimes
= =times
01555 024561416
01369 01969st
Then the effect of tension-stiffening at the P-1 cross-section is
σtimes
∆ = =times
04 328523
1232 001219s MPa
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
155
Meanwhile in the mid span P-1P-2 σtimes
∆ = =times
04 329495
1416 00s MPa
As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are
o Support P-1 cross section σs0 =6594 MPa
o Mid span P-1P-2 cross section σs0 =2745 MPa
Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are
o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa
o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa
As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified
According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and
φ = =32
32 353129
mm
As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled
664 CONTROL OF CRACKING UNDER INDIRECT LOADING
It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested
From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A
we can get
σ = s s c ct eff ct sk k kf A A
Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant
In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2
This gives
o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa
o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa
High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives
o Support P-1 cross-section φlowast= φmiddot2932=18125 mm
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
156
o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm
The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2
o Support P-1 cross-section 23018 MPa gt18894 MPa
o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa
Hence both sections are verified
67 Shear connection at steel-concrete interface
671 RESISTANCE OF HEADED STUDS
The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663
= (1) (2)min( )Rd Rd RdP P P
P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud
π
γ=
2
(1)08
4u
Rdv
df
P
P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the
stud
α
γ=
2(2) 029 ck cm
Rdv
d f EP
With
α = +
02 1schd
for 3le schd
le4
α = 10 for schd
gt4
Where
γv is the partial factor The recommended value is γv=125
d is the diameter of the shank of the headed stud (16ledle25mm)
fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)
fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa
Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)
hsc is the overall nominal height of the stud
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
157
In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then
π timestimes times
= = times
2
(1) 6
2208 450
4 01095 10 N=01095 MN125RdP
= = gtgt200
909 422
schd
α = 10 and times sdot times
= =times2
(2) 029 1 22 35 340771401226 MN
125RdP
Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP
For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)
Then sdot = times075 01095 MN=00766 MNs Rd
k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P
Fig 621 Detail of headed studs connection
672 DETAILING OF SHEAR CONNECTION
The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))
Maximum longitudinal spacing between rows of connectors
According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness
When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
158
However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange
as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax
lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length
lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case
Where tf is the thickness of the upper flange and fy the yield strength of the steel flange
Table 63 summarizes the results of applying both conditions to our case
Table 63 Maximum longitudinal spacing for rows of studs
Upper Steel flange tf (mm) fy (Nmm2) smax eD
40 55 80
120
345 335 325 295
726 800 800 800
297 414
Only applies for flanges in compression (not in tension)
This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)
le times9 235D fe t fy
Fig 622 Detailing
Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
159
In this example (Fig 621) minus minus
= minus = minus = gt0 1000 750 22114 25
2 2 2 2f
D
b b de
Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)
Fig 623 Minimum dimensions of a headed stud
As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm
EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be
le sdot15 fd t
This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm
This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa
Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf
Minimum spacing between rows of connectors
According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm
Criteria related to the stud anchorage in the slab
Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))
Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
160
6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)
Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section
Figs 624 amp 625 View and detail of an upper flange connection
Fig 626 View of the lower flange connection of a steel girder
673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS
When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to
ν =c k
L k
S VI
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
161
Where
νLk is the longitudinal shear force per unit length at the interface concrete-steel
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section
I is the second moment of area of the composite cross-section
Vk is the shear force for the considered load case and coming from the elastic global cracked analysis
According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)
The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case
For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by
ν ν ν = min max( ) max ( ) ( )L k k kx x x
Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example
In each cross-section of the deck there should be enough studs to resist all the shear force per unit length
The following should be therefore verified at all abscissa x
ν le sdot sdot ( ) ( P )iL k s Rd
i
Nx kL
with
sdot = sdot sdot 1 4s RD s RD of studk P k P
Where
νLk is the shear force per unit length in the connection under the characteristic SLS combination
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71
For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model
00 60 125 250 350 420 500 625
800 875 1000 1080 1125 1200 1320 1400
1500 1625 1700 1760 1875 1940 2000
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
162
For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)
Table 64 Shear force per unit length at SLS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLk (MNm) 0842 0900 0900 0989 0943 0906
The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
sdot= =
(4middot P ) 03064 MN031 m
max ( ) 0989 MNms Rd
L k
k
x on a safe side 030 m
Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length
The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm
Fig 627 SLS shear force per unit length resisted by the headed studs
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
163
674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE
6741 Elastic design
Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph
In each cross-section the shear force per unit length at ULS is therefore given by
ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x
With
ν =c Ed
L Ed
S VI
Where
νLEd is the design longitudinal shear force per unit length at the concrete-steel interface
Sc is the moment of area of the concrete slab with respect to the centre of gravity of the
composite cross-section
I is the second moment of area of the composite cross-section
VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure
Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example
According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria
o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist
ν le sdot sdot ( ) 11 iL Ed RD
i
Nx PL
with
= sdot 1 4RD RD of studP P
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71
o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
164
ν leinti+1
i
x
x
( ) ( )L Ed i RDx dx N P with
= sdot 1 4RD RD of studP P
Where xi and xi+1 designates the abscissa at the border of the segment Li
For the design of the connection at ULS we have considered the same segment division as used for the SLS verification
In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)
Table 65 Design shear force per unit length at ULS at segment 50-625 m
x (m) 50+ 54- 54+ 60- 60+ 625-
νLEd (MNm) 1124 1203 1203 1323 1264 1213
The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)
( )ν
times sdot times= = 1
110 (4 P ) 11 0438 MN0365 m
max ( ) 1323 MNmRd stud
L kEd x
And the second condition
νsdot
= leinti+1
i
x 1
x
(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud
L Ed x dx MNs
Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m
Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
165
Fig 628 ULS shear force per unit length resisted by the headed studs
6742 Design with plastic zones in sagging bending areas
If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))
As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections
In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)
675 SYNOPSIS OF THE DESIGN EXAMPLE
Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
166
Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning
As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient
Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing
676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS
In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions
Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68
The fatigue load model FLM3 induces the following stress ranges
o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange
Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
167
pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area
ντ
π∆
∆ =
32
4
L FLM
i
i
NdL
Where
Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li
Li is the length of a segment with constant row spacing
d is the diameter of the shank of the headed stud
∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing
o ∆σp normal stress range in the upper steel flange to which the studs are welded
6761 Equivalent constant amplitude stress range
For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))
∆τE2 = λvmiddot∆τ
Where
∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank
λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve
For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))
Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)
o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span
o λv2 is the factor for the traffic volume
λ
=
18
12
0 0
obsmv
NQQ N
Where
=
sumsum
188
1i i
mi
n QQ
n (EN-1993-2 952 (3)) is the average gross weight (kN) of the
lorries in the slow lane
Q0=480KN
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
168
N0=05x106
Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))
Qi is the gross weight in kN of the lorry i in the slow lane
ni is the number of lorries of gross weight Qi in the slow lane
Table 66 Traffic assumption for obtaining λv2
Lorry Q (kN) Long distance
1 2 3 4 5
200 310 490 390 450
20 5
50 15 10
If we substitute table 66 values into the previous equations then we obtain
Qm1=45737 kN
λ = =245737 0952
480v
o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)
o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10
In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders
ηλ
η
= +
188
2 2 24
1 1 1
1 mv
m
N QN Q
η = minus12
eb
With
e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)
b is the distance between the main girders (in the example 70 m)
η = + =11 175 0752 70
and η = minus =21 175 0252 70
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
169
The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example
This gives finally λv4=10
Then λv=155middot0952middot10middot10=1477
For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)
σ λφ σ σ∆ = minusE max minf f
Where
σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)
ψ ψge gt
+ + + +
sum sum 11 1 2
1 1 k j k i k i fat
j iG P Q Q Q
λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5
φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ
=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)
6762 Fatigue verifications
For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank
γ τ τ γminus∆ le ∆2 Ff E c Mf s
Where
∆τE2 is the equivalent constant range of shear stress for two millions cycles
∆τE2 = λvmiddot∆τ (see paragraph 761)
∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa
γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10
γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10
Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
170
γ σσ γ
∆le
∆E2
c
10
Ff
Mf
γ ττ γ
∆le
∆E2
c
10
Ff
Mf s and
γ σ γ τσ γ τ γ
∆ ∆+ le
∆ ∆E2 E2
c c
13
Ff Ff
Mf Mf s
Where
∆σE is the stress range in the flange connected (see paragraph 761)
∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa
γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135
In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection
Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS
Fig 630 Fatigue verification of the connection
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
171
Fig 631 Spacing of the rows of connectors under the fatigue ULS
677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS
The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions
The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions
Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases
The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)
All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions
This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
172
Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10
The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows
ν = = 0643 MNmL Ed
L Edeff
V
b (rectangular shear stress block)
ν= = = 1
max
4 04380681 m
0643Rd stud
L Ed
Ps
This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design
Notes
o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side
Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder
o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
173
References
EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings
EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules
EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules
and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and
rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-
concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of
composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford
Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul
174
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 CHS ltFEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002gt13 CHT ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt13 CZE ltFEFF005400610074006f0020006e006100730074006100760065006e00ed00200070006f0075017e0069006a007400650020006b0020007600790074007600e101590065006e00ed00200064006f006b0075006d0065006e0074016f002000410064006f006200650020005000440046002c0020006b00740065007200e90020007300650020006e0065006a006c00e90070006500200068006f006400ed002000700072006f0020006b00760061006c00690074006e00ed0020007400690073006b00200061002000700072006500700072006500730073002e002000200056007900740076006f01590065006e00e900200064006f006b0075006d0065006e007400790020005000440046002000620075006400650020006d006f017e006e00e90020006f007400650076015900ed007400200076002000700072006f006700720061006d0065006300680020004100630072006f00620061007400200061002000410064006f00620065002000520065006100640065007200200035002e0030002000610020006e006f0076011b006a016100ed00630068002egt13 DAN 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 DEU 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 ESP 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 ETI ltFEFF004b00610073007500740061006700650020006e0065006900640020007300e4007400740065006900640020006b00760061006c006900740065006500740073006500200074007200fc006b006900650065006c007300650020007000720069006e00740069006d0069007300650020006a0061006f006b007300200073006f00620069006c0069006b0065002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e00740069006400650020006c006f006f006d006900730065006b0073002e00200020004c006f006f0064007500640020005000440046002d0064006f006b0075006d0065006e00740065002000730061006100740065002000610076006100640061002000700072006f006700720061006d006d006900640065006700610020004100630072006f0062006100740020006e0069006e0067002000410064006f00620065002000520065006100640065007200200035002e00300020006a00610020007500750065006d006100740065002000760065007200730069006f006f006e00690064006500670061002e000d000agt13 FRA 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 GRE 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HEB 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 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN ltFEFF004b0069007600e1006c00f30020006d0069006e0151007300e9006701710020006e0079006f006d00640061006900200065006c0151006b00e90073007a00ed007401510020006e0079006f006d00740061007400e100730068006f007a0020006c006500670069006e006b00e1006200620020006d0065006700660065006c0065006c0151002000410064006f00620065002000500044004600200064006f006b0075006d0065006e00740075006d006f006b0061007400200065007a0065006b006b0065006c0020006100200062006500e1006c006c00ed007400e10073006f006b006b0061006c0020006b00e90073007a00ed0074006800650074002e0020002000410020006c00e90074007200650068006f007a006f00740074002000500044004600200064006f006b0075006d0065006e00740075006d006f006b00200061007a0020004100630072006f006200610074002000e9007300200061007a002000410064006f00620065002000520065006100640065007200200035002e0030002c0020007600610067007900200061007a002000610074007400f3006c0020006b00e9007301510062006200690020007600650072007a006900f3006b006b0061006c0020006e00790069007400680061007400f3006b0020006d00650067002egt13 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH 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 LVI 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 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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