Concise Eurocode 2 for Bridges

A cement and concrete industry publication

For the design of concrete bridges to BS EN 1992-1-1 and BS EN 1992-2 and their National Annexes

O Brooker BEng CEng MICE MIStructE

P A Jackson BSc(Hons) PhD CEng FICE FIStructE

S W Salim BEng(Hons) PhD CEng MICE

ForewordThe introduction of European standards to UK construction is a significant event as for the first time all design and construction codes within the EU will be harmonised. The ten design standards, known as the Eurocodes, will affect all design and construction activities as current British Standards for structural design are due to be withdrawn in March 2010.

The cement and concrete industry recognised the need to enable UK design professionals to use Eurocode 2, Design of concrete structures, quickly efficiently and with confidence. Supported by government, consultants and relevant industry bodies, the Concrete Industry Eurocode 2 Group (CIEG) was formed in 1999 and this group has provided the guidance for a coordinated and collaborative approach to the introduction of Eurocode 2.

As a result, a range of resources is being developed and made available through The Concrete Centre (see www.eurocode2.info). One of those resources, Concise Eurocode 2, published in 2006, is targeted at structural engineers designing concrete framed buildings. Whilst there are many similarities in the design of buildings and bridges, there are also significant differences and hence Eurocode 2 has a distinct part for the design of bridges. This publication is based on the style of Concise Eurocode 2, but has been completely revised and rewritten to suit the requirements of Eurocode 2, Part 2 and the current design practices for concrete bridge design.

Relevant extracts have been incorporated from Precast Eurocode 2: Design manual published by British Precast, which is a similar document for designers of precast concrete. The authors are grateful for the permission granted by British Precast.

AcknowledgementsThe Concrete Centre would to thank Neil Loudon and Hideo Takano, both of the Highways Agency, for their support and comments in producing this document. We would also like to thank Steve Denton of Parsons Brinckerhoff, Chris Hendy of Atkins and Paul White of Halcrow for their helpful comments. Thanks are also due to Gillian Bond, Sally Huish and the design team at Michael Burbridge Ltd for their work on the production.

The copyright of British Standards extracts reproduced in this document is held by the British Standards Institution (BSI). Extracts have been reproduced with BSI’s permission under the terms of Licence No: 2009RM0003. No other use of this material is permitted. This publication is not intended to be a replacement for the standard and may not reflect the most up-to-date status of the standard. British Standards can be obtained in PDF or hard copy formats from the BSI online shop: www.bsigroup.com/Shop or by contacting BSI Customer Services for hard copies only: Tel:+44 (0)20 8996 9001, Email: cservices@bsigroup.com.

Published by The Concrete Centre, part of the Mineral Products Association Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB Tel: +44 (0)1276 606800 Fax: +44 (0)1276 606801 www.concretecentre.com

Cement and Concrete Industry Publications (CCIP) are produced through an industry initiative to publish technical guidance in support of concrete design and construction.

CCIP publications are available from the Concrete Bookshop at www.concretebookshop.com Tel: +44 (0)7004 607777

CCIP-038Published July 2009ISBN 978-1-904818-82-3Price Group P© MPA – The Concrete Centre

All advice or information from MPA - The Concrete Centre is intended only for use in the UK by those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by Mineral Products Association or its subcontractors, suppliers or advisors. Readers should note that the publications from MPA - The Concrete Centre are subject to revision from time to time and should therefore ensure that they are in possession of the latest version.

Printed by Michael Burbridge Ltd, Maidenhead, UK.

i

Symbols iv

1 Introduction 1

1.1 Scope 2

2 Basis of design 3

2.1 General 3

2.2 Basicrequirements 3

2.3 Limitstatedesign 4

2.4 Assumptions 9

2.5 Foundationdesign 10

3 Materials 11

3.1 Concrete 11

3.2 Steelreinforcement 13

3.3 Prestressingsteel 14

4 Durability and cover 17

4.1 General 17

4.2 Coverforbond,cmin,b 18

4.3 Coverfordurability,cmin,dur 18

4.4 Chemicalattack 22

4.5 Dcdevandotherallowances 23

5 Structural analysis 25

5.1 General 25

5.2 Idealisationofthestructure 25

5.3 Methodsofanalysis 27

5.4 Loading 29

5.5 Geometricalimperfections 29

5.6 Designmomentsincolumns 31

5.7 Corbels 36

5.8 Lateralinstabilityofslenderbeams 38

6 Bending and axial force 39

6.1 Assumptions 39

7 Shear 41

7.1 General 41

7.2 Resistanceofmembersnotrequiringshearreinforcement 41

7.3 Resistanceofmembersrequiringshearreinforcement 44

Contents

ConciseEurocode2forBridges

ii

8 Punching shear 50

8.1 General 50

8.2 Appliedshearstress 50

8.3 Controlperimeters 54

8.4 Punchingshearresistancewithoutshearreinforcement 55

8.5 Punchingshearresistancewithshearreinforcement 56

8.6 Punchingshearresistanceadjacenttocolumns 56

8.7 Controlperimeterwhereshearreinforcementisnolongerrequired,uout 56

8.8 Distributionofshearreinforcement 57

8.9 Punchingshearresistanceoffoundationbases 58

9 Torsion 59

9.1 General 59

9.2 Torsionalresistances 59

9.3 Combinedtorsionandshear 61

10 Strut-and-tie models, bearing zones and partially loaded areas 62

10.1 Designwithstrut-and-tiemodels 62

10.2 Partiallyloadedareas 65

10.3 Bearingzonesofbridges 66

11 Prestressed members and structures 67

11.1 General 67

11.2 BrittleFracture 67

11.3 Prestressingforceduringtensioning 69

12 Fatigue 72

12.1 Verificationconditions 72

12.2 Internalforcesandstressesforfatigueverification 72

12.3 Verificationofconcreteundercompressionorshear 73

12.4 Limitingstressrangeforreinforcementundertension 74

13 Serviceability 76

13.1 General 76

13.2 StressLimitation 76

13.3 Calculationofcrackwidths 76

13.4 Controlofcracking 79

13.5 Minimumreinforcementareasofmainbars 80

13.6 Controlofdeflection 83

14 Detailing – general requirements 85

14.1 General 85

14.2 Spacingofbars 85

14.3 Mandrelsizesforbentbars 85

14.4 Anchorageofbars 86

14.5 Ultimatebondstress 88

14.6 AnchorageoftendonsatULS 89

14.7 Anchorageoftendonsattransferofprestress 90

14.8 Laps 90

iii

15 Detailing – particular requirements 94

15.1 General 94

15.2 Beams 94

15.3 One-wayandtwo-wayspanningslabs 98

15.4 Flatslabs 98

15.5 Columns 100

15.6 Walls 101

15.7 Pilecaps 102

15.8 Boredpiles 103

15.9 Requirementsforvoidedslabs 103

15.10 Prestressing 104

15.11 Connections 105

15.12 Bearings 106

16 Design for the execution stages 109

17 Design aids 110

17.1 Designforbending 110

17.2 Designforbeamshear 112

17.3 Designforpunchingshear 114

17.4 Designforaxialloadandbending 115

18 References 122

iv

Symbols and abbreviations used in this publication

Symbol Definition

IxI Absolutevalueofx

1/r Curvatureataparticularsection

A Cross-sectionalarea;Accidentalaction

A, B, C Variablesusedinthedeterminationofllim

Ac Cross-sectionalareaofconcrete

Ac,eff Effectiveareaofconcreteintension

Act Areaofconcreteinthatpartofthesectionthatiscalculatedtobeintensionjustbeforetheformationofthefirstcrack

Ad Designvalueofanaccidentalaction

Ak Areaenclosedbythecentrelinesofconnectingwallsincludingtheinnerhollowarea(torsion)

Ap Areaofprestressingtendonortendons

Ap' AreaofprestressingtendonswithinAc,eff

As Cross-sectionalareaofreinforcement

As,min Minimumcross-sectionalareaofreinforcement

As,prov Areaofsteelprovided

As,req Areaofsteelrequired

As1 Areaofreinforcingsteelinlayer1

As2 Areaofcompressionsteel(inlayer2)

Asl Areaofthetensilereinforcementextendingatleastlbd+dbeyondthesectionconsidered

AsM(AsN) Totalareaofreinforcementrequiredinsymmetrical,rectangularcolumnstoresistmoment(axialload)usingsimplifiedcalculationmethod

Ast Cross-sectionalareaoftransversesteel(atlaps)

Asw Cross-sectionalareaofshearreinforcement

Asw Areaofpunchingshearreinforcementinoneperimeteraroundthecolumn

Asw,min Minimumcross-sectionalareaofshearreinforcement

Asw,min Minimumareaofpunchingshearreinforcementinoneperimeteraroundthecolumn

a Distance,allowanceatsupports

a Geometricdata

Da Deviationforgeometricaldata

a Anexponent(inconsideringbiaxialbendingofcolumns)

a Projectionofthefootingfromthefaceofthecolumnorwall

ab Halfthecentre-to-centrespacingofbars(perpendiculartotheplaneofthebend)

al Distancebywhichthelocationwhereabarisnolongerrequiredforbendingmomentisdisplacedtoallowfortheforcesfromthetrussmodelforshear.(‘Shift’distanceforcurtailment)

av Distancebetweenbearingsorfaceofsupportandfaceofload

a1,b1 Dimensionsofthecontrolperimeteraroundanelongatedsupport(punchingshear)

b Overallwidthofacross-section,orflangewidthinaT-orL-beam

b0 Widthofthebottomflangeofthesection

be Effectivewidthofaflatslab(adjacenttoperimetercolumn)

beff Effectivewidthofaflange

beq(heq) Equivalentwidth(height)ofcolumn=b(h)forrectangularsections

bmin MinimumwidthofwebonT-,I-orL-beams

bt Meanwidthofthetensionzone.ForaT-beamwiththeflangeincompression,onlythewidthofthewebistakenintoaccount

v

Symbol Definition

bw WidthofthewebonT-,I-orL-beams.Minimumwidthbetweentensionandcompressionchords

by,bz Dimensionsofthecontrolperimeter(punchingshear)

Dc Permitteddeviationfromcnom(BSEN13760)

Dc,dev Allowancemadeindesignfordeviation

cmin Minimumcover(duetotherequirementsforbond,cmin,bordurabilitycmin,dur)

cnom Nominalcover(minimumcoverplusallowancefordeviations)

cy,cx Columndimensionsinplan

c1,c2 Dimensionsofarectangularcolumn.Foredgecolumns,c1ismeasuredperpendiculartothefreeedge(punchingshear)

D Diameterofacircularcolumn;Diameterofmandrel;Diameter

DEd Fatiguedamagefactor

d Effectivedepthtotensionsteel

d2 Effectivedepthtocompressionsteel

dc Effectivedepthofconcreteincompression

deff Effectivedepthoftheslabtakenastheaverageoftheeffectivedepthsintwoorthogonaldirections(punchingshear)

dg Largestmaximumaggregatesize

dl Ashortlengthofaperimeter(punchingshear)

E Effectofaction;Elasticmodulus

Ec,Ec(t) Tangentmodulusofelasticityofnormalweightconcreteatastressofsc=0andattime,t,days

Ec,eff Effectivemodulusofelasticityofconcrete

Ecd Designvalueofmodulusofelasticityofconcrete

Ecm Secantmodulusofelasticityofconcrete

Ed Designvalueoftheeffectofactions

EI Bendingstiffness

Ep Designvalueofelasticityofprestressingsteel

Es Designvalueofmodulusofelasticityofreinforcingsteel

Exp. Expression

EQU Staticequilibrium

e Eccentricity

e2 Deflection(usedinassessingM2inslendercolumns)

ei Eccentricityduetoimperfections

epar Eccentricityparalleltotheslabedgeresultingfromamomentaboutanaxisperpendiculartotheslabedge(punchingshear)

ey,ez Eccentricity,MEd/VEdalongyandzaxesrespectively(punchingshear)

F Action

Fbt Tensileforceinthebaratthestartofthebendcausedbyultimateloads

Fc(Fs) Forceinconcrete(steel)

Fcd Designvalueoftheconcretecompressionforceinthedirectionofthelongitudinalmemberaxis

Fcr Absolutevalueofthetensileforcewithintheflangeimmediatelypriortocrackingduetothecrackingmomentcalculatedwithfct,eff

Fd Designvalueofanaction

FE Tensileforceinreinforcementtobeanchored

FEd Compressiveforce,designvalueofsupportreaction

Fk Characteristicvalueofanaction

Symbols and abbreviations used in this publication

vi

Symbol Definition

Frep Representativeaction(=c Fkwherec=factortoconvertcharacteristictorepresentativeaction)

FRs Resistingtensileforceinsteel

Fs Tensileforceinthebar

Ftd Designvalueofthetensileforceinlongitudinalreinforcement

DFtd Additionaltensileforceinlongitudinalreinforcementduetothetrussshearmodel

Fwd Designshearstrengthofweld,designvalueoftheforceinstirrupsincorbels

FWk Characteristicvalueofwindforce(AnnexA2,BSEN1990)

f Frequency

fbd Ultimatebondstress

fc Compressivestrengthofconcrete

fcd Designvalueofconcretecompressivestrength

fcd,fat Designfatiguestrengthofconcrete

fcd,pl Designcompressivestrengthofplainconcrete

fck Characteristiccompressivecylinderstrengthofconcreteat28days

fck(t0) Characteristicconcretecompressivestrengthattimeofloading

fck,cube Characteristiccompressivecubestrengthofconcreteat28days

fcm Meanvalueofconcretecylindercompressivestrength

fct,d Designtensilestrengthofconcrete(actfct,k/gC)

fct,eff Meantensilestrengthofconcreteeffectiveatthetimecracksmaybefirstexpectedtooccur.fct,eff=fctmattheappropriateage

fct,k Characteristicaxialtensilestrengthofconcrete

fctb Tensilestrengthpriortocrackinginbiaxialstateofstress

fctm Meanvalueofaxialtensilestrengthofconcrete

fctx Appropriatetensilestrengthforevaluationofcrackingbendingmoment

fctk,0.05 5%fractilevalueofaxialtensilestrengthofconcrete

fctk,0.95 95%fractilevalueofaxialtensilestrengthofconcrete

fcvd Concretedesignstrengthinshearandcompression(plainconcrete)

fp Tensilestrengthofprestressingsteel

fp0.1 0.1%proof-stressofprestressingsteel

fp0.1k Characteristic0.1%proof-stressofprestressingsteel

fp0.2k Characteristic0.2%proof-stressofprestressingsteel

fpk Characteristictensilestrengthofprestressingsteel

fsc CompressivestressincompressionreinforcementatULS

ft Tensilestrengthofreinforcement

ft,k Characteristictensilestrengthofreinforcement

fy Yieldstrengthofreinforcement

fyd Designyieldstrengthoflongitudinalreinforcement,Asl

fyk Characteristicyieldstrengthofreinforcement

fywd Designyieldstrengthoftheshearreinforcement

fywd,ef Effectivedesignstrengthofpunchingshearreinforcement

fywk Characteristicyieldstrengthofshearreinforcement

Gk Characteristicvalueofapermanentaction

gk Characteristicvalueofapermanentactionperunitlengthorarea

Hi Horizontalactionappliedatalevel

h Overalldepthofacross-section;Height

vii

Symbol Definition

h0 Notionalsizeofcross-section

hf Depthoffooting;Thicknessofflange

hH Verticalheightofadroporcolumnheadbelowsoffitofaslab(punchingshear)

hs Depthofslab

I Secondmomentofareaofconcretesection

i Radiusofgyration

J Creepfunction

K MEd/bd2fck.Ameasureoftherelativecompressivestressinamemberinflexure

K Factortoaccountforstructuralsystem(deflection)

K' ValueofKabovewhichcompressionreinforcementisrequired

Kc Factorforcrackingandcreepeffects

Kr Correctionfactorforcurvaturedependingonaxialload

Ks Factorforreinforcementcontribution

Kh Factorfortakingaccountofcreep

k Coefficientorfactor

k Unintentionalangulardisplacementforinternaltendons

kc Coefficientallowingforthenatureofthestressdistributionwithinthesectionimmediatelypriortocrackingandforthechangeoftheleverarmasaresultofcracking(minimumareas)

kt Factorincrackwidthcalculationswhichdependsonthedurationofloading

l Clearheightofcolumnbetweenendrestraints

l Heightofthestructureinmetres

l(orL) Length;Span

l0 Effectivelength(ofcolumns)

l0 Distancebetweenpointsofzeromoment

l0 Designlaplength

lbd Designanchoragelength

lb,eq Equivalentanchoragelength

lb,min Minimumanchoragelength

lb,rqd Basicanchoragelength

leff Effectivespan

lH Horizontaldistancefromcolumnfacetoedgeofadroporcolumnheadbelowsoffitofaslab(punchingshear)

ln Cleardistancebetweenthefacesofsupports

ls Floortoceilingheight

lx,ly Spansofatwo-wayslabinthexandydirections

M Bendingmoment.Momentfromfirstorderanalysis

M' Momentresistanceofasinglyreinforcedsection(abovewhichcompressionreinforcementisrequired)

M0,Eqp Firstorderbendingmomentinquasi-permanentloadcombination(SLS)

M01,M02 FirstorderendmomentsatULSincludingallowancesforimperfections

M0Ed Equivalentfirstordermomentincludingtheeffectofimperfections(ataboutmidheight)

M2 Nominalsecondordermomentinslendercolumns

MEd Designvalueoftheappliedinternalbendingmoment

MEdy,MEdz Designmomentintherespectivedirection

Mfreq Appliedbendingmomentduetofrequentcombination

MRdy,MRdz Momentresistanceintherespectivedirection

viii

Symbol Definition

MRd,max Maximumtransversemomentresistance

Mrep Crackingbendingmoment

m Numberofverticalmemberscontributingtoaneffect

m Mass;Slabcomponents

N Axialforce

NA NationalAnnex

Na,Nb LongitudinalforcescontributingtoHi

NEd Designvalueofaxialforce(tensionorcompression)atULS

NDP NationallyDeterminedParameter(s)aspublishedinacountry’sNationalAnnex

n AxialstressatULS

n Ultimateaction(load)perunitlength(orarea)

n Platecomponents

n Numberofbars

nb Numberofbarsinthebundle

P Prestressingforce

P0 Initialforceattheactiveendofthetendonimmediatelyafterstressing

Qc Characteristicconstructionload

Qfat Characteristicfatigueload

Qk Characteristicvalueofavariableaction

Qk1(Qki) Characteristicvalueofaleadingvariableaction(Characteristicvalueofanaccompanyingvariableaction)

QSn,k Characteristicvalueofsnowload

qk Characteristicvalueofavariableactionperunitlengthorarea

qud Maximumvalueofcombinationreachedinnon-linearanalysis

R Resistance

R/A' Verticalbearingresistanceperunitarea(foundations)

Rd Designvalueoftheresistancetoanaction

RH Relativehumidity

r Radius;Correctingfactorforprestress

rcont Thedistancefromthecentroidofacolumntothecontrolsectionoutsidethecolumnhead

rinf,rsup Allowanceinserviceabilityandfatiguecalculationsforpossiblevariationsinprestress

rm RatiooffirstorderendmomentsincolumnsatULS

S Internalforcesandmoments;Firstmomentofarea

S,N,R Cementtypes

SLS Serviceabilitylimitstate(s)–correspondingtoconditionsbeyondwhichspecifiedservicerequirementsarenolongermet

s Spacingofthestirrups;Spacingbetweencracks

sr Radialspacingofperimetersofshearreinforcement

sr,max Maximumfinalcrackspacing

st Tangentialspacingshearreinforcementalongperimetersofshearreinforcement

T Torsionalmoment;Tensileforce

TEd Designvalueoftheappliedtorsionalmoment

Tk Characteristicvalueofthermalactions

TRd Designtorsionalresistancemoment

TRd,max Maximumdesigntorsionalresistancemomentresistance

t Thickness;Timebeingconsidered;Breadthofsupport;Timeaftertensioning

ix

Symbol Definition

t0 Theageofconcreteatthetimeofloading

t0,T Temperatureadjustedageofconcreteatloadingindays

tef,i Effectivewallthickness(torsion)

tinf Thicknessofthebottomflangeofthesection

ULS Ultimatelimitstate(s)–associatedwithcollapseorotherformsofstructuralfailure

u Perimeterofconcretecross-section,havingareaAc

u Perimeterofthatpartwhichisexposedtodrying

u Circumferenceofouteredgeofeffectivecross-section(torsion)

u Componentofthedisplacementofapoint

u0 Perimeteradjacenttocolumns(punchingshear)

u1 Basiccontrolperimeter,(at2dfromfaceofload)(punchingshear)

u1* Reducedcontrolperimeteratperimetercolumns(at2dfromfaceofload)(punchingshear)

ui Lengthofthecontrolperimeterunderconsideration(punchingshear)

uk PerimeteroftheareaAk(torsion)

uout Perimeteratwhichshearreinforcementisnolongerrequired

V Shearforce

VEd Designvalueoftheappliedshearforce

VEd,red Appliedshearforcereducedbytheforceduetosoilpressurelessselfweightofbase(punchingshear,foundations)

VRd,c Shearresistanceofamemberwithoutshearreinforcement

VRd,max Shearresistanceofamemberlimitedbythecrushingofcompressionstruts

VRd,s Shearresistanceofamembergovernedbytheyieldingofshearreinforcement

v Transverseshearorcomponentofthedisplacementofapoint

vEd Punchingshearstress

vEd Shearstressforsectionswithout shearreinforcement(=VEd/bwd)

vEd,z Shearstressforsectionswith shearreinforcement(=VEd/bwz=VEd/bw0.9d)

vRd,c Designshearresistanceofconcretewithoutshearreinforcementexpressedasastress

vRd,cs Designpunchingshearresistanceofconcretewith shearreinforcementexpressedasastress(punchingshear)

vRd,max Resistanceofconcretestrutsexpressedasastress

W1 Factorcorrespondingtoadistributionofshear(punchingshear)

w Componentofthedisplacementofapoint

wk Crackwidth

wmax Limitingcalculatedcrackwidth

X Advisorylimitofpercentageofcoupledtendonsatasection

X0,XA,XC, ConcreteexposureclassesXD,XF,XS

x Neutralaxisdepth

x Distanceofthesectionbeingconsideredfromthecentrelineofthesupport

x, y, z Co-ordinates;Planesunderconsideration

xc Depthofthecompressionzone

xu Depthoftheneutralaxisattheultimatelimitstateafterredistribution

z Leverarmofinternalforces

zcp Distancebetweencentreofgravityofconcretesectionandtendons

zs Leverarmforprestress

a Angle;Angleofshearlinkstothelongitudinalaxis;Ratio

a Longtermeffectscoefficient

x

Symbol Definition

a Ratiobetweenprincipalstresses

a Deformationparameter

a1,a2,a3 Factorsdealingwithanchorageandlapsofbarsa4,a5,a6

a1,a2,a3 Factorsusedincreepcalculations

acc(act) Acoefficienttakingintoaccountlongtermeffectsofcompressive(tensile)loadandthewayloadisapplied

acw Coefficienttakingaccountofthestateofstressinthecompressionchord

ae Effectivemodularratio

ah Reductionfactorfory

b Angle;Ratio;Coefficient

b Factordealingwitheccentricity(punchingshear)

b(fcm) Factortoallowfortheeffectofconcretestrengthonthenotionalcreepcoefficient

bH Coefficentdependingontherelativehumidityandthenotionalmembersize

b(t0) Factortoallowfortheeffectofconcreteageatloadingonthenotionalcreepcoefficient

b(t,t0) Coefficienttodescribethedevelopmentofcreepwithtimeafterloading

g Partialfactor

gA Partialfactorforaccidentalactions,A

gC Partialfactorforconcrete

gC,fat Partialfactorforfatigueofconcrete

gF Partialfactorforactions,F

gF,fat Partialfactorforfatigueactions

gf Partialfactorforactionswithouttakingaccountofmodeluncertainties

gg Partialfactorforpermanentactionswithouttakingaccountofmodeluncertainties

gG Partialfactorforpermanentactions,G

gM Partialfactorforamaterialproperty,takingaccountofuncertaintiesinthematerialpropertyitself,ingeometricdeviationandinthedesignmodelused

gP Partialfactorforactionsassociatedwithprestressing,P

gQ Partialfactorforvariableactions,Q

gS Partialfactorforreinforcingsteelorprestressingsteel

gS,fat Partialfactorforreinforcingorprestressingsteelunderfatigueloading

gSH Partialfactorforshrinkage

d Ratiooftheredistributedmomenttotheelasticbendingmoment.

ec Compressivestraininconcrete

ec1 Compressivestrainintheconcreteatthepeakstressfc

ec2 Compressivestrainlimitinconcreteforconcreteinpureaxialcompressionorstraininconcreteatreachingmaximumstrengthassuminguseoftheparabolic-rectangularrelationship

ec3 Compressivestrainlimitinconcreteforconcreteinpureaxialcompressionorstraininconcreteatreachingmaximumstrengthassuminguseofthebilinearstress-strainrelationship

eca Autogenousshrinkagestrain

ecc Creepstrain

ecd Dryingshrinkagestrain

ecm Meanstraininconcretebetweencracks

ecs Totalshrinkagestrain

ecu Ultimatecompressivestrainintheconcrete

ecu2 Ultimatecompressivestrainlimitinconcretewhichisnotfullyinpureaxialcompressionassuminguseoftheparabolic-rectangularstress-strainrelationship(numericallyecu2=ecu3)

xi

Symbol Definition

ecu3 Ultimatecompressivestrainlimitinconcretewhichisnotfullyinpureaxialcompressionassuminguseofthebilinearstress-strainrelationship

ep(0) Initialstraininprestressingsteel

Dep Changeinstraininprestressingsteel

es Straininreinforcingsteel

esm Meanstraininreinforcement

eu Strainofreinforcementorprestressingsteelatmaximumload

eud Designlimitforstrainforreinforcingsteelintension= 0.9euk

euk Characteristicstrainofreinforcement(orprestressingsteel)atmaximumload

ey Reinforcementyieldstrain

n Factordefiningeffectivestrength(=1for≤C50/60)

n1 Coefficientforbondconditions

n2 Coefficientforbardiameter

np1 Coefficientthattakesintoaccountthetypeoftendonandthebondsituationatrelease

y Angle;Angleofcompressionstruts(shear)

yfat Inclinationofcompressivestruts

yi Inclinationusedtorepresentimperfections

l Slendernessratio

l Damageequivalentfactorsinfatigue

l Factordefiningtheheightofthecompressionzone(=0.8for≤C50/60)

llim Limitingslendernessratio(ofcolumns)

m Coefficientoffrictionbetweenthetendonsandtheirducts

m Characteristicvalueofthetensilestrengthofprestressingsteel

v Poisson'sratio

v1 Strengthreductionfactorforconcretecrackedinshear

j Creepredistributionfunction

j Bondstrengthratio

j1 Adjustedareaofbondstrength

r Requiredtensionreinforcementratio.AssumeAs/bd

r Ovendrydensityofconcreteinkg/m3

r' Reinforcementratioforrequiredcompressionreinforcement,As2/bd

r0 Referencereinforcementratiofck0.5x10–3

r1 Percentageofreinforcementlappedwithin0.65l0fromthecentrelineofthelapbeingconsidered

r1000 Valueofrelaxationloss(in%)at1000hoursaftertensioningandatameantemperatureof20°C

rl Reinforcementratioforlongitudinalreinforcement

rw Reinforcementratioforshearreinforcement

sc Compressivestressintheconcrete

scp Compressivestressintheconcretefromaxialloadorprestressing

scu Compressivestressintheconcreteattheultimatecompressivestrainecu

sgd Designvalueofthegroundpressure

spi Theabsolutevalueofinitialprestress

spm0 Theabsolutevalueofinitialprestressduringpost-tensioning

sRd,max Designstrengthofconcretestrut

ss StressinreinforcementatSLS

ss Absolutevalueofthemaximumstresspermittedinthereinforcementimmediatelyaftertheformationofthecrack

xii

Symbol Definition

ssc(sst) Stressincompression(andtension)reinforcement

ssd Designstressinthebarattheultimatelimitstate

ssr Stressinthetensionreinforcementcalculatedonthebasisofacrackedsectionundertheloadingconditionscausingfirstcracking

t Torsionalshearstress

F DynamicfactoraccordingtoBSEN1991-2

h0 Notionalcreepcoefficient

h(∞,t0) Finalvalueofcreepcoefficient

hef Effectivecreepfactor

hfat Damageequivalentimpactfactorinfatigue

hnl(∞,t0) Non-linearnotionalcreepcoefficient

hp Equivalentdiameteroftendon

h(t,t0) Creepcoefficient,definingcreepbetweentimestandt0,relatedtoelasticdeformationat28days

hRH Factortoallowfortheeffectofrelativehumidityonthenotionalcreepcoefficient

f Bardiameter;Diameterofprestressingduct

feq Equivalentbardiameter

fm Mandreldiameter

fn Equivalentdiameterofabundleofreinforcingbars

X Ageingcoefficient

c Factorsdefiningrepresentativevaluesofvariableactions

c0 Combinationvalueofavariableaction(e.g.usedwhenconsideringULS)

c1 Frequentvalueofavariableaction(e.g.usedwhenconsideringwhethersectionwillhavecrackedornot)

c2 Quasi-permanentvalueofavariableaction(e.g.usedwhenconsideringdeformation)

w Mechanicalreinforcementratio=As fyd/Ac fcd≤1

1

Introduction

1 IntroductionBS EN 1992-1-1 (Eurocode 2: Design of concrete structures Part 1-1[1]) sets out general rulesfor the design of concrete structures and rules for the design of buildings. BS EN 1992-2(Eurocode 2 - Part 2 Concrete bridges - Design and detailing rules)[2] provides additional oramendedguidancetoPart1-1forbridgestructures.

TheaimofthisConcise Eurocode 2 for BridgesistodistilfromallrelevantpartsofBSEN1992andtheUKNationalAnnexes materialthatwillbecommonlyusedinthedesignofnormalbridgestructures. Each country can publish non-contradictory, complementary information, and forconcretebridgedesign,PD6687,Part2 [3]givesusefulguidance.Materialfromthisdocumentisalsoincludedwhereappropriate,andpresentedonapaleyellowbackgroundtodistinguishitfromthemaintext.

As far as possible, the Eurocode clauses are repeated verbatim. One of the objectives is toembed the UK National Annex values into the document for ease of use. Due to the wayNationally Determined Parameters (NDPs) are introduced in the Eurocodes it has beennecessaryinsomeplacestomodifythetextforclarityofreading.IthasnotbeentheintentiontomodifythemeaningofthetextandclearlyifthereisanydoubtastothemeaningthentheoriginalEurocodeversionshouldbeadopted.

Further,someoftheoriginaltexthasbeenmodifiedtoreduceitslength,whilekeepingthesamemeaning.Inthiscasethetexthasbeengivenagreybackgroundtodrawthereader’sattentionto the fact that the text is not strictly from theCode. Likewise other text, derived formulae,tablesandillustrationsthatareprovidedtoassistthedesignersbutthatarenottakendirectlyfrom the original have been given a grey background.As before, it is intended to convey theoriginalmeaningandwhereanydoubtexiststhemeaningofEurocode2shouldbeadopted.

The NDPs are recognition that each Member State of the EU is responsible for determiningmatters such as safety and current practice and allow individual countries to set their ownvalues.Asnotedabove,theUKvalueshavebeenadoptedthroughout,buthavebeenhighlightedwithagreenbackgroundsothatitiscleartothereaderwhatNDPvaluehasbeenused.

Guide to presentation

Greyshadedtext,tablesandfigures

ModifiedEurocode2textandadditionaltext,derivedformulae,tablesandillustrationsnot fromEurocode2

Yellowshadedtext,tablesandfigures

AdditionaltextfromPD6687[6]orPD6687-2[3]

BS EN 1992-1-1 6.4.4

Relevantcodeandclausesorfigurenumbers

BS EN 1992-1-1 NA FromtherelevantUKNationalAnnex

BS EN 1992-1-1 6.4.4 & NA FrombothEurocode2-1-1andUKNationalAnnex

Section 5.2 Relevantpartsofthispublication

1.0 NationallyDeterminedParameter.UKvalueshavebeenusedthroughout

For ease of reference, this guide is repeated on the inside back cover.

2

Scope

Thispublicationisintendedtocoverthedesignofatypicalbridge;thereareparticulartypesofbridgessuchassuspensionbridgesandsegmentalbridgesthatshouldnotbedesignedwithoutreference to theCode itself. It should also be noted that not every method presented in theCodeisgivenhere.Generally,thesimplestandmoreconservativemethodshavebeenincludedandthereforethereadermayfindtherearebenefitstobegainedbyusingothermethodsandshouldconsulttheCodeontheseoccasions.

Thispublicationdoesnotcoverthemethodofdesigningconcreteelementsusingmembranerules.Membraneelementsmaybeusedforthedesignoftwo-dimensionalconcreteelementssubject to a combination of internal forces evaluated by means of a linear finite elementanalysis.ThereadershouldrefertoBSEN1992-2AnnexLL inconjunctionwithAnnexFandCl. 6.109 for detailed guidance. For the design or verification of shell elements subject tobending alone (i.e. with zero membrane forces) the approaches given byWoodArmer[4] andDenton&Burgoyne[5]maygenerallybeused.

1.1

3

Basisofdesign

Basis of design

General

BSEN1992-1-1[1]andBSEN1992-2[2]shouldbeusedinconjunctionwithBSEN1990:Basis of structural design[7],which:

■ Establishesprinciplesandrequirementsforthesafety,serviceabilityanddurabilityofstructures.

■ Describesthebasisfortheirdesignandverification.■ Givesguidelinesforrelatedaspectsofstructuralreliability.

Basic requirements

General

Astructureshouldbedesignedandexecuted(constructed)insuchawaythatitwill,duringitsintendedlife,withappropriatedegreesofreliabilityandinaneconomicalway:

■ Sustainallactionsandinfluenceslikelytooccurduringexecutionanduse.■ Meetthespecifiedserviceabilityrequirementsforastructureorastructuralmember.

Itshouldbedesignedtohaveadequatestructuralresistance,serviceabilityanddurability.

Astructureshouldbedesignedandexecutedinsuchawaythatitwillnotbedamagedbyeventssuchasexplosion,impactandtheconsequencesofhumanerrors,toanextentdisproportionatetotheoriginalcause.

Avoidance of damage

Potential damage should be avoided or limited by appropriate choice of one or more of thefollowing:

■ Avoiding,eliminatingorreducingthehazardstowhichthestructurecanbesubjected.■ Selectingastructuralformwhichhaslowsensitivitytothehazardsconsidered.■ Selectingastructuralformanddesignthatcansurviveadequatelytheaccidentalremoval

ofanindividualstructuralmemberoralimitedpartofthestructureortheoccurrenceoflocaliseddamage.

■ Avoidingasfaraspossiblestructuralsystemsthatcancollapsewithoutwarning.■ Tyingthestructuralmemberstogether.

Limit states principles

BSEN1990impliesthatthedesignshouldbeverifiedusinglimitstatesprinciples.

Anindicativevalueof120yearsisgivenintheUKNationalAnnexforthedesignworkinglifeofbridges.ItcangenerallybeassumedthattheguidancegiveninBS8500[8]foratleasta100-year'intendedworkinglife'willbeappropriateforan'indicativedesignworkinglife'of120years.

BS EN 1990 2.1(1), (2) & (4)

BS EN 1990 1.1.1(1)

BS EN 1992-1-1 1.1.1(3)

BS EN 19902.1(5)

BS EN 19903.1(1)

BS EN 19902.3 & NA

2

2.1

2.2

2.2.1

2.2.2

2.2.3

4

Limit state design

Limit states are states beyond which the structure no longer fulfils the relevantdesigncriteria:

■ Ultimatelimitstates(ULS)areassociatedwithcollapseorotherformsofstructuralfailure.

■ Serviceabilitylimitstates(SLS)correspondtoconditionsbeyondwhichspecifiedservicerequirementsarenolongermet.

Limitstatesshouldbeverifiedinallrelevantdesignsituationsselected,takingintoaccountthecircumstancesunderwhichthestructureisrequiredtofulfilitsfunction.

Design situations

Normally,innon-seismiczones,thefollowingdesignsituationsshouldbeconsidered:

■ Persistentsituationswhichrefertotheconditionsofnormaluse.■ Transientsituationswhichrefertotemporaryconditions,suchasduringexecutionorrepair.■ Accidentalsituationswhichrefertoexceptionalconditionsapplicabletothestructureorto

itsexposuree.g.fire,explosion,impactortheconsequencesoflocalisedfailure.

Actions

Actionsrefertoasetofforces(loads)appliedtothestructure(directaction),ortoasetofimposeddeformationsoraccelerationscaused,forexample,bytemperaturechanges,moisturevariation,unevensettlementorearthquakes(indirectaction).

■ Permanentactionsrefertoactionsforwhichthevariationinmagnitudewithtimeisnegligible.

■ Variableactionsareactionsforwhichthevariationinmagnitudewithtimeisnotnegligible.

■ Accidentalactionsareactionsofshortdurationbutofsignificantmagnitudethatareunlikelytooccuronagivenstructureduringthedesignworkinglife.

Thecharacteristicvalue,Fk,ofanactionisitsmainrepresentativevalueandshallbespecifiedby:

■ Ameanvalue –generallyusedforpermanentactions.■ Anuppervalue withanintendedprobabilityofnotbeingexceeded orlowervalue

withanintendedprobabilityofbeingachieved–normallyusedforvariableactionswith knownstatisticaldistributions,suchaswindorsnow.

■ Anominalvalue –usedforsomevariableandaccidentalactions.

The values of actions given in the various parts of BS EN 1991: Actions on structures[9] aretakenascharacteristicvalues.

Verification

Verification,usingthepartialfactormethod,isdetailedinBSEN1990[4].Inthismethoditisverifiedthat,inallrelevantdesignsituations,norelevantlimitstateisexceededwhendesignvaluesforactionsandresistancesareusedinthedesignmodels.

BS EN 19903.1 & 3.4

BS EN 19903.2

BS EN 19901.5.3.1

BS EN 19901.5.3.3

BS EN 19901.5.3.4

BS EN 19901.5.3.5

BS EN 19904.1.2(1)

BS EN 1990

BS EN 1991

2.3

2.3.1

2.3.2

2.3.3

5

BasisofdesignBasisofdesign

Design values of actions

Thedesignvalue,Fd,ofanaction,F,canbeexpressedingeneraltermsasFd=gFcFk

wheregF =partialfactorfortheactionwhichtakesaccountofthepossibilityofunfavourable deviationsoftheactionvaluesfromtherepresentativevalues.c =afactorfortheaction c canhavethevalue1.0,c0orc1orc2 whichisusedtoobtainthecharacteristic,

combination,frequentandquasi-permanentvaluesrespectively.Itadjuststhevalueoftheactiontoaccountforthejointprobabilityoftheactionsoccurringsimultaneously.

SeeTables2.1to2.3whicharederivedfromBSEN1990anditsNationalAnnex[7a].Fk= characteristicvalueofanaction.

Table 2.1

Values of c factors for road bridges

Action Symbol c0 c1 c2

Traffic loads (see BS EN 1991-2, table 4.4)

gr1aa TS 0.75 0.75 0

UDL 0.75 0.75 0

Pedestrianandcycle-trackloadsb 0.40 0.40 0

gr1ba Singleaxle 0 0.75 0

gr2 Horizontalforces 0 0 0

gr3 Pedestrianloads 0 0.40 0

gr4 Crowdloading 0 0.75 0

gr5c VerticalforcesfromSVandSOVVehicles 0 1.0 0

Wind forces F Wk Persistentdesignsituations 0.50 0.20 0

F Wk Duringexecution 0.80 – 0

F* W Duringexecution 1.0 – 0

Thermal actions T k 0.60d 0.60 0.50

Snow loads Q Sn,k (duringexecution) 0.80 – –

Construction loads Qc 1.0 – 1.0

Key

a Thevaluesofc0,c1andc2forgr1aandgr1baregivenforroadtrafficcorrespondingtoadjustingfactorsaQi,aqi ,aqrandbQ=1

b Thevalueofthepedestrianandcycle-trackload,giveninTable4.4aofEN1991-2,isa'reduced'valueaccompanyingthecharacteristicvalueofLM1andshouldnotbefactoredagainbyc1.However,whengr1aiscombinedwithleadingnon-trafficactions,thisvalueshouldbefactoredbyc0

c InaccordancewithBSEN1991-2Cl.4.5.2,thefrequentvalueofgr5doesnotneedtobeconsidered.

d Thec0valueforthermalactionsmayinmostcasesbereducedto0forultimatelimitstatesEQU,STRandGEO

Table 2.2

Values of c factors for footbridges

Action Symbol c0 c1 c2

Traffic loads gr1 0.4 0.4 0

Qfwk0 0 0

gr2 0 0 0

Wind forces F Wk0.3 0.2 0

Thermal actions T k 0.6a 0.6 0.5

Snow loads Q Sn,k(duringexecution) 0.8 – 0

Construction loads Qc 1.0 – 1.0

Key

a Thec0valueforthermalactionsmayinmostcasesbereducedto0forultimatelimitstatesEQU,STRandGEO

BS EN 1990 NA table NA. A.2.1

BS EN 1990 NA table NA. A.2.2

2.3.4

BS EN 19906.3.1

6

Table 2.3

Values of c factors for railway bridges

Actions c0 c1 c2a

Individual components of traffic actionsb

LM71 0.80 c 0

SW/0 0.80 c 0

SW/2 0 1.00 0

Unloadedtrain 1.00 – –

HSLM 1.00 1.00 0

TrackingandbrakingCentrifugalforcesInteractionforcesduetodeformationunderverticaltrafficloads

Individualcomponentsoftrafficactionsindesignsituationswherethetrafficloadsareconsideredasasingle(multi-directional)leadingactionandnotasgroupsofloadsshouldusethe

samevaluesofcfactorsasthoseadoptedfortheassociatedverticalloads

Nosingforces 1.00 0.80 0

Non-publicfootpathsloads 0.80 0.50 0

Realtrains 1.00 1.00 0

Horizontalearthpressureduetotrafficloadsurcharge 0.80 c 0

Aerodynamiceffects 0.80 0.50 0

Main traffic actions (groups of loads)

gr11(LM71+SW/0) Max.vertical1withmax.longitudinal 0.80 0.80 0

gr12(LM71+SW/0) Max.vertical2withmax.transverse

gr13(Braking/traction) Max.longitudinal

gr14(Centrifugal/nosing) Max.lateral

gr15(Unloadedtrain) Lateralstabilitywith'unloadedtrain'

gr16(SW/2) SW/2withmax.longitudinal

gr17(SW/2) SW/2withmax.transverse

gr21(LM71+SW/0) Max.vertical1withmax.longitudinal 0.80 0.70 0

gr22(LM71+SW/0) Max.vertical2withmax.transverse

gr23(Braking/traction) Max.longitudinal

gr24(Centrifugal/nosing) Max.lateral

gr26(SW/2) SW/2withmax.longitudinal

gr27(SW/2) SW/2withmax.transverse

gr31(LM71+SW/0) Additionalloadcases 0.80 0.60 0

Other operating actions

Aerodynamiceffects 0.80 0.50 0

Generalmaintenanceloadingfornon-publicfootpaths 0.80 0.50 0

Wind forces d F Wk0.75 0.50 0

F** W 1.00 0 0

Thermal actionse T K 0.60 0.60 0.50

Snow loads Q Sn,k (duringexecution) 0.80 – 0

Construction loads Qc 1.00 – 1.00

Key

a Ifdeformationisbeingconsideredforpersistentandtransientdesignsituations,c2shouldbetakenequalto1.00forrailtrafficactions.Forseismicdesignsituations,seeTableNAA2.5ofBSEN1990NA

b Minimumcoexistantfavourableverticalloadwithindividualcomponentsofrailtrafficactions(e.g.centrifugal,tractionorbraking)is0.5LM71,etc.

c 0.8 if1trackonlyisloaded

0.7 if2tracksaresimultaneouslyloaded

0.6 if3ormoretracksaresimultaneouslyloadedd Whenwindforcesactsimultaneouslywithtrafficactions,thewindforcec0FWk shouldbetakenasnogreaterthanF** W

(seeBSEN1991-1-4).SeeA2.2.4(4)ofBSEN1990e SeeBSEN1991-1-5

BS EN 1990 table A.2.3

7

BasisofdesignBasisofdesign

Combinations of actions

Ultimate limit states

Thefollowingultimatelimitstatesshallbeverifiedasrelevant:

EQU Lossofstaticequilibriumofthestructureoranypartofitconsideredasarigidbody.STR Internalfailureorexcessivedeformationofthestructureorstructuralmembers.GEO Failureorexcessivedeformationofthestructurewherethestrengthsofsoilorrockare

significantinprovidingresistance.FAT Fatiguefailureofthestructureorstructuralmembers.

ThepartialfactorsandcombinationsofactionsfortheselimitstatesaregiveninTables2.4to2.7.

Table 2.4Recommended partial factors

Action EQU (Set A) STR/GEO (Set B) STR/GEO (Set C)

Permanent actions gG,sup gG,inf gG,sup gG,inf gG,sup gG,inf

Concrete self-weight 1.05 0.95 1.35 0.95 1.00 1.00

Steel self-weight 1.05 0.95 1.20 0.95 1.00 1.00

Superimposed dead a 1.05 0.95 1.20 0.95 1.00 1.00

Road surfacing a 1.05 0.95 1.20 0.95 1.00 1.00

Weight of soil 1.05 0.95 1.35 0.95 1.00 1.00

Self-weight of other materials listed in BS EN 1991-1-1, tables A.1-A.6

1.05 0.95 1.35 0.95 1.00 1.00

Creep and shrinkage – – 1.20 0 1.00 0

Settlement (linear structural analysis)

– – 1.20 0 1.00 0

Settlement (non-linear structural analysis)

– – 1.35 0 1.00 0

Variable actions (gQ) Unfavourable Favourable Unfavourable Favourable Unfavourable Favourable

Road traffic actions (gr1a, gr1b, gr2, gr5, gr6)

1.35 0 1.35 0 1.15 0

Pedestrian actions (gr3, gr4)

1.35 0 1.35 0 1.15 0

Rail traffic actions (LM71, SW/0, HSLM)

1.45 0 1.45 0 1.25 0

Rail traffic actions (SW/2 and other load models representing controlled exceptional traffic)

1.40 0 1.40 0 1.20 0

Rail traffic actions (real trains)

1.70 0 1.70 0 1.45 0

Wind actions 1.70 0 1.70 0 1.45 0

Thermal actions 1.55 0 1.55 0 1.30 0

Key

a SeeTableNA.1ofBSEN1991-1-1[9]forguidanceonthicknessesforballast,waterproofing,surfacesandothercoatings.NoteFordesignvaluesforself-weightofwater,groundwaterpressureandearthpressuresrefertoBSEN1997-1.

BS EN 19906.4.1

2.3.5

BS EN 1990 tables NA.A.2.4(A), (B) & (C)

8

Table 2.7Combinations of fatigue actions

Action Permanent actions Prestress Leading variable action

Accompanying variable actions

Fatigue actionFavourable Unfavourable

Non-cyclic Gk,j,inf Gk,j,supP c1,1Qk,1 c2,iQk,i

–

Cyclic Gk,j,inf Gk,j,supP c1,1Qk,1 c2,iQk,i Qfat

Serviceability limit states

ThecombinationsofactionsfortheserviceabilitylimitstatearegiveninTable2.8.

Table 2.8Combinations of actions for the serviceability limit state

Combination Permanent actions Prestress Variable actions

Favourable Unfavourable Leading Others

Characteristic Gk,j,sup Gk,j,infP Qk,1 c0,iQk,i

Frequent Gk,j,sup Gk,j,infP c1,1Qk,1 c2,iQk,i

Quasi-permanent Gk,j,sup Gk,j,infP c2,1Qk,1 c2,iQk,i

Actions to consider

Thermaleffects,differentialsettlements/movements,creepandshrinkageshouldbetakenintoaccountwhencheckingserviceabilitylimitstates.

Thermaleffects,differentialsettlements/movements,creepandshrinkageshouldbeconsideredforultimatelimitstatesonlywheretheyaresignificant(e.g.fatigueconditions,intheverificationofstabilitywheresecondordereffectsareofimportance,etc.).Inothercasestheyneednotbeconsidered,providedthattheductilityandrotationcapacityoftheelementsaresufficient.

Wherethermaleffectsaretakenintoaccounttheyshouldbeconsideredasvariableactionsandappliedwithapartialfactorandcfactor,whichcanbedeterminedfromBSEN1990AnnexA2.

2.3.6

Table 2.5Combinations of actions for EQU, STR and GEO limit states

Persistent and transient design situation

Permanent actions Prestress Leading variable action

Accompanying variable actionsUnfavourable Favourable

Exp. (6.10) gG,supGkj,sup g G,infGkj,infg PP gQ,1Qk,1 g Q,ic 0,iQk,i

NoteForpartialfactorsseeTable2.4(exceptseeTable2.9forg P)

Table 2.6Combinations for accidental situations

Accidental design situation

Permanent actions Prestress Accidental action

Accompanying variable actions

Unfavourable Favourable Main Others

Exp. (6.11a/b) Gk,j,sup Gk,j,infP Ad

c1,1 Qk,1 c2,iQk,i

BS EN 1992-1-12.3.1.2(3)

BS EN 1990table A2.5

BS EN 1992-1-16.8.3

BS EN 1990table A2.6

BS EN 1992-1-12.3.1.2, 2.3.1.3& 2.3.2.2

BS EN 1990 tables NA.A.2.4(A), (B) & (C)

9

Basisofdesign

Differentialsettlements/movementsofthestructureduetosoilsubsidenceshouldbeclassifiedasapermanentaction,Gsetwhichis introducedassuchincombinationsofactions.Apartialsafetyfactorforsettlementeffectsshouldbeapplied.

When creep is taken into account its design effects should be evaluated under the quasi-permanentcombinationofactionsirrespectiveofthedesignsituationconsideredi.e.persistent,transientoraccidental.Inmostcasestheeffectsofcreepmaybeevaluatedunderpermanentloadsandthemeanvalueofprestress.

Thedesignvaluesforvehicle impactsonsupportingstructuresandsubstructuresaregiveninBSEN1991-1-1[9]section4.3.ThedeisgnvaluesforvehicleimpactsonparapetsaregiveninBSEN1991-2[9]section4.8.

AppropriatevaluesforpartialactionsaregiveninTable2.9

Table 2.9Values for partial factors applied to actions

Action Ultimate limit state Servicability limit state

STR/GEO EQU FAT Favourable Unfavourable

Favourable Unfavourable Favourable Unfavourable

Shrinkage gSH=0 gSH=1.0 – – – – –

Prestress effects gP,fav=0.9 gP,unfav=1.1 gP,fav=0.9 gP,unfav=1.2 – rinf=1.0 rsup=1.0

Fatigue – – – – gF,fat=1.0 – –

Material properties

Material properties are specified in terms of their characteristic values, which in generalcorrespond to a defined fractile of an assumed statistical distribution of the propertyconsidered(usuallythelower5%fractile).

ThevaluesofgCandgS,partialfactorsformaterials,areindicatedinTable2.10.

Table 2.10Partial factors for materials

Design situation gC – concrete gS – reinforcing steel gS – prestressing steel

ULS – Persistent and transient 1.50 1.15 1.15

Accidental 1.20 1.00 1.00

Fatigue 1.50 1.15 1.15

SLS 1.00 1.00 1.00

Assumptions

InadditiontotheassumptionsinBSEN1990,itisassumedthat:

■Structuresaredesignedbyappropriatelyqualifiedandexperiencedpersonnel.■Adequatesupervisionandqualitycontrolisprovided.■Constructioniscarriedoutbypersonnelhavingtheappropriateskillandexperience.■MaterialsandproductswillbeusedasspecifiedinEurocode2orintherelevantmaterialor

productspecifications.■Thestructurewillbeadequatelymaintainedandwillbeusedinaccordancewiththe

designbrief.■TherequirementsforexecutionandworkmanshipgiveninENV13670[10]arecompliedwith.

2.3.7

2.4

BS EN 1992-1-12.3.1.3(1) & (4)

BS EN 1992-1-12.3.2.2(3)

BS EN 1992-1-1 2.4.2.4(1) & NA

BS EN 1992-1-1 table 2.1 N & NA

BS EN 1992-1-11.3

10

2.5

AtthetimeofwritingBSEN13670[11] isexpectedtobepublishedinlate2009,andwillreplace ENV 13670. Once published it is anticipated that standard specifications will beupdatedtorefertoit.Intheinterimexistingspecificationsshouldbeadapted.

Foundation design

ThedesignofconcretefoundationsissubjecttoEurocode7[12]forthegeotechnicalaspectsandtoEurocode2forthestructuralconcretedesign.FurtherguidanceonthegeotechnicaldesigncanbefoundinPD6694-1[13].

Eurocode7iswiderangingandprovidesalltherequirementsforgeotechnicaldesign.Itstatesthatnolimitstatee.g.equilibrium,stability,strengthorserviceability,asdefinedbyBSEN1990,shallbeexceeded.TherequirementsforULSandSLSdesignmaybeaccomplishedbyusing,inanappropriatemanner,thefollowingaloneorincombination:

■ Calculations.■ Prescriptivemeasures.■ Testing.■ Observationalmethods.

The foundation design and the derivation of design resistance are covered by theGeotechnical Design Report. For simple structures, this report can be combined with theground investigation report but it is still a distinct requirement. Both the ULS and SLSconditions must be met but the definition of the SLS criteria is not possible without theliaisonwiththebridgedesignerandafullEurocode7compatibledesigncannotbecarriedoutbyapartyinisolationfromtherestofthestructuredesignteam.

BS EN 19972.1(4)

BS EN 19972.4.6.4

11

Materials

BS EN 1992-1-1 3.1.2(1)

BS EN 1992-1-1 4.4.1.2(5) & NA

BS EN 1992-1-1 table 3.1

BS EN 1992-23.1.2 (102) & NA

BS EN 1992-1-13.1.2 (2) & NA

BS EN 1992-1-1 3.1.6(1) & NA

BS EN 1992-1-1 3.1.3(4)

BS EN 1992-1-1 3.1.3(5)

3

3.1

3.1.1

Materials

Concrete

Strength and other properties

The compressive strength is denoted by concrete strength classes which relate to thecharacteristic(5%)cylinderstrengthfck,orthecubestrengthfck,cube,inaccordancewithBSEN206-1Concrete: Specification, performance, production and conformity [14].

IntheUK,BS8500 [8]complementsBSEN206-1andtheguidancegivenintheformershouldbefollowed.

Concrete strength classes and properties are shown inTable 3.1. In the notation used forcompressivestrengthclass,‘C’referstonormalweightconcrete,thefirstnumberreferstothecylinderstrengthfckandthesecondtocubestrengthfck,cube.

Thestrengthclasses(C)inBSEN1992-2aredenotedbythecharacteristiccylinderstrengthfckdetermined at 28 days with a minimum value ofC25/30 and a maximum value ofC70/85.The shear strength of concrete classes higher thanC50/60 should be determined by tests orlimitedtothatofC50/60.

Thevalueofthedesigncompressivestrengthofconcrete,fcd,isdefinedas:

fcd=accfck/gC

where fck =characteristiccompressivecylinderstrengthofconcreteat28days gC =partialfactorforconcrete(SeeTable2.9) acc =acoefficienttakingaccountoflongtermeffectsonthecompressivestrengthandof

unfavourableeffectsresultingfromthewaytheloadisapplied. IntheUKacciseither1.0or0.85dependingonthesituation.Thecorrectvaluesareusedintheappropriateclausesbelow.Generallyitis1.0forshearand0.85inothercircumstances

Thevalueofconcretedesigntensilestrengthfctdisdefinedas:fctd= 1.0 fctk,0.05/gC

where fctk,0.05=5%fractilevalueofaxialtensilestrengthofconcrete

Poisson'sratiomaybetakenequalto0.2foruncrackedconcreteand0forcrackedconcrete.

Unlessmoreaccurateinformationisavailable,thelinearcoefficientofthermalexpansionmaybetakenequalto10x10–6K–1.

Table 3.1Concrete strength classes and properties

Property Strength class (MPa)

C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75 C70/85 C28/35a C32/40a

fck 25 30 35 40 45 50 55 60 70 28 32

fck, cube 30 37 45 50 55 60 67 75 85 35 40

fcm 33 38 43 48 53 58 63 68 78 36 40

fctm 2.6 2.9 3.2 3.5 3.8 4.1 4.2 4.4 4.6 2.8 3.0

fctk,0.05 1.8 2.0 2.2 2.5 2.7 2.9 3.0 3.1 3.2 1.9 2.1

fctk,0.95 3.3 3.8 4.2 4.6 4.9 5.3 5.5 5.7 6.0 3.6 3.9

Ecm,(GPa) 31 33 34 35 36 37 38 39 41 32 33

KeyaDeriveddata

BS EN 1992-1-1 table 3.1

12

BS EN 1992-1-13.1.4(2)

BS EN 1992-1-1B.1(1)

BS EN 1992-1-1B.1(2)

Creep

Thecreepcoefficient,h(t,t0)isrelatedtoEc,thetangentmodulus,whichmaybetakenas

1.05Ecm.

Thecreepcoefficienth(t,t0)maybeobtainedfromFigure3.1ofBSEN1992-1-1,orcalculatedfrom:

h(t,t0)=h0bc(t,t0)

where h0= notionalcreepcoefficientandmaybeestimatedfrom:

= hRHb(fcm)b (t0)

where hRH = factortoallowfortheeffectofrelativehumidityonthenotionalcreep

coefficient: = 1+1–RH/100forfcm≤35MPa 0.1h0

1/3

= [1+a1(1–RH/100)]a2forfcm>35MPa 0.1h0

1/3

RH =relativehumidityoftheambientenvironmentin% b (fcm) =factortoallowfortheeffectofconcretestrengthonthenotionalcreep

coefficient =16.8/fcm

0.5

fcm =meancompressivestrengthofconcreteinMPaattheageof28days

b (t0) =factortoallowfortheeffectofconcreteageatloadingonthenotionalcreepcoefficient

=1/(0.1+t00.20) h0 =notionalsizeofthememberinmm =2Ac/u Ac =cross-sectionalarea u =perimeterofthememberincontactwiththeatmosphere bc(t,t0)=coefficienttodescribethedevelopmentofcreepwithtimeafter loading =[(t – t0)/(bH+t – t0)]0.3

where t =ageofconcreteindaysatthemomentconsidered t0 =ageofconcreteatloadingindays t – t0 =non-adjusteddurationofloadingindays bH =coefficient depending on the relative humidity (RH in %) and the

notionalmembersize(h0inmm) =1.5[1+(0.012RH)18]h0+250≤1500forfcm≤35MPa =1.5[1+(0.012RH)18]h0+250a3≤1500a3forfcm>35MPa a1 =(35/fcm)0.7

a2 =(35/fcm)0.2

a3 =(35/fcm)0.5

Theeffectoftypeofcementonthecreepcoefficientofconcretemaybetakenintoaccountbymodifyingtheageofloadingt0accordingtothefollowingExpression:t0=t0,T(9/(2+t0,T

1.2)+1)a≥0.5

where t0,T =temperatureadjustedageofconcreteatloadingindays(seebelow) a =powerwhichdependsontypeofcement =-1forcementClassS(cementClassCEM32.5N) =0forcementClassN(cementClasses32.5R&CEM42.5N) =1forcementClassR(cementClassesCEM42.5R,CEM52.5N&CEM52.5R)

3.1.2

13

Materials

CementclassescanbespecifiedusingBSEN197-1[15].WherethecementClassisnotknown,generally Class R may be assumed. Where the ground granulated blastfurnace slag (ggbs)contentexceeds35%ortheflyashcontentexceeds20%ofthecementcombination,ClassNmaybeassumed.Whereggbsexceeds65%orpfaexceeds35%,ClassSmaybeassumed.

The effect of elevated or reduced temperatures within the range 0–80°C on the maturity ofconcretemaybetakenintoaccountbyadjustingtheconcreteageaccordingtothefollowingExpression: ntT=Se – (4000/[273+T(Dti)]–13.65)Dt i=1

where tT =temperature-adjustedconcreteagewhichreplacestinthecorrespondingequations T(Dti ) =temperaturein°CduringthetimeperiodDti Dti =numberofdayswhereatemperatureTprevails

The mean coefficient of variation of the above predicted creep data, deduced from acomputeriseddatabankoflaboratorytestresults,isoftheorderof20%.

Thecreepdeformationofconcreteecc(∞,t0)attimet=∞foraconstantcompressivestressscappliedattheconcreteaget0,isgivenby:

ecc(∞,t0)=h(∞,t0)(sc/Ec)

Whenthecompressivestressofconcreteatanaget0exceedsthevalue0.45fck(t0)thencreepnon-linearityshouldbeconsidered.Suchahighstresscanoccurasaresultofpretensioning,e.g.in precast concrete members at tendon level. In such cases the non-linear notional creepcoefficientshouldbeobtainedasfollows:

hnl(∞,t0)=h(∞,t0)exp[1.5(ks–0.45)]

where hnl(∞,t0)=non-linearnotionalcreepcoefficient,whichreplacesh(∞,t0) ks =stress–strengthratiosc/fck(t0) sc =compressivestress fck(t0) =characteristicconcretecompressivestrengthatthetimeofloading

Shrinkage

Thetotalshrinkagestrainiscomposedoftwocomponents,thedryingshrinkagestrainandtheautogenousshrinkagestrain.Thedryingshrinkagestraindevelopsslowly,sinceitisafunctionofthe migration of the water through the hardened concrete.The autogenous shrinkage straindevelopsduringhardeningoftheconcrete:themajorpartthereforedevelopsintheearlydaysaftercasting.Autogenousshrinkage isa linearfunctionoftheconcretestrength. Itshouldbeconsideredspecificallywhennewconcreteiscastagainsthardenedconcrete.

Hencethevaluesofthetotalshrinkagestrainfollowfrom:ecs=ecd+eca

where ecs=totalshrinkagestrain ecd=dryingshrinkagestrain(seeTable3.2) eca=autogenousshrinkagestrain(seeTable3.2)

Steel reinforcement

ThepropertiesofsteelreinforcementtoBS4449:2005[16]areshowninTable3.3.ThisBritishStandardcomplementsBSEN10080[17]andAnnexCofBSEN1992-1-1.

AnnexCallowsforastrengthrangebetween400and600MPa.BS4449:2005adopts500MPa.

BS EN 1992-1-13.1.4(3)

BS EN 1992-1-13.1.4(4)

BS EN 1992-1-13.1.4(6)

BS EN 1992-1-13.2

Materials

BS EN 1992-1-1B.1(3)

3.1.3

3.2

14

Table 3.2Long-term (70-year) shrinkage strains

Concrete strength at 28 days ( fck)

Strain due to drying shrinkage (x 103)

Strain due to autogenous shrinkage (x 103)

Total shrinkage strains (x 103)

20 0.517 0.025 0.542

25 0.489 0.038 0.527

30 0.463 0.050 0.513

35 0.438 0.063 0.501

40 0.415 0.075 0.490

45 0.393 0.088 0.481

50 0.372 0.100 0.472

60 0.333 0.125 0.458

70 0.298 0.150 0.448

Notes1ThevaluesshownassumeClassRcement(ClassNandClassSwillhavelowervalues).

2Thedryingshrinkagevaluesassumeanotionalmembersize,h0,of150mm.Forh0of300mmmultiplyvaluesby0.81andforh0of500mmorgreater,multiplyvaluesby0.75.

Table 3.3Properties of reinforcement

Property Class

A B C

Characteristic yield strength fyk or f0.2k (MPa) 500 500 500

Minimum value of k = (ft /fy)k ≥1.05 ≥1.08 ≥1.15<1.35

Characteristic strain at maximum force euk (%) ≥2.5 ≥5.0 ≥7.5

NoteTablederivedfromBSEN1992-1-1AnnexC,BS4449:2005andBSEN10080.ThenomenclatureusedinBS4449:2005differsfromthatusedinAnnexCandusedhere.

ClassBorClassCreinforcementshouldbeused.Forsteelfabricreinforcement,ClassAmayalsobeusedprovideditisnottakenintoaccountintheevaluationoftheultimateresistance.

Prestressing steel

Typical prestressing strand properties are shown inTable 3.4.The manufacturer’s technicaldatasheetsshouldbereferredfordetailedinformation.

PropertiesofprestressingsteelsshouldbeinaccordancewithEN10138.However,untilthisstandardispublishedBS5896[18]maybeused.

The0.1%proofstress(fp0.1k)andthespecifiedvalueoftensilestrength(fpk)areusedtodefinethecharacteristicvaluesoftheprestressingsteels.

Thedesignvaluesfortheprestressingsteelarederivedbydividingthecharacteristicvaluesby the partial safety factor for prestressing steel gS. For ultimate limit state verification,gS=1.15forpersistentandtransientdesignsituationsand1.0foraccidentaldesignsituations.

ThemodulusofelasticityEpcanbeassumedequalto205GPaforwiresandbarsand195GPaforstrand.

BS EN 1992-1-1table C1

BS EN 1992-2 3.2.4 & NA

BS EN 1992-1-1 3.3.6(2) & (3)

BS EN 1992-1-1 3.3.2(1)

BS EN 1992-1-1 3.3.3(1)

3.3

15

MaterialsMaterials

Table 3.4Dimensions and properties of low relaxation strand and wire for prestressed concrete

Type of strand

Nominal diameter (mm)

Nominal tensile strength (MPa)

Steel area (mm²)

Nominal mass (g/m)

Characteristic breaking load (kN)

Characteristic 0.1% proof load (kN)

Characteristic load at 1% elongation (kN)

7 wire standard

15.2 1860 139 1090 259 220 228

15.2 1670 139 1090 232 197 204

12.5 1860 93 730 173 147 152

12.5 1770 93 730 164 139 144

11.0 1770 71 557 125 106 110

9.3 1860 52 408 97 82 85

9.3 1770 52 408 92 78 81

7 wire super 15.7 1860 150 1180 279 237 246

15.7 1770 150 1180 265 225 233

12.9 1860 100 785 186 158 163

11.3 1860 75 590 139 118 122

9.6 1860 55 432 102 87 90

8.0 1860 38 298 70 59 61

7 wire drawn 18.0 1770 223 1750 380 323 334

15.2 1820 165 1295 300 255 264

12.7 1860 112 890 209 178 184

Relaxation of prestressing steel

BSEN1992-1-1definesthreeclassesofrelaxation.

Class1:ordinarywireandstrandClass2:lowrelaxationwireandstrandClass3:hotrolledandprocessedbars

Thedesigncalculationofthelossesduetorelaxationoftheprestressingsteelshouldbebasedon the loss at 1000 hr (r1000) after tensioning at a mean temperature of 20°C and initialprestressof70%(0.7fpk).Thevaluesofr1000canbetakenfromthecertificateorassumedtobe:

Class1–8%Class2–2.5%Class3–4%

The relaxation loss may be obtained from manufacturer’s test certificates or they can becalculated,baseduponthefollowingequations(seealsoTable3.5):

Class1 spr tr1000spi

D5. 39 e 6.7m 10–5

1000=

0.75 (1– m)

Class2 spr tr1000spi

D0. 66 e 9.1m 10–5

1000=

0.75 (1– m)

Class3 spr tr1000spi

D1. 98 e8m 10–5

1000=

0.75 (1– m)

where

Dspr =absolutevalueoftherelaxationlossesoftheprestress

spi =absolutevalueoftheinitialprestress

=spm0forpost-tensioning (seeSection11.3.2)

=maximumtensilestressappliedtothetendonminustheimmediatelossesoccurringduringthestressingprocessforpre-tensioning (seeSection11.3.3)

BS EN 1992-1-1 3.3.2(4)

BS EN 1992-1-1 3.3.2(5)

BS EN 1992-1-1 3.3.2(6)

BS EN 1992-1-1 3.3.2(7)

3.3.1

16

t =timeaftertensioning(inhours) μ =spiIfpk,wherefpkisthecharacteristicvalueofthetensilestrengthofthe

prestressingsteel r1000 =valueofrelaxationloss(%),at1000hoursaftertensioningandatamean

temperatureof20°C

The long-term (final) values of the relaxation losses may be estimated from t = 500,000hours.

Relaxationlossesareverysensitivetotemperatureofthesteelwhereheattreatmentisapplied(e.g.bysteam)(seeBSEN1992-1-1Cl.10.3.2.1).Otherwisewherethetemperatureisgreaterthan50°C,therelaxationlossesshouldbeverified.

Table 3.5Relaxation losses based on using Expressions (3.28 to 3.30) in BS EN 1992-1-1

Class r1000 (%) μ = spi/fpkt (hours) Dspr/spi%

1 8 0.80 500,000 23.3

0.76 21.5

0.72 19.8

0.68 18.2

0.64 16.8

0.60 15.5

2 2.5 0.80 6.1

0.76 5.1

0.72 4.3

0.68 3.6

0.66 3.0

0.60 2.5

3 4 0.80 12.1

0.76 10.6

0.72 9.3

0.68 8.1

0.64 7.1

0.60 6.2

Relaxation lossesaresensitivetovariations instress levelsovertimeandcanthereforebereduced by taking into consideration of other time-dependent losses occurring within thestructure at the same time (such as creep and shrinkage). Previous UK practice is to basedesignontherelaxationlossof1000hourswithoutconsideringtheinteractionwithcreepandshrinkage.

BS EN 1992-1-1 3.3.2(8)

BS EN 1992-1-1 3.3.2(9)

17

Durabilityandcover

Durability and cover

General

A durable structure shall meet the requirements of serviceability, strength and stabilitythroughout its design working life, without significant loss of utility or excessive unforeseenmaintenance.

Inordertoachievetherequireddesignworkinglifeofthestructure,adequatemeasuresshallbetakentoprotecteachstructuralelementagainsttherelevantenvironmentalactions.Exposureconditionsarechemicalandphysicalconditionstowhichthestructureisexposedinadditiontomechanicalactions.

Requirements of durability should be considered at all stages of design and construction,includingtheselectionofmaterials,constructiondetails,executionandqualitycontrol.

Half-jointsshouldnotbeusedinbridgesunlessthereareadequateprovisionsforinspectionandmaintenance. Water penetration or the possibility of leakage from the carriageway intothe inside of voided structures should be considered in the design. For concrete surfacesprotectedbywaterproofingtheexposureclassis XC3 .

Where de-icing salt is used, all exposed concrete surfaces within 10m of the carriagewayhorizontally or within 5m above the carriageway should be considered as being directlyaffected by de-icing salts. Top surfaces of supports under expansion joints should also beconsideredasbeingdirectlyaffectedbyde-icingsalts.Theexposureclassesforsurfacesdirectlyaffectedbyde-icingslatsare XD3 and XF2 or XF4 asappropriate.

Adequatecoverisrequiredtoensuresafetransmissionofbondforces(seeSection4.2)andprotectionofsteelagainstcorrosion(seeSections4.3and4.4).

The concrete cover to reinforcement is the distance from the outer surface of thereinforcementtothenearestconcretesurface.Drawingsshouldspecifythenominalcover.Asillustrated in Figure 4.1, the nominal cover should satisfy the minimum requirements inrespectofbondanddurability,andallowforthedeviationtobeexpectedinexecution(seeSection4.5).

Figure 4.1Determination

of cover

Nominalcover,cnom

Minimumcover,cmin

(forbond,cmin,bor

durabilitycmin,dur)

Designallowancefor

deviation,Dcdev

BS EN 1992-1-14.1

BS EN 1992-1-1 4.3(1), 4.2(1)

BS EN 1992-1-1 4.3(2)

BS EN 1992-1-1 4.4.1.2(1)

BS EN 1992-2 4.2(106) & NA

BS EN 1992-1-1 4.4.1.3(3)

BS EN 1992-2 4.2(104), (105) & NA, PD 6687-2 5.1

4

4.1

18

Cover for bond, cmin,b

Inordertotransmitbondforcessafelyandtoensureadequatecompaction,theminimumcovershouldnotbelessthancmin,binTable4.1.

Table 4.1Minimum cover, cmin,b, requirements for bond

Reinforcement type and arrangement cmin,b

Individual bars Diameterofbar,f

Bundled bars Equivalentdiameterofbars,fn

Post-tensioned circular ducts Diameterofductor80mmwhicheverissmaller

Post-tensioned rectangular ducts Smallerdimensionorhalfgreaterdimensionwhicheverisgreater,butnotmorethan80mm

Pre-tensioned strand or wire 1.5timesthediameter

Pre-tensioned indented wire 2.5timesthediameter

Cover for durability, cmin,dur

Environmental conditions are classified according toTable 4.2, which is based on BS 8500.ConcretecompositionandminimumcoversrequiredfordurabilityindifferentenvironmentalconditionsaresetoutinTable4.3,derivedfromBS8500[8].Thesetablesgiverecommendationsfornormalweightconcreteusingmaximumaggregatesizeof20mmforselectedexposureclassesandcovertoreinforcement.

InaccordancewithBS8500 ,specialattentionshouldbegiventotheconcretecompositionand aggregates, when considering freeze/thaw attack, chemical attack or abrasionresistance.

Table 4.2Exposure Classes

Class Class description Informative example applicable to the United Kingdom

No risk of corrosion or attack (X0 class)

X0 Forconcretewithoutreinforcementorembeddedmetalallexposuresexceptwherethereisfreeze/thaw,abrasionorchemicalattack.

Unreinforcedconcretesurfacesinsidestructures.UnreinforcedconcretecompletelyburiedinsoilclassedasAC–1andwithhydraulicgradientnotgreaterthan5.Unreinforcedconcretepermanentlysubmergedinnon-aggressivewater.Unreinforcedconcreteincyclicwetanddryconditionsnotsubjecttoabrasion,freezingorchemicalattack.Note:Forreinforcedconcrete,useatleastXC1.

Corrosion induced by carbonation (XC classes)a (Where concrete containing reinforcement or other embedded metal is exposed to air and moisture)

XC1 Dryorpermanentlywet. Reinforcedandprestressedconcretesurfacesinsideenclosedstructuresexceptareasofstructureswithhighhumidity.Reinforcedandprestressedconcretesurfacespermanentlysubmergedinnon-aggressivewater.

XC2 Wet,rarelydry. ReinforcedandprestressedconcretecompletelyburiedinsoilclassedasAC–1andwithahydraulicgradientnotgreaterthan5.

XC3&

XC4

Moderatehumidityorcyclicwetanddry.

Externalreinforcedandprestressedconcretesurfacesshelteredfrom,orexposedto,directrain.Reinforcedandprestressedconcretesurfacesinsidestructureswithhighhumidity(e.g.poorlyventilated,bathrooms,kitchens).Reinforcedandprestressedconcretesurfacesexposedtoalternatewettinganddrying.Interiorconcretesurfacesofpedestriansubwaysnotsubjecttode-icingsalts,voidedsuperstructuresorcellularabutments.Reinforcedorprestressedconcretebeneathwaterproofing.

BS 8500 table A.1

4.2

4.3

BS EN 1992-1-1table 4.2

BS EN 1992-1-14.4.1.2(3) & NA

BS EN 1992-1-14.4.1.2(5) & NA

19

Durabilityandcover

Table 4.2Exposure Classes (continued)

Class Class description Informative example applicable to the United Kingdom

Corrosion induced by chlorides other than from sea water (XD classes)a (Where concrete containing reinforcement or other embedded metal is subject to contact with water containing chlorides, including de-icing salts, from sources other than from sea water)

XD1 Moderatehumidity Concretesurfacesexposedtoairbornechlorides.Reinforcedandprestressedconcretewallandstructuresupportsmorethan10mhorizontallyfromacarriageway.Bridgedecksoffitsmorethan5mverticallyabovethecarriageway.Partsofstructuresexposedtooccasionalorslightchlorideconditions.

XD2 Wet,rarelydry. Reinforcedandprestressedconcretesurfacestotallyimmersedinwatercontainingchloridesb.Buriedhighwaystructuresmorethan1mbelowadjacentcarriageway.

XD3 Cyclicwetanddry. Reinforcedandprestressedconcretesurfacesdirectlyaffectedbyde-icingsaltsorspraycontainingde-icingsalts(e.g.walls;abutmentsandcolumnswithin10mofthecarriageway;parapetedgebeamsandburiedstructureslessthan1mbelowcarriagewaylevel,pavementsandcarparkslabs).

Corrosion induced by chlorides from sea water (XS classes)a (Where concrete containing reinforcement or other embedded metal is subject to contact with chlorides from sea water or air carrying salt originating from sea water)

XS1 Exposedtoairbornesaltbutnotindirectcontactwithseawater.

Externalreinforcedandprestressedconcretesurfacesincoastalareas.

XS2 Permanentlysubmerged. Reinforcedandprestressedconcretecompletelysubmergedandremainingsaturated,e.g.concretebelowmid-tidelevelb.

XS3 Tidal,splashandsprayzones. Reinforcedandprestressedconcretesurfacesintheuppertidalzonesandthesplashandsprayzonesc.

Freeze/thaw attack (XF classes) (Where concrete is exposed to significant attack from freeze/thaw cycles whilst wet)

XF1 Moderatewatersaturationwithoutde-icingagent.

Verticalconcretesurfacessuchasfacadesandcolumnsexposedtorainandfreezing.Non-verticalconcretesurfacesnothighlysaturated,butexposedtofreezingandtorainorwater.

XF2 Moderatewatersaturationwithde-icingagent.

Concretesurfacessuchaspartsofbridges,whichwouldotherwisebeclassifiedasXF1butwhichareexposedtode-icingsaltseitherdirectlyorassprayorrun-off.

XF3 Highwatersaturationwithoutde-icingagent.

Horizontalconcretesurfaces,suchaspartsofbuildings,wherewateraccumulatesandwhichareexposedtofreezing.Concretesurfacessubjectedtofrequentsplashingwithwaterandexposedtofreezing.

XF4 Highwatersaturationwithde-icingagentorseawaterd.

Horizontalconcretesurfaces,suchasroadsandpavements,exposedtofreezingandtode-icingsaltseitherdirectlyorassprayorrun-off.Concretesurfacessubjectedtofrequentsplashingwithwatercontainingde-icingagentsandexposedtofreezing.

Chemical attack (ACEC classes) (Where concrete is exposed to chemical attack. Note: BS 8500-1 refers to ACEC classes rather than XA classes used in BS EN 206-1)

RefertoSection4.4

Key

a Themoistureconditionrelatestothatintheconcretecovertoreinforcementorotherembeddedmetalbut,inmanycases,conditionsintheconcretecovercanbetakenasbeingthatofthesurroundingenvironment.Thismightnotbethecaseifthereisabarrierbetweentheconcreteanditsenvironment.

b Reinforcedandprestressedconcreteelements,whereonesurfaceisimmersedinwatercontainingchloridesandanotherisexposedtoair,arepotentiallyamoreseverecondition,especiallywherethedrysideisatahighambienttemperature.Specialistadviceshouldbesoughtwherenecessary,todevelopaspecificationthatisappropriatetotheactualconditionslikelytobeencountered.

c ExposureXS3coversarangeofconditions.Themostextremeconditionsareinthesprayzone.TheleastextremeisinthetidalzonewhereconditionscanbesimilartothoseinXS2.TherecommendationsgiventakeintoaccountthemostextremeUKconditionswithinthisclass.

d ItisnotnormallynecessarytoclassifyintheXF4exposureclassthosepartsofstructureslocatedintheUnitedKingdomwhichareinfrequentcontactwiththesea.

20

Table 4.3Selecteda recommendations for normal-weight reinforced concrete quality for combined exposure classes and cover to reinforcement

Exposure conditions Cement/ combina-tion desig-nationsb

Minimum strength classc, maximum w/c ratio, minimum cement or combination

Typical example

Primary Secondary At least 50-year working life

Nominal cover to reinforcementd

15 +Dcdev 20 +Dcdev 25 +Dcdev 30 +Dcdev 35 +Dcdev 40 +Dcdev 45 +Dcdev

Internalelementsorpermanentlywetelements

XC1 – AllC20/25,0.70,240orRC20/25

<<< <<< <<< <<< <<< <<<

BuriedconcreteinAC–1groundconditionse

XC2 AC–1 All – –C25/30,0.65,260orRC25/30

<<< <<< <<< <<<

Verticalsurfaceprotectedfromdirectrainfall

XC3/4

– AllexceptIVB-V

–C40/50,0.45,340orRC40/50

C30/37,0.55,300orRC30/37

C28/35,0.60,280orRC28/35

C25/30,0.65,260orRC25/30

<<< <<<

Verticalsurfaceexposedtorainandfreezing

XF1 AllexceptIVB-V

–C40/50,0.45,340orRC40/50

C30/37,0.55,300orRC30/37

C28/35,0.60,280orRC28/35

<<< <<< <<<

Exposedhorizontalsurfaces

XF3 AllexceptIVB-V

–C40/50,0.45,340gorRC40/50XFg

<<< <<< <<< <<< <<<

XF3(airentrained)

AllexceptIVB-V

– – C30/37,0.55,300g,h

C28/35,0.60,280g,horPAV2

C25/30,0.60,280g, h,jorPAV1

<<< <<<

Elementssubjecttoairbornechlorides

XD1f XF1 All – – C40/50,0.45,360

C32/40,0.55,320

C28/35,0.60,300 <<< <<<

Exposedverticalsurfacesnearcoast

XS1f

XF1

CEMI,IIA,IIB-S,SRPC

– – – SeeBS8500 C35/45,0.45,360

C32/40,0.50,340 <<<

IIB-V,IIIA – – – SeeBS8500

C32/40,0.45,360

C28/35,0.50,340

C25/30,0.55,320

– IIIB – – – C32/40,0.40,380

C25/30,0.50,340

C25/30,0.50,340

C25/30,0.55,320

Exposedhoriz.surfacesnearcoast

XF3orXF4

CEMI,IIA,IIB-S,SRPC

– – – SeeBS8500 C40/50,0.45,360g <<< <<<

Elementssubmergedinwatercontainingchlorides

XD2orXS2f –

CEMI,IIA,IIB-S,SRPC

– – – C40/50,0.40,380

C32/40,0.50,340

C28/35,0.55,320 <<<

IIB-V,IIIA – – – C35/45,0.40,380

C28/35,0.50,340

C25/30,0.55,320 <<<

IIIB,IVB-V – – – C32/40,0.40,380

C25/30,0.50,340

C20/25,0.55,320 <<<

Elementssubjecttomoderatewatersaturationwithde-icingagentandfreezing

XD3f

XF2

IIB-V,IIIA – – – – – C35/45,0.40,380

C32/40,0.45,360

CEMI,IIA,IIB-S,SRPC

– – – – – SeeBS8500 C40/50,0.40,380

IIIB,IVB-V – – – – – C32/40,0.40,380

C32/400.45,360

Elementssubjecttowatersaturationwithde-icingagentandfreezing

XF4k IIB-V,IIIA – – – – – C40/50,0.45,380g

C40/50,0.45,360g

XF4(airentrained)

CEMI,IIA,IIB-S,SRPC

– – – – – SeeBS8500 C28/35,0.40,380g

IIB-V,IIIA – – – – – C28/35,0.40,380g,h

C28/350.45,360g,h

Elementsintidal,splashandsprayzones

XS3 –

CEMI,IIA,IIB-S,SRPC

– – – – – – SeeBS8500

IIB-V,IIIA – – – – – C35/45,0.40,380

C32/40,0.45,360

IIIB,IVB-V – – – – – C32/40,0.40,380

C28/35,0.45,360

Key

aThistablecomprisesaselectionofcommonexposureclasscombinations.Requirementsforothersetsofexposureclasses,e.g.XD2,XS2andXS3shouldbederivedfromBS8500–1:2006,AnnexA.

bSeeTable4.4(CEMIisPortlandcement,IIAtoIVBarecement/combinations.)

cForprestressedconcretetheminimumstrengthclassshouldbeC28/35.

dDcdevisanallowancefordeviations.

21

Durabilityandcover

for either at least a 50-year or 100-year intended working life and 20 mm maximum aggregate size

content (kg/m3), and equivalent designated concrete where applicable

At least 100-year working life

Nominal cover to reinforcementd

50 +Dcdev 15 +Dcdev 25 +Dcdev 30 +Dcdev 35 +Dcdev 40 +Dcdev 45 +Dcdev 50 +Dcdev 55 +Dcdev 60 +Dcdev 65 +Dcdev

<<<C20/25,0.70,240RC20/25

<<< <<< <<< <<< <<< <<< <<< <<< <<<

<<< –C25/30,0.65,260RC25/30

<<< <<< <<< <<< <<< <<< <<< <<<

<<< – –C40/50,0.45,340RC40/50

C35/45,0.50,320RC35/45

C30/37,0.55,300RC30/37

C28/35,0.60,280RC28/35

C25/30,0.65,260RC25/30

<<< <<< <<<

<<< – –C40/50,0.45,340RC40/50

C35/45,0.50,320RC35/45

C30/37,0.55,300RC30/37

C28/35,0.60,280RC28/35

<<< <<< <<< <<<

<<< – –

C40/50,0.45,340g

RC40/50 <<< <<< <<< <<< <<< <<< <<<

<<< – – – C35/45,0.50,320g,h

C30/37,0.55,300g,h

C28/35,0.60,280g,h

orPAV2

C25/300.60,280g,h,j

orPAV1<<< <<< <<<

<<< – – C45/55,

0.40,380C40/50,0.45,360

C35/45,0.50,340

C32/40,0.55,320

C28/35,0.60,300 <<< <<< <<<

<<< – – – – – SeeBS8500

C40/50,0.40,380

C35/45,0.45,360 <<< <<<

<<< – – – C35/45,0.40,380

C32/40,0.45,360

C28/35,0.50,340

C25/30,0.55,320 <<< <<< <<<

<<< – – – C35/45,0.45,360

C30/37,0.50,340

C28/35,0.55,320

C25/30,0.55,320 <<< <<< <<<

<<< – – – – – SeeBS8500 C40/50,0.40,380g <<< <<< <<<

<<< – – – – C35/45,0.45,360

C32/40,0.50,340

C28/35,0.55,320 <<< <<< <<<

<<< – – – – C32/40,0.45,360

C28/35,0.50,340

C25/30,0.55,320 <<< <<< <<<

<<< – – – – C28/35,0.45,360

C25/30,0.50,340

C20/25,0.55,320 <<< <<< <<<

C32/40,0.50,340

– – – – – SeeBS8500 C35/45,0.40,380

C32/40,0.45,360

C28/35,0.50,340

C25/30,0.55320

C35/45,0.45,360

– – – – – – – SeeBS8500 C40/50,0.40,380

C35/45,0.45,360

C32/40,0.50,340

– – – – – C32/40,0.40,380

C28/35,0.45,360

C25/30,0.50,340 <<< <<<

C40/50,0.45,340

– – – – – SeeBS8500 C40/50,0.40,380g

C40/50,0.45,360g

C40/50,0.45,340g

C40/50,0.45,340g

C28/35,0.45,360g – – – – – – – See

BS8500C28/35,0.40,380g

C28/35,0.45,360g

C28/35,0.50,340g,h – – – – – SeeBS8500 C28/35,

0.40,380g,hC28/35,0.45,360g,h

C28/35,0.50,340g,h

C28/35,0.55,320g,h

C40/50,0.40,380

– – – – – – – – SeeBS8500 C40/50,0.40,380

C28/35,0.50,340

– – – – – SeeBS8500 C35/45,0.40,380

C32/40,0.45,360

C28/35,0.50,340

C25/30,0.55,320

C25/30,0.50,340

– – – – – C32/40,0.40,380

C28/35,0.45,360

C25/30,0.50,340 <<< <<<

e Forsectionslessthan140mmthickrefertoBS8500.

f AlsoadequateforexposureclassXC3/4.

g Freeze/thawresistingaggregatesshouldbespecified.

h Airentrainedconcreteisrequired.

j Thisoptionmaynotbesuitableforareassubjecttosevereabrasion.

k Notrecommendedforpavementsandhardstandings–seeBS8500-1,A.4.3.

– Notrecommended

<<< Indicatesthatconcretequalityincelltotheleftshouldnotbereduced

22

Table 4.4Cement and combination typea

Broad designationb

Composition Cement/combination types (BS 8500)

CEM I Portlandcement CEMI

SRPC Sulfate-resistingPortlandcement SRPC

IIA Portlandcementwith6–20%flyash,groundgranulatedblastfurnaceslag,limestone,or6–10%silicafumec

CEMII/A-L,CEMII/A-LL,CIIA-L,CIIA-LL,CEMII/A-S,CIIA-S,CEMII/A-V,CIIA-V,CEMII/A–D

IIB-S Portlandcementwith21–35%groundgranulatedblastfurnaceslag

CEMII/B-S,CIIB-S

IIB-V Portlandcementwith21–35%flyash CEMII/B-V,CIIB-V

IIB+SR Portlandcementwith25–35%flyash CEMII/B-V+SR,CIIB-V+SR

IIIAd, e Portlandcementwith36–65%groundgranulatedblastfurnaceslag

CEMIII/A,CIIIA

IIIA+SRe Portlandcementwith36–65%groundgranulatedblastfurnaceslagwithadditionalrequirementsthatenhancesulfateresistance

CEMIII/A+SRf,CIII/A+SRf,CIIIA+SR

IIIBe, g Portlandcementwith66–80%groundgranulatedblastfurnaceslag

CEMIII/B,CIIIB

IIIB+SRe Portlandcementwith66–80%groundgranulatedblastfurnaceslagwithadditionalrequirementsthatenhancesulfateresistance

CEMIII/B+SRf,CIIIB+SRf

IVB-V Portlandcementwith36–55%flyash CEMIV/B(V),CIVB

Keya Thereareanumberofcementsandcombinationsnotlistedinthistablethatmaybespecifiedfor

certainspecialistapplications.SeeBRESpecialDigest[19]forthesulfate-resistingcharacteristicsofothercementsandcombinations.

b Theuseofthesebroaddesignationsissufficientformostapplications.Whereamorelimitedrangeofcementorcombinationstypesisrequired,selectfromthenotationsgiveninBS8500–2:2006,Table1.

c WhenIIAorIIA–Disspecified,CEMIandsilicafumemaybecombinedintheconcretemixerusingthek-valueconcept;seeBSEN206–1:2000,Cl.5.2.5.2.3.

d WhereIIIAisspecified,IIIA+SRmaybeused.

e Inclusiveoflowearlystrengthoption(seeBSEN197–4andthe‘L’classesinBS8500–2:2006,TableA.1).

f ‘+SR’indicatesadditionalrestrictionsrelatedtosulfateresistance.SeeBS8500–2:2006,Table1,footnoteD.

g WhereIIIBisspecified,IIIB+SRmaybeused.

Chemical attack

Whereplainorreinforcedconcreteisincontactwiththeground,furtherchecksarerequiredtoachievedurability.Anaggressivechemicalenvironmentforconcreteclass(ACECclass)shouldbeassessedforthesite.BRE Special Digest 1[19]givesguidanceontheassessmentoftheACECclassandthis isnormallycarriedoutaspartoftheinterpretivereportingforaground investigation. Knowing theACEC class, a design chemical class (DC class) can beobtainedfromTable4.5.Ingeneral,fullyburiedconcreteintheUKneednotbedesignedtobefreeze-thawresisting.

For designated concretes, an appropriate foundation concrete (FND designation) can beselectedusingTable4.6.AnFNDconcretehasthestrengthclassofC25/30.Whereahigherstrengthisrequired,eitherforitsstrengthorwherethefoundationisclassifiedasXD2orXD3, a designed concrete should be specified. For designed concretes, the concreteproducershouldbeadvisedoftheDC–class.

BS 8500 table A.6

4.4

23

Durabilityandcover

4.5 Dcdev and other allowances

Tocalculatethenominalcover,cnom,anadditiontotheminimumcovershallbemadeindesignto allow for the deviation (Dcdev). In the UK the recommended value is 10mm. In certainsituationstheaccepteddeviationandhenceallowanceDcdevmaybereduced:

■ Wherefabricationissubjectedtoaqualityassurancesystem,inwhichthemonitoringincludesmeasurementsoftheconcretecover,theallowanceindesignfordeviationDcdevmaybereduced:10mm≥Dcdev≥5mm

■ Whereitcanbeassuredthataveryaccuratemeasurementdeviceisusedformonitoring,andnon-conformingmembersarerejected(e.g.precastelements),theallowanceindesignfordeviationDcdevmaybereduced:10mm≥Dcdev≥0mm

DcdevisrecognisedinBS8500asDc.

Theminimumcoverforconcretecastonpreparedground(includingblinding)is 40mm andthatforconcretecastdirectlyagainstsoilis 65mm.

Forunevensurfaces(e.g.exposedaggregate)theminimumcovershouldbeincreasedbyatleast5mm.

Table 4.5Selection of the DC–class and the number of additional protection measures (APMs) where the hydrostatic head of groundwater is not more than five times the section width a, b, c, d, e

ACEC-class (aggressive chemical environment for concrete class)

Intended working life

At least 50 years At least 100 years

AC–1s, AC–1 DC–1 DC–1

AC–2s, AC–Z DC–2 DC–2

AC–2z DC–2z DC–2z

AC–3s DC–3 DC–3

AC–3z DC–3z DC–3z

AC–3 DC–3 RefertoBS8500

AC–4s DC–4 DC–4

AC–4z DC–4z DC–4z

AC–4 DC–4 RefertoBS8500

AC–4ms DC–4m DC4m

AC–4m DC–4m RefertoBS8500

AC–5 DC–4f DC–4f

AC–5z DC–4zf DC–4z/1f

AC–5m DC–4mf DC–4mf

Keya Wherethehydrostaticheadofgroundwaterisgreaterthanfivetimesthesectionwidth,refertoBS

8500.

b ForguidanceonprecastproductsseeSpecialDigest1[19].

c ForstructuralperformanceoutsidethesevaluesrefertoBS8500.

d Forsectionwidths<140mmrefertoBS8500.

e Whereanysurfaceattackisnotacceptablee.g.withfrictionpiles,refertoBS8500.

f ThisshouldincludeAPM3(surfaceprotection),wherepracticable,asoneoftheAPMs;refertoBS8500.

BS EN 1992-1-1 4.4.1.3(1)&(3) & NA

BS EN 1992-1-1 4.4.1.3(4) & NA

BS EN 1992-1-1 4.4.1.2(11)

BS 8500 table A.9

24

BS EN 1992-2 4.4.1.2(114)

BS 8500 table A.1

BS EN 1992-2 4.4.1.2(115)

Table 4.6Guidance on selecting designated concrete for reinforced concrete foundations

DC-Class Appropriate designated concrete

DC–1 RC 25/30

DC–2 FND2

DC–2z FND2z

DC–3 FND3

DC–3z FND3z

DC–4 FND4

DC–4z FND4z

DC–4m FND4m

NoteStrength class for all FND concrete is C25/30.

Bare concrete decks of road bridges, without waterproofing or surfacing, should be classified as Abrasion Class XM2.

Where a concrete surface is subject to abrasion caused by ice or solid transportation in running water, the cover should be increased by a minimum of 10 mm.

25

Structuralanalysis

Structural analysis

General

Thepurposeofstructuralanalysis istoestablishthedistributionofeither internal forcesandmomentsorstresses,strainsanddisplacementsoverthewholeorpartofastructure.Additionallocalanalysisshallbecarriedoutwherenecessary.

Whendesigningabridgedeckslabofboxbeamorbeamandslabconstruction,itisnecessarytoconsider,inadditiontooverallglobaleffects,thelocaleffectsinducedinthetopslabbywheelloads.CurrentpracticeistouseelasticanalysisandoftenassumefullfixityattheslabandwebjunctionsanduseeitherPucher’sinfluencesurfaces,Westergaard’sequations,orFEanalysis.

Idealisation of the structure

Definitions

Forbridgestructuresthefollowingcanbeapplied:

■ Abeamisamemberforwhichthespanisnotlessthanthreetimesitsdepth.Ifnot,itisadeepbeam.

■ Aslabisamemberforwhichtheminimumpaneldimensionisnotlessthanfivetimestheoverallthickness.

■ Aone-wayspanningslabhaseithertwoapproximatelyparallelunsupportededgesor,whensupportedonfouredges,theratioofthelongertoshorterspanexceeds2.0.

■ Acolumnisamemberforwhichthesectiondepthdoesnotexceedfourtimesitswidthandtheheightisatleastthreetimesthesectiondepth.Ifnot,itisawall.

Effective flange width

Theeffectivewidthofaflange,beff,shouldbebasedonthedistance,l0,betweenpointsofzeromomentsasshowninFigure5.1anddefinedinFigure5.2.

beff=bw+beff,1+beff,2

where beff,1 = (0.2b1+0.1l0)but≤0.2l0and≤b1 beff,2 = tobecalculatedinasimilarmannertobeff,1butb2shouldbesubstituted forb1intheabove

l1 l2 l3

l0=0.85l1 l0=0.15(l1+l2) l0=0.7l2 l0=0.15l2+l3

Figure 5.1Elevation showing definition of l0 for calculation of flange width

BS EN 1992-1-15.1.1(1)

BS EN 1992-1-1 5.3.1

BS EN 1992-1-1 5.3.2.1(2)&(3)

BS EN 1992-1-1fig. 5.2

5

5.1

5.2

5.2.1

5.2.2

26

Effective span

Theeffectivespan,leff,ofamembershouldbecalculatedasfollows:leff=ln+a1+a2

where ln=cleardistancebetweenthefacesofthesupports;valuesfora1anda2,ateachendof

thespan,maybedeterminedfromtheappropriateaivaluesinFigure5.3wheretisthewidthofthesupportingelementasshown.

beff

beff,1 beff,2

bw

bw

b1 b1 b2 b2

b

Figure 5.2Section showing effective flange width parameters

h

ln

ai=MIN(ah;at)

a) Non-continuous members b) Continuous members

ai=MIN(ah;at)leff

t

t

t

t

h

ln

ln

ai=MIN(ah;at)

c) Supports considered fully restrained d) Bearing provided

leff

ai=MIN(ah;at)

e) Cantilever

leff

leff

leff

ai ln

cL

ln

h

h

Figure 5.3Effective span, leff, for different support conditions

BS EN 1992-1-1fig. 5.3

BS EN 1992-1-1fig. 5.4

BS EN 1992-1-1 5.3.2.2(1)

5.2.3

27

Structuralanalysis

Methods of analysis

Ultimate limit states (ULS)

Thetypeofanalysisshouldbeappropriatetotheproblembeingconsidered.Thefollowingarecommonlyused:linearelasticanalysis,linearelasticanalysiswithlimitedredistribution,andplasticanalysis.

Fordeterminationoftheactioneffects,linearelasticanalysismaybecarriedoutassuming:

■ Uncrackedcross-sections.■ Linearstress–strainrelationships.■ Theuseofmeanvaluesofelasticmodulus.

Ifa linearelasticanalysiswith limitedredistribution isundertaken,shearsandreactionsused in the design should be taken as those either prior to redistribution or afterredistribution,whicheverisgreater.

Incontinuousbeamsorslabswhich:

■ Arepredominantlysubjecttoflexure■ Havetheratiooflengthsofadjacentspansintherangeof0.5to2.0

redistributionofbendingmomentmaybecarriedoutwithoutexplicitcheckontherotationcapacityprovidedthat:

d≥ 0.44 + 1.25(0.6+0.0014/ecu2) xu/d forfck≤50MPad≥ 0.54 + 1.25(0.6+0.0014/ecu2) xu/d forfck>50MPad≥ 0.85whereClassBandClassCreinforcementisused

where d = theratiooftheredistributedmomenttothemomentinthelinearelasticanalysis xu= thedepthoftheneutralaxisattheultimatelimitstateafterredistribution d = theeffectivedepthofthesection

Redistributionshouldnotbecarriedoutincircumstanceswheretherotationcapacitycannotbedefinedwithconfidence(e.g.incurvedandorskewedbridges).

Itisrecommendedthatmomentredistributionisnotusedforsectionsdeeperthan1.2munlessarigorousanalysisofrotationcapacityisundertaken.

Thefollowingrulesmaybeusedforsolidconcreteslabswithfck≤50MPa.

d≥ 0.4 + 1.0 xu/d≥0.7wherethereinforcementisClassBorClassC

NoredistributionisallowedforClassAreinforcement.

Whereused,plasticanalysisshouldbebasedeitheronstatic(lowerbound)orkinematic(upperbound) methods.The ductility of the critical sections should be sufficient for the envisagedmechanism to be formed.The required ductility may be deemed to be satisfied if all of thefollowingarefulfilled:

■ xu/d≤0.15forfck≤50MPa■ xu/d≤0.10forfck≥50MPa■ ReinforcementiseitherClassBorC;and■ Ratioofthemomentsatinternalsupportstothemomentsinthespanisbetween0.5and2.0.

Forsolidslabsxu/d≤0.25maybeusedwhenfck≤50MPa.

BS EN 1992-1-1 5.1.1(6)

BS EN 1992-1-1 5.4(2)

BS EN 1992-2 5.5(104) & NA

PD 6687-26.4

BS EN 1992-1-15.6.1(3) & (2)

BS EN 1992-25.6.2(102)

BS EN 1992-2 5.5(104)

PD 6687-2 6.6

BS EN 1992-2 5.5 (105)

5.3

5.3.1

28

Non-linearanalysisshouldbeundertakenusingmodel factorsandmaterialmodels,whichgiveresultsthaterronthesafeside.Typically,thismaybeachievedbyusingdesignmaterialproperties and applying design actions. However, in some situations, underestimatingstiffnessthroughtheuseofdesignpropertiescanleadtounsaferesults.Suchsituationscaninclude cases where indirect actions such as imposed deformations are significant, caseswhere the failure load is associated with a local brittle failure mode, and cases where theeffectoftensionstiffeningisunfavourable.Insuchsituations,sensitivityanalysesshouldbeundertaken to investigate the effect of variations in material properties, including spatialvariations,toprovideconfidencethattheresultsoftheanalysisdoerronthesafeside.

Fornon-linearanalysisthatconsidersonlydirectandflexuraleffects,referencemaybemadetoBSEN1992-2,Cl.5.8.6.Suchanalysisshouldaccountfortheeffectsoflong-termloading.EffectsnotconsidereddirectlyintheanalysisshouldbeconsideredseparatelyinaccordancewithSections6to11.

Non-linearanalysisthatdeterminesshearandtorsionalstrengthdirectlyhasnotyetreachedastagewhereitcanbefullycodified.Particularanalysesmaybeusedwhentheyhavebeenshownbycomparisonwithteststogivereliableresults,withtheagreementoftheNationalAuthority.

Serviceability limit states (SLS)

Linearelasticanalysismaybecarriedoutassuming:

■ Uncrackedcross-sections.■ Linearstress–strainrelationships.■ Theuseofmeanvaluesofelasticmodulus.

The moments derived from elastic analysis should not be redistributed but a gradualevolutionofcrackingshouldbeconsidered,whichrequiresanon-linearanalysisallowingfortheeffectofcrackingandtensionstiffening.Un-crackedglobalanalysisinaccordancewithBS EN 1992-1-1 Cl. 5.4 (2) may always be used as a conservative alternative to suchconsiderations.

General note

Regardlessofthemethodofanalysisused,thefollowingapply.

■ Whereabeamorslabismonolithicwithitssupports,thecriticaldesignmomentatthesupportmaybetakenasthatatthefaceofthesupport.Thedesignmomentandreactiontransferredtothesupportingelement(e.g.column,wall,etc.)shouldbegenerallytakenasthegreateroftheelasticorredistributedvalues.Themomentatthefaceofthesupportshouldnotbetakenaslessthan 65% ofthefullfixedendmoment.

■ Whereabeamorslabiscontinuousoverasupportwhichisconsideredtoprovidenorestrainttorotation(e.g.overwalls)andtheanalysisassumespointsupport,thedesignsupportmomentcalculatedonthebasisofaspanequaltothecentre-to-centredistancebetweensupports,maybereducedbyanamountDMEdasfollows:

DMEd=FEd,supt/8

where FEd,sup=designsupportreaction t =breadthofbearing

BS EN 1992-1-1 5.4

BS EN 1992-2 5.7 (105) & NA

5.3.2

5.3.3

BS EN 1992-1-1 5.3.2.2(3)

BS EN 1992-1-1 5.3.2.2(104)

29

Structuralanalysis

Loading

Combinations of actions

Thefollowingcombinationsofactionsshouldbeusedwhereappropriate.

Ultimate Limit State Persistent or transient design situations:gGGk + gp P + gQ,1 Qk,1 + S gQ,ic0,i Qk,i i >1

Accidental design situations:Gk + P + Ad + c1,1Qk,1 + S c2,i Qk,i i >1

Note:c2,1maybesubstitutedforc1,1dependingontheaccidentaldesignsituation.

Serviceability Limit StateCharacteristic combination of actions:

Gk + P + Qk,1 + S c0,i Qk,i i >1

Tobeusedforstresslimitationcheckforconcreteandsteel.

Frequent combination of actions:Gk + P + c1,1 Qk,1+ S c2,i

Qk,i i >1

Tobeusedfordecompressioncheckorcrackwidthcheckforprestressedconcretewithbondedtendons.

Quasi-permanent combination of actions:Gk + P + S c2,i

Qk,i i >1

Tobeusedforcrackwidthcheckforreinforcedconcreteandprestressedconcretewithoutbondedtendonsanddeformationcheck.

TermsCombinationvalueofavariableaction:c0QFrequentvalueofavariableaction:c1QQuasi-permanentvalueofavariableaction:c2Q

Load casesInconsideringthecombinationsofactions(seeSection6andAnnexA2ofBSEN1990)therelevantloadcasesshallbeconsideredtoenablethecriticaldesignconditionstobeestablishedatallsections,withinthestructureorpartofthestructureconsidered.

Geometrical imperfections

General

Theunfavourableeffectsofpossibledeviationsinthegeometryofthestructureandthepositionofloadsshallbetakenintoaccountintheanalysisofmembersandstructures.

Imperfections shall be taken into account in ultimate limit states in persistent and accidentaldesignsituations.

BS EN 1992-1-1 5.2(1)

BS EN 1990 6.4.3

BS EN 1992-2 5.1.3

BS EN 1992-1-1 5.2(2)

5.4

5.4.1

5.5

5.5.1

30

Imperfections and global analysis of structures

Imperfectionsmayberepresentedbyaninclinationyigivenby:

y1=(1/200) ah

where ah = 2/l0.5≤1.0 l = lengthorheightinmetres

Forisolatedmemberstheeffectoftheimperfectionsmayberepresentedasaneccentricityorbyatransverseforce.

Theeccentricity,ei,givenbyei=yil0/2wherel0istheeffectivelength

Thetransverseforceisappliedinthepositionthatgivesmaximummoment.

Hi=y1Nk

where Hi= actionappliedatthatlevel N = axialload k = 1.0forunbracedmembers(seeFigure5.4a) = 2.0forbracedmembers(seeFigure5.4b)

Forarchbridges,theshapeofimperfectionsinthehorizontalandverticalplanesshouldbebasedontheshapeofthefirsthorizontalandverticalbucklingmodeshaperespectively.Eachmodeshapemaybeidealisedbyasinusoidalprofile.Theamplitudeshouldbetakenasa=y1l/2,wherelisthehalfwavelength.

Thedispositionofimperfectionsusedinanalysisshouldreflectthebehaviourandfunctionofthestructureanditselements.Theshapeofimperfectionshouldbebasedontheanticipatedmode of buckling of the member. For example, in the case of bridge piers, an overall leanimperfectionshouldbeusedwherebucklingwillbeinaswaymode(“unbraced”conditions),whilealocaleccentricitywithinthemembershouldbeusedwherebothendsofthememberareheldinposition(“braced”conditions).

In using Expression (5.2) of Part 1-1 the eccentricity, ei, derived should be taken as theamplitude of imperfection over the half wavelength of buckling; Figure 5.5 shows theimperfectionsuitableforapierrigidlybuiltinformomentateachend.Aleanimperfectionshould however be considered in the design of the positional restraints for braced members.FurtherguidanceandbackgroundaregiveninHendyandSmith.[20]

b) Braced isolated membersa) Unbraced isolated members

ei ei

N NN N

Hi

l = l0/2 Hi l = l0

Figure 5.4Examples of the effects of geometric imperfections

BS EN 1992-2 5.2(105)

BS EN 1992-1-1 5.2(7)

BS EN 1992-1-1 Exp. (5.2)

BS EN 1992-25.2(106)

PD 6687-2 6.2

BS EN 1992-1-1fig. 5.1a

5.5.2

31

Structuralanalysis

5.6

5.6.1

PD 6687-2fig. 1

BS EN 1992-1-1 5.8.1

BS EN 1992-1-1 5.8.3.2(3)

ei eei

l0 yI

l0 = l/2e = 2ei= yI/2

b) Angular imperfectiona) Sinusoidal imperfection

Figure 5.5Imperfections for pier built in at both ends

Design moments in columns

Definitions

Bracing members

Bracing members are members that contribute to the overall stability of the structure,whereasbracedmembersdonot contributetotheoverallstabilityofthestructure.

Effective length l0Forbracedmembers:

l0=0.5l[(1+k1/(0.45+k1))(1+k2/(0.45+k2))]0.5

Forunbracedmembersl0isthelargerofeither:

l0=l[1+10k1k2/(k1+k2)]0.5orl0=l[1+k1/(1.0+k1)][1+k2/(1.0+k2)]

where l = clearheightofthecolumnbetweentheendrestraints k1,k2 = relativeflexibilitiesofrotationalrestraintsatends1and2respectively

ExamplesofdifferentbucklingmodesandcorrespondingeffectivelengthfactorsforisolatedmembersareshowninFigure5.6.PD6687-2[3]notesthattheeffectivelengthsshowndonotcovertypicalbridgecasesandprovidesadditionalexamples,whicharegiveninTable5.1.

BS EN 1992-1-1 5.8.3.2(2)PD 6687-2, 6.71

32

y

y

y

l

M

a) l0 = l b) l0 = 2l c) l0 = 0.7l d) l0 = l/2 e) l0 = l f) l/2 < l0 < l g) l0 > 2l

Figure 5.6Examples of different buckling modes and corresponding effective lengths for isolated members

Slenderness ratio, lSlendernessratiol=l0/i

where i=theradiusofgyrationoftheuncrackedconcretesection

Ignoringreinforcement:

l =3.46l0 /hforrectangularsections =4.0l0 /dforcircularsections

where h=thedepthinthedirectionunderconsideration d=thediameter

Limiting slenderness ratio llimThe limiting slenderness ratio, llim, above which second order effects should be considered,isgivenby

llim=20ABC/n0.5

where A = 1/(1+0.2hef)(ifhefisnotknownAmaybetakenas0.7) where hef = effectivecreepfactor=h(∞,t0)M0Eqp/M0Ed

h(∞,t0) = finalcreepcoefficient(seeSection3.1.2)

M0Eqp = thefirstorderbendingmomentinthequasi-permanentloadcombination(SLS)

M0Ed = thefirstorderbendingmomentindesignloadcombination(ULS)

B = (1+2w)0.5(ifwisnotknownBmaybetakenas1.1) where w = mechanicalreinforcementratio =(As/Ac)(fyd/fcd) As =totalareaoflongitudinalreinforcement

C = 1.7–rm(Ifrmisnotknown,Cmaybetakenas0.7 where rm = M01/M02,whereM01andM02arethefirstorderendmomentsatULSwith

M02numericallylargerthanM01.IfM01andM02givetensiononthesamesidethenrmispositive(andC<1.7),seeFigure5.7

rm = 1.0forunbracedmembersandbracedmembersinwhichthefirstordermomentsarecausedlargelybyimperfectionsortransverseloading

BS EN 1992-1-1 5.8.3.2(1)

BS EN 1992-1-1fig. 5.7

BS EN 1992-1-1 5.8.3.1(1) & NA

BS EN 1992-1-1 5.8.4

BS EN 1992-1-1 3.1.4(4), 3.1.4(5)

33

Structuralanalysis

Table 5.1Effective height, l0 for columns

Case Idealized column and buckling mode Restraints Effective

height l0Location Position Rotation

1

l

Top Full Fulla 0.70l

Bottom Full Fulla

2

l

Top Full None 0.85l

Bottom Full Fulla

3

l

Top Full None 1.0l

Bottom Full None

4

Elastometricbearingb

l

Top Nonec Nonec 1.3l

Bottom Full Fulla

5

l

Top None None 1.4l

Bottom Full Fulla

6

l

Top None Fulla 1.5l

Bottom Full Fulla

7

orl l

Top None None 2.3l

Bottom Full Fulld

NotesTheheightofthebearingsisnegligiblecomparedwiththatofthecolumn.

Keya Rotationalrestraintisatleast4(EI)/l,where(EI)istheflexuralrigidityofthecolumnb Mayalsobeusedwithrollerbearingsprovidedthattherollersareheldinplacebyaneffectivemeans,suchasracksc Lateralandrotationalrigidityofelastomericbearingsarenegligibled Rotationalrestraintisatleast8(EI)/l,where(EI)istheflexuralrigidityofthecolumn

PD 6687-2table 1

34

n = NEd/(Ac fcd) where NEd=designvalueofaxialforce

Note:hefmaybetakenas0ifallthefollowingconditionsaremet:■h(∞,t0) ≤2.0;■l ≤75;and■M0Ed /NEd ≥h,thedepthofthecross-sectionintherelevantdirection.

Figure 5.7Values of C

for different values of rm

a) C = 0.7, rm = 1.0 b) C = 1.7, rm = 0 c) C = 2.7, rm = – 1.0

M01=M02

M02 M02 M02

M01=–M020

Design bending moments

Non-slender columns

Whenl≤llimi.e.whennon-slender,thedesignbendingmomentinacolumnis

MEd=M02

where MEd = designmoment

M02,M01 = firstorderendmomentsatULSincludingallowancesforimperfections.M02isnumericallylargerthanM01.Attentionshouldbepaidtothesignofthebendingmoments.Iftheygivetensiononthesameside,M01andM02shouldhavethesamesign

M02 = M+eiNEd

where M = largestmomentfromfirstorderanalysis(elasticmomentswithout

redistribution)andignoringeffectofimperfections NEd= designvalueofaxialforce ei = eccentricityduetoimperfections=yil0/2

Forcolumnsinbracedsystemsei=l0/400(i.e.yi=l/200formostbracedcolumns).Thedesigneccentricityshouldbeatleast(h/30)butnotlessthan20mm.

where y = inclinationusedtorepresentimperfections l0 = effectivelengthofcolumn h = depthofthesectionintherelevantdirection

Slender columns (nominal curvature method)Thismethodisprimarilysuitableforisolatedmemberswithconstantnormalforceandadefinedeffectivelength l0.Themethodgivesanominalsecondordermomentbasedonadeflection,whichinturnisbasedontheeffectivelengthandanestimatedmaximumcurvature. Other methodsareavailableinBSEN1992-1-1.

Thedesignmomentis:MEd=M0Ed+M2

where

BS EN 1992-1-1 5.8.3.1(1) & NA

BS EN 1992-1-15.8.8.1(1)

BS EN 1992-1-1 5.8.3.1(1)

BS EN 1992-1-1 5.2.7

BS EN 1992-1-1 6.1(4)

BS EN 1992-1-1 5.8.3.2(3)

BS EN 1992-1-15.8.8.2(1)

5.6.2

BS EN 1992-1-1 5.8.4(4)

35

Structuralanalysis

M0Ed = firstordermoment,includingtheeffectofimperfections(andmaybetakenasM0E) M2 = nominalsecondordermoment

ThemaximumvalueofMEdisgivenbythedistributionsofM0EdandM2;thelattermaybetakenasparabolicorsinusoidalovertheeffectivelength.

Forbracedstructures (seeFigure5.8):

MEd=MAX{M0e+M2;M02;M01+0.5M2}

Forunbracedstructures:

MEd=M02+M2

Formomentswithoutloadsappliedbetweentheirends,differingfirstorderendmomentsM01

andM02(seeabove)maybereplacedbyanequivalentfirstorderendmomentM0e:M0e=0.6M02+0.4M01≥0.4M02

ThenominalsecondordermomentM2is

M2=NEde2

where NEd = designvalueofaxialforce e2 = deflection = (1/r)lo

2/c 1/r = curvature=KrKh(fyd/(Es0.45d))

Kr = (nu–n)/(nu–nbal)≤1.0

Note:Krmaybederivedfromcolumncharts.

nu = 1+w w = mechanicalreinforcementratio =(As /Ac)( fyd/fcd)asinSection5.6.1above n = NEd/Ac fcdasdefinedinSection5.6.1above nbal = valueofnatmaximummomentofresistanceandmaybetakenas0.4 Kh =1+bhef≥1.0

b = 0.35+(fck/200)–(l/150)

l = slendernessratiol0 /i

PD 6687-12.11

BS EN 1992-1-15.8.8.2(2)

BS EN 1992-1-15.8.8.2(3)

BS EN 1992-1-15.8.8.2(4)

BS EN 1992-1-1 5.8.8.3

Figure 5.8Moments in

braced columns

+ =

a) First order moments for non-slender columns

b) Additional second order moments for slender columns

c) Total moment diagram for slender columns

M2=NEde2

M02

M02M e1NEd

M0eM0e+M2

M01 0.5M2 M01+0.5M2

36

i = radiusofgyrationoftheuncrackedconcretesection hef = effectivecreepcoefficientasdefinedinSection5.6.1 l0 = effectivelengthofcolumn Es = 200GPa c = factordependingonthecurvaturedistribution(seebelow)

Forconstantcrosssection,c=10(≈p2)isnormallyused.Ifthefirstordermomentisconstant,alowervalueshouldbeconsidered(8isalowerlimit,correspondingtoconstanttotalmoment).

Biaxial bending

Separatedesignineachprincipaldirection,disregardingbiaxialbending,maybeundertakenasafirststep.Nofurthercheckisnecessaryif:

0.5 ≤ ly/lz≤2.0and,forrectangularsections,and0.2 ≥ (ey/heq)/(ez/beq)≥5.0

where

ly,lz = slendernessratiosl0/iwithrespecttothey-andz-axes

ey = MEdy/NEd

heq = 3.46iz (=hforrectangularsections)

ez = MEdz/NEd

beq = 3.46iy (=bforrectangularsections)

where NEd = designvalueofaxialforce MEdy,MEdz= designmomentintherespectivedirection.(Momentsdueto

imperfectionsneedbeincludedonlyinthedirectionwheretheyhavethemostunfavourableeffect.)

Note:forsquarecolumns(ey/heq)/(ez/beq)=MEdy/MEdz

Ifthisconditionisnotsatisfied,andintheabsenceofanaccuratecross-sectiondesignforbiaxialbending,thefollowingsimplifiedcriterionmaybeused:

(MEdz/MRdz)a+(MEdy/MRdy)a≤1.0

where MRdy,MRdz = designmomentaroundtherespectiveaxisincludingsecondordermoment inthedirectionwhereitwillgivethemostunfavourableeffect. a = anexponent:forcircularorellipticalsections,a=2.0,forrectangular

sections,interpolatebetween = 1.0forNEd/NRd=0.1 = 1.5forNEd/NRd=0.7 = 2.0forNEd/NRd=1.0

Corbels

Definition

Corbelsareshortcantileversprojectingfromcolumnsorwallswiththeratioofshearspan(i.e.thedistancebetweenthefaceoftheappliedloadandthefaceofthesupport)tothedepthofthecorbelintherange0.5to2.0.

5.6.3

5.7

5.7.1

BS EN 1992-1-15.8.9(2)

BS EN 1992-1-15.8.9(3)

BS EN 1992-1-15.8.9(2)

BS EN 1992-1-15.8.9(4)

BS EN 1992-1-1 3.2.7(4)

BS EN 1992-1-1 5.8.8.2(4)

37

StructuralanalysisStructuralanalysis

Analysis

Corbels(ac<z0)maybedesignedusingstrutandtiemodels(seeFigure5.9)orasshortbeams

designedforbendingandshear.

Theinclinationofthestrutislimitedby1.0≤tany≤2.5.

Ifac≤0.5hcclosedhorizontalorinclinedlinkswithAs,lnk≥0.5As,mainshouldbeprovidedinadditiontothemaintensionreinforcement(seeFigure5.10a).

Ifac>0.5hcandFEd>VRd,c(seeSection7.2.1)closedverticallinkswithAs,lnk≥0.5FEd/fydshouldbeprovidedinadditiontothemaintensionreinforcement(seeFigure5.10b).

Themaintensionreinforcementshouldbeanchoredatbothends.Itshouldbeanchoredinthesupportingelementonthefarfaceandtheanchoragelengthshouldbemeasuredfromthe location of the vertical reinforcement in the near face.The reinforcement should beanchoredinthecorbelandtheanchoragelengthshouldbemeasuredfromtheinnerfaceoftheloadingplate.

If there are special requirements for crack limitation, inclined stirrups at the re-entrantopeningcanbeeffective.

ThecheckofthecompressionstrutcaneffectivelybemadebylimitingtheshearstresssuchthatFEd≤0.5bwdv'fcd

where v' = 1–(fck/250)

fcd = accfck/gC

acc= 0.85

FEd

Ftd

FEd

aH

HEd

z0hc

d

y

sRd,max

ac

Fwd

Key

Fwd = designvalueofforce

instirrup

= tie

= compressionstrut

Figure 5.9Corbel strut-and-tie model

PD 6687 B3

BS EN 1992-1-16.5.2(2)

PD 6687fig. B4

5.7.2

38

5.8

As,mainAnchorage devices

or loops

Links

a) Reinforcement for ac ≤ 0.5hc b) Reinforcement for ac > 0.5hc

As,lnk ≥ k1As,main

SAs,lnk ≥ As,main

Figure 5.10Corbel detailing

Lateral instability of slender beams

Lateralinstabilityofslenderbeamsshallbetakenintoaccountwherenecessary,e.g.forprecastbeamsduringtransportanderection,forbeamswithoutsufficientlateralbracinginthefinishedstructureetc.Geometricimperfectionsshallbetakenintoaccount.Alateraldeflectionofl/300should be assumed as a geometric imperfection in the verification of beams in unbracedconditions, with l = total length of beam. In finished structures, bracing from connectedmembersmaybetakenintoaccount

Second order effects in connection with lateral instability may be ignored if the followingconditionsarefulfilled:

persistentsituations:l0t/b≤50/(h/b)1/3andh/b≤2.5transientsituations:l0t/b≤70/(h/b)1/3andh/b≤3.5

where l0t= distancebetweentorsionalrestraints h = totaldepthofbeamincentralpartofl0t b = widthofcompressionflange

Torsionassociatedwithlateralinstabilityshouldbetakenintoaccountinthedesignofsupportingstructures.

PD 6687fig. B5

BS EN 1992-1-15.9

39

Bendingandaxialforce

Bending and axial force

Assumptions

Indeterminingtheresistanceofsections,thefollowingassumptionsaremade.

■ Planesectionsremainplane.■ Straininthebondedreinforcement,whetherintensionorcompression,isthesameasthat

inthesurroundingconcrete.■ Tensilestrengthoftheconcreteisignored.■ RectangularstressdistributioninthesectionisasshowninFigure6.1.Otherstress–strain

relationshipsaregiveninBSEN1992-1-1Cl.3.1.7.■ StressesinreinforcementarederivedfromFigure6.2.Theinclinedbranchofthedesignline

maybeusedwhenstrainlimitsarechecked.■ Forsectionsnotfullyincompression,thecompressivestraininconcreteshouldbelimited

toecu2(seeFigure6.3).■ Forsectionsinpureaxialcompression,thecompressivestraininconcreteshouldbelimited

toec2(seeFigure6.3).■ Forsituationsintermediatebetweenthesetwoconditions,thestrainprofileisdefinedby

assumingthatthestrainisec2athalfthedepthofthesection(seeFigure6.3).

ExpressionsderivedfromFigures6.1to6.3areprovidedinSection17.

Table 6.1

Values for n and l when fck > 50

fck ecu3a nb lc

55 0.00313 0.98 0.79

60 0.00288 0.95 0.78

70 0.00266 0.90 0.75

Key

a ecu3(%)=2.6+35[(90–fck)/100]4

b n =1–(fck–50)/200

c l =0.8–(fck–50)/400

BS EN 1992-1-1 fig. 6.1

BS EN 1992-1-1 3.1.7(3), fig. 3.5

BS EN 1992-1-16.1(2)

BS EN 1992-1-1 fig. 3.5

6

6.1

ecu3

fyd

Fs

Fc

nfcd

Ac x l x

d

As

es

z

Forfck ≤ 50MPa,ecu3=0.0035,n =1andl=0.8.ForotherconcreteclassesseeTable6.1

x = neutralaxisdepth Fc(Fs) = forceinconcrete(steel)

ecu3 = ultimatecompressivestraininconcrete d = effectivedepth

es = tensilestraininreinforcement z = leverarm

Figure 6.1Rectangular stress distribution

40

euk

Idealised

Design

Strain, e

Stre

ss, s

eud

fyk

kfyk

fyd=fyk/gS

kfyk/gS

kfyk

fyd/Es

BS EN 1992-1-1fig. 3.8

Where

k = (ft/fy)k(SeeTable3.3)

fyk = characteristicyieldstrengthofreinforcement

fyd = designyieldstrengthofreinforcement

ft = tensilestrengthofreinforcement

gS = partialfactorforreinforcingsteel= 1.15eud= designstrainlimitforreinforcing

steel= 0.9eukeuk = characteristicstrainofreinforcementat

maximumforce(seeTable3.3)

Figure 6.2Idealised and design stress–strain diagrams for reinforcing steel (for tension and compression)

ep(0)

eudec2 ecu2

(ecu3)(ec3)

es,ep

Dep

ec

hd

ey

As2

Ap

As1

0

a) Section b) Strain

(1–ec2/ecu2)hor(1–ec3/ecu3)h

Concretecompressionstrainlimit

ConcretepurecompressionstrainlimitReinforcingsteel

tensionstrainlimit

Where

As1 = areaofreinforcingsteelinlayer1

Ap = areaofprestressingsteel

d = effectivedepth

h = overalldepthofsection

ec = compressivestraininconcrete

es = straininreinforcingsteel

ep(0) = initialstraininprestressingsteel

Dep = changeinstraininprestressingsteel

eud = designstrainlimitforreinforcingsteelintension

ec3 = compressivestrainlimitinconcreteforconcreteinpureaxialcompressionassumingbilinearstress–strainrelationship(seeFigure3.4ofBSEN1992-1-1).

ec3(‰) = 1.75forfck≤50MPa

ec3(‰) = 1.75+0.55[(fck–50)/40]forfck>50MPa

ecu2 = (=ecu3)compressivestrainlimitinconcretenotfullyinpureaxialcompression

ecu3(‰)=3.5forfck≤50MPa.

ecu3(‰) = 2.6+0.35[(90–fck)/100]4forfck>50MPa

ey = reinforcementyieldstrain

Figure 6.3Possible strain distributions in the ultimate limit state

BS EN 1992-1-1fig. 6.1

41

Shear

Shear

General

Definitions

Fortheverificationoftheshearresistancethefollowingsymbolsaredefined:VRd,c = designshearresistanceofamemberwithoutshearreinforcementVRd,s = designvalueoftheshearforcethatcanbesustainedbytheyieldingshear

reinforcementVRd,max = designvalueofthemaximumshearforcethatcanbesustainedbythemember,

limitedbycrushingofthecompressionstruts

Theseresisttheappliedshearforce,VEd.

Requirements for shear reinforcement

If VEd ≤ VRd,c, no calculated shear reinforcement is necessary. However, minimum shearreinforcementshouldstillbeprovided(seeSection15.2.6)exceptin:

■ Slabs,whereactionscanberedistributedtransversely.Membersofminorimportance,whichdonotcontributesignificantlytotheoverall■■

resistanceandstabilityofthestructure(e.g.lintelswithaspanoflessthan2m).

If VEd > VRd,c shear reinforcement is required such that VRd,s > VEd.The resistance of theconcretetoactasastrutshouldalsobechecked.

Inmemberssubjectpredominantlytouniformlydistributedloading,thefollowingapply:

Shearatthesupportshouldnotexceed■■ VRd,max.Requiredshearreinforcementshouldbecalculatedatadistance■■ dfromthefaceofthesupportandcontinuedtothesupport.

The longitudinaltensionreinforcementshouldbeabletoresisttheadditionaltensile forcecausedbyshear(seeSection15.2.2).

TheUKNAlimitsshearstrengthofconcretehigherthanC50/60tothatofC50/60.

Shear and transverse bending

Duetothepresenceofcompressivestressfieldsarisingfromshearandbending,theinteractionbetweenlongitudinalshearandtransversebendinginthewebsofboxgirdersectionsshouldbeconsideredinthedesign.WhenVEd/VRd,max<0.2orMEd/MRd,max<0.1,thisinteractioncanbedisregarded(whereVRd,maxandMRd,maxrepresentrespectivelythemaximumwebcapacityforlongitudinalshearandtransversebending).

FurtherinformationontheinteractionbetweenshearandtransversebendingmaybefoundinAnnexMMofBSEN1992-2.

Resistance of members not requiring shear reinforcement

General situation

Thedesignvaluefortheshearresistanceisgivenby:

VRd,c= [(0.18/gC)k(100rlfck)1/3+0.15scp]bwd

≥ ( 0.035k1.5fck0.5 +0.15scp)bwd

BS EN 1992-1-1 6.2.1(1)

BS EN 1992-1-1 6.2.1(3)

BS EN 1992-1-1 6.2.1(4)

BS EN 1992-1-1 6.2.1(5)

BS EN 1992-1-1 6.2.1(8)

BS EN 1992-1-1 6.2.1(7)

BS EN 1992-2 3.1.2(2) & NA

BS EN 1992-26.2.106 (101)

BS EN 1992-26.2.2(101) & NA

7

7.1

7.1.1

7.1.2

7.1.3

7.2

7.2.1

42

where k = 1+(200/d)0.5≤2.0(dinmm;seeTable7.1) gC= 0.15 rl = Asl/(bwd)≤0.02

where Asl = areaofthetensilereinforcementextendingatleastlbd+dbeyondthesection

considered(seeFigure7.1);theareaofbondedprestressingsteelmaybeincludedinthecalculationofAsl.Inthiscaseaweightedmeanvalueofdmaybeused.

lbd = designanchoragelength bw = smallestwidthofthecross-sectioninthetensilearea scp= NEd/Ac<0.2fcd(MPa)

where NEd = axialforceinthecross-sectionduetoloadingorprestressinginnewtons

(NEd>0forcompression).TheinfluenceofimposeddeformationsonNEdmaybeignored.

AC = areaofconcretecross-section(mm2)

Table 7.1

VRd,c ' shear resistance without shear reinforcement where scp = 0 (MPa)

rl = As/(bd) Effective depth d (mm)

≤200 225 250 275 300 350 400 450 500 600 750

0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.43 0.41 0.40 0.38 0.36

0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.45

0.75% 0.68 0.66 0.64 0.63 0.62 0.59 0.58 0.56 0.55 0.53 0.51

1.00% 0.75 0.72 0.71 0.69 0.68 0.65 0.64 0.62 0.61 0.59 0.57

1.25% 0.80 0.78 0.76 0.74 0.73 0.71 0.69 0.67 0.66 0.63 0.61

1.50% 0.85 0.83 0.81 0.79 0.78 0.75 0.73 0.71 0.70 0.67 0.65

1.75% 0.90 0.87 0.85 0.83 0.82 0.79 0.77 0.75 0.73 0.71 0.68

≥ 2.00% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71

k 2.000 1.943 1.894 1.853 1.816 1.756 1.707 1.667 1.632 1.577 1.516

Notes

1 TablederivedfromBSEN1992-1-1andtheUKNationalAnnex.

2 Tablecreatedforfck=30MPaassumingverticallinks.

3 Forrl≥0.4%andfck = 25MPa,applyfactorof0.94 fck = 45MPa,applyfactorof1.14 fck = 35MPa,applyfactorof1.05 fck ≥ 50MPa,applyfactorof1.19 fck = 40MPa,applyfactorof1.10

Uncracked regions in prestressed membersIn prestressed single-span members without shear reinforcement, the shear resistance of theregionscrackedinbendingmaybecalculatedusingtheExpressioninSection7.2.1.Inregionsuncracked in bending (where the flexural tensile stress is smaller than fctk,0.05/gC) the shearresistanceshouldbelimitedbythetensilestrengthoftheconcrete.Intheseregionstheshearresistanceisgivenby:

VRd,c=(Ibw/S)(fctd2+alscpfctd)0.5

where I = secondmomentofarea

bw = widthofthecross-sectionatthecentroidalaxis,allowingforthepresenceofducts(seebelow)

BS EN 1992-1-1 6.2.2(2)

7.2.2

43

Shear

S = firstmomentofareaaboveandaboutthecentroidalaxis

al = lx/lpt2≤1.0forpretensionedtendons

= 1.0forothertypesofprestressing

lx = distanceofsectionconsideredfromthestartingpointofthetransmissionlength

lpt2= upperboundvalueofthetransmissionlengthoftheprestressing(Seesection14.6)

scp= concretecompressivestressatthecentroidalaxisduetoaxialloadingand/orprestressing(scp=NEd /AcinMPa,NEd>0incompression)

Alternatively,wherethereisnoaxialforce,includingprestressingVRd,c=bwdvRd,cwithvRd,cavailablefromTable7.1

InmostpracticalcasesifvEd<vRd,cshearreinforcementwillnotberequired

where

vEd = shearstressforsectionswithoutshearreinforcement=VEd/bwd.

vRd,c maybeinterpolatedfromTable7.1.

Short span shear enhancement

TheapproachinBSEN1992-1-1ofapplyingareductionfactortotheloadisnotsuitableforcaseswithmultiple,indirectordistributedloads.Therefore,intheNAtoBSEN1992-2,theexpressionforCRd,chasbeenmodifiedfromtherecommendedvaluesothattheeffectsofshearenhancementaretakenintoaccountthroughincreasingtheshearresistanceofmembersneartosupports.SeeFigure7.2.

Formemberswithactionsappliedatadistanceavwhere0.5d≤av≤2d:

kgC(100r1 fck)b + 0.15scpVRd,c =

0.18av

2d[ ] bw d

providedthattheshearforce,VEd,isnotmultipliedbyb(BSEN1992-1-1,Cl.6.2.2(6))andthelongitudinalreinforcementisfullyanchoredatthesupport.

Figure 7.1Definition of Asl

a) End support

b) Internal support

Sectionconsidered Section

considered

Sectionconsidered

45º

45º

Asl Asl

Asl

Ibd Ibd

Ibd

VEd VEd

VEd

d

d

45º

BS EN 1992-2 fig. 6.3

BS EN 1992-2 NA 6.2.2(101)

PD 6687-2 7.2.2

7.2.3

44

Figure 7.2Loads near supports b) Corbel

av

a) Beam with direct support

av

d

d

Resistance of members requiring shear reinforcement

Basis

ThedesignofmemberswithshearreinforcementisbasedonthetrussmodelshowninFigure7.3. AsimplifiedversionofthisdiagramisshowninFigure7.4.

b) Web thickness bw

bw bw

a) Truss model

Ftd

d

TensilechordShearreinforcement

CompressionchordStruts

Fcd

s

VM

N

V

V(coty–cota)

ya

z=

0.9daz

az

Figure 7.3Truss model and notation for shear reinforced members

Figure 7.4Variable strut angle, y

Concretestrutincompression

Longitudinalreinforcementintension

Verticalshearreinforcement

y

BS EN 1992-2 fig. 6.5

BS EN 1992-1-1 6.2.3

7.3

7.3.1

BS EN 1992-1-1 fig. 6.4

45

Shear

Shear resistance check

TheresistanceoftheconcretesectiontoactasastrutVRd,maxshouldbecheckedtoensurethatitequalsorexceedsthedesignshearforce,VEdi.e.ensurethat:

VRd,max = acwbwzv1fcd(coty+tany)≥VEdwithverticallinks = acwbwzv1fcd(coty+cota)/(1+cot2y)≥VEdwithinclinedlinkswhere z = leverarm(SeeSection7.3.3)

v1 = 0.6[1–(fck/250)](1–0.5cosa) fcd = 1.0 fck/ 1.5 y = angleofinclinationofthestrut,suchthatcotyliesbetween1.0and2.5. a = angleofinclinationofthelinkstothelongitudinalaxisForverticallinkscota=0. acw = coefficienttakingaccountofthestateofthestressinthecompressionchord(see

Table7.2) = 1 fornon-prestressedstructures

= (1+scp/fcd)for0<scp≤0.25fcd

= 1.25for0.25fcd<scp≤0.5fcd

= 2.5(1–scp/fcd)for0.5fcd<scp<1.0fcd

where scp=meancompressivestress,measuredpositive,intheconcreteduetothedesign

axialforce.

scpshouldbeobtainedbyaveragingitovertheconcretesectiontakingaccountofthereinforcement.Thevalueofscpneednotbecalculatedatadistancelessthan0.5dcotyfromtheedgeofthesupport.

The values ofv1 andacw should not give rise to a value of VRd,max greater than 200bw2 at

sectionsmorethanadistancedfromtheedgeofasupport.Forthispurpose,thevalueofbwdoesnotneedtobereducedforducts.

Table 7.2Values for acw

fck fcd Mean compressive stress, scp

0 0.5 1 2 3 4 5 10 20 30

20 13.3 1 1.04 1.08 1.15 1.23 1.25 1.25 0.63 — —

25 16.7 1 1.03 1.06 1.12 1.18 1.24 1.25 1.00 — —

30 20.0 1 1.03 1.05 1.10 1.15 1.20 1.25 1.25 — —

35 23.3 1 1.02 1.04 1.09 1.13 1.17 1.21 1.25 0.36 —

40 26.7 1 1.02 1.04 1.08 1.11 1.15 1.19 1.25 0.63 —

45 30.0 1 1.02 1.03 1.07 1.10 1.13 1.17 1.25 0.83 —

50 33.3 1 1.02 1.03 1.06 1.09 1.12 1.15 1.25 1.00 0.25

60 40.0 1 1.01 1.03 1.05 1.08 1.10 1.13 1.25 1.25 0.63

70 46.7 1 1.01 1.02 1.04 1.06 1.09 1.11 1.21 1.25 0.89

In the case of straight tendons, a high level of prestress (scp/fcd > 0.5) and thin webs, if thetensionandthecompressionchordsareabletocarrythewholeprestressingforceandblocksareprovidedattheextremityofbeamstodispersetheprestressingforce(seeFigure7.5),itmaybeassumedthattheprestressingforceisdistributedbetweenthechords.Inthesecircumstances,thecompressionfieldduetoshearonlyshouldbeconsideredintheweb(acw=1).

Pd

Pd,t

Pd,c

Pd = Pd,c + Pd,t

Figure 7.5Dispersion of prestressing by end blocks within the chords

BS EN 1992-2 6.2.3(103) & NA

BS EN 1992-2 6.2.3(103) & NA

BS EN 1992-2 fig. 6.101

7.3.2

BS EN 1992-1-1 Exp. (6.9) Exp. (6.14) & NA

46

Themaximumeffectivecross-sectionalareaoftheshearreinforcementAsw,maxforcoty=1isgivenby:

aacwv1 fcdAsw,max fywd

bw s≤

Lever arm, z

Intheshearanalysisofreinforcedconcrete,theapproximatevaluez=0.9dmaynormallybeused.Thisisnotappropriatewhen:

Thereisanaxialforceorprestress,or■■

Thewidthatthecentroidisgreaterthantheminimumcross-sectionwidthin■■

compression,orThecross-sectionhasatensionflangebutnocompressionflange■■

Insuchcasestheleverarmshouldbedeterminedbasedonananalysisofthesection.

Shear reinforcement required, Asw/s

The cross-sectional area of the shear reinforcement required is calculated using the shearresistance:

VRd,s=(Asw/s) z fywd(coty+cota)sina≤VRd,max

where Asw = cross-sectionalareaoftheshearreinforcement.(ForAsw,minseeSection15.2.6) s = spacingofthestirrups z = leverarm(SeeSection7.3.3) fywd= fywk/gS=designyieldstrengthoftheshearreinforcement

a = angleofthelinkstothelongitudinalaxis

Forverticallinks,cota=0andsina=1.0,and:

Asw/s≥VEd/ (z fywdcoty)

Webs containing metal ducts

Wherethewebcontainsgroutedmetalductswithadiameterf>bw/8theshearresistancevRd,maxshouldbecalculatedonthebasisofanominalwebthicknessgivenby:

bw,nom=bw–0.5SfwherefistheouterdiameteroftheductandSfisdeterminedforthemostunfavourablelevel.

Forgroutedmetalductswithf≤bw/8,bw,nom=bw

Fornon-groutedducts,groutedplasticductsandunbondedtendonsthenominalwebthicknessis:

bw,nom=bw–1.2Sf

Thevalue1.2isintroducedtotakeaccountofsplittingoftheconcretestrutsduetotransversetension.Ifadequatetransversereinforcementisprovidedthisvaluemaybereducedto1.0.

Additional tensile forces

Theadditionaltensile force,D Ftd, inthe longitudinal reinforcementduetoshearVEdmaybecalculatedfrom:

D Ftd=0.5VEd(coty–cota)MEd/z+D FtdshouldbetakenasnotgreaterthanMEd,max/z

BS EN 1992-1-1 Exp. (6.15)

BS EN 1992-1-1 Exp. (6.13)

PD 6687-2 7.2.4.1

BS EN 1992-1-16.2.3(1)

BS EN 1992-1-1 Exp. (6.8)

BS EN 1992-1-1 6.2.3(6)

BS EN 1992-1-1 Exp. (6.16)

BS EN 1992-1-1Exp. (6.17)

BS EN 1992-1-1Exp. (6.18)

7.3.3

7.3.4

7.3.5

7.3.6

47

Shear

where MEd,max=maximummomentalongthebeam

Thisadditionaltensileforcegivesrisetothe‘shift’ruleforthecurtailmentofreinforcement(seeSection15.2).

In the case of bonded prestressing, located within the tensile chord, the resisting effect ofprestressingmaybetakenintoaccountforcarryingthetotallongitudinaltensileforce.Inthecase of inclined bonded prestressing tendons in combination with other longitudinalreinforcement/tendonstheshearstrengthmaybeevaluated,byasimplification,superimposingtwodifferenttrussmodelswithdifferentgeometry(Figure7.6);aweightedmeanvaluebetweeny1andy2maybeusedforconcretestressfieldverificationwithExpression(6.9).

y2y1

Figure 7.6Superimposed resisting model for shear

Members with actions applied near bottom of section

Whereloadisappliednearthebottomofasection,sufficientshearreinforcementtocarrytheload to the top of the section should be provided in addition to any shear reinforcementrequiredtoresistshear.

Shear between web and flanges of T-sections

Thelongitudinalshearstress,vEd,atthejunctionbetweenonesideofaflangeandthewebisdeterminedbythechangeofthenormal(longitudinal)forceinthepartoftheflangeconsidered,accordingto:

vEd=DFd/(hfDx)

where hf = thicknessofflangeatthejunctions Dx = lengthunderconsideration,seeFigure7.7 DFd = changeofthenormalforceintheflangeoverthelengthDx

A

A

Fd

Fd

Sf

beff

Asf

hf

Fd + DFd

Fd + DFd

Dx

bw

yf

Longitudinal baranchored beyondthis projected point

Compressive struts

Figure 7.7Notations for the connection between flange and web

BS EN 1992-2 6.2.3(107)

BS EN 1992-2 fig. 6.102N

BS EN 1992-1-1 6.2.1(9)

BS EN 1992-26.2.4(103)

BS EN 1992-1-1fig. 6.7

7.3.7

7.3.8

48

ThemaximumvaluethatmaybeassumedforDxishalfthedistancebetweenthesectionwherethemomentis0andthesectionwherethemomentismaximum.WherepointloadsareappliedthelengthDxshouldnotexceedthedistancebetweenpointloads.

Alternatively,consideringalengthDxofthebeam,thesheartransmittedfromthewebtotheflangeisvEdDx/zandisdividedintothreeparts:oneremainingwithinthewebbreadthandtheothertwogoingouttotheflangeoutstands.Itshouldbegenerallyassumedthattheproportionof the force remaining within the web is the fraction bw/beff of the total force. A greaterproportion may be assumed if the full effective flange breadth is not required to resist thebendingmoment.InthiscaseacheckforcracksopeningatSLSmaybenecessary.

Therateofchangeoftheflangeforcescanbeunderestimatediftheeffectsofwebshearontheflangeforcesarenotincluded,particularlyforcompressionflanges.Thechordforcesasdeterminedforthedesignofthewebreinforcementshouldthereforebeused.

Forcompressionflanges,Fdmaybecalculatedasfollows:

Fd=(beff–bw)Fcd/(2beff)whenhf>xcFd=(beff–bw)fcdhf/2 whenhf≤xc

where xc = depthofthecompressionzone Fcd = totalforceinthecompressionchordofthesheartrussintheweb

Fortensionflanges,Fdmaybecalculatedbydeterminingtheproportionofthetotaltensionchordforce,Ftd,carriedineachsideoftheflange.

ThetransversereinforcementperunitlengthAsf /sfmaybedeterminedasfollows:

(Asf fyd /sf)≥vEdhf/cotyf

Topreventcrushingofthecompressionstrutsintheflange,thefollowingconditionshouldbesatisfied:

VEd≤ 0.6(1–fck/250) fcdsinyfcosyf

where

fcd= 1.0 fck/ 1.5

Thepermittedrangeofthevaluesforcotyfare:

1.0 ≤cotyf≤ 2.0 forcompressionflanges(45°≥yf≥26.5°)

1.0 ≤cotyf≤1.25fortensionflanges(45°≥yf≥38.6°)

IfvEdislessthanorequalto 0.4 fctdnoextrareinforcementabovethatforflexureisrequired.

Longitudinaltensionreinforcementintheflangeshouldbeanchoredbeyondthestrutrequiredto transmit the force back to the web at the section where this reinforcement is required(SeeSection(A–A)ofFigure7.7).

Interface shear between concretes placed at different times

Whencompositeactionisassumedbetweentwolayersofconcretecastatdifferenttimes,itisnecessarytopreventslipbetweenthetwolayers.Thiswillresultinshearstressattheinterface,whichshouldbeverified.Theforceattheinterfaceistheflangeforceinthenewconcretecausedbythebendingmomentonthecompositesection.

The shear stress at the interface between concrete cast at different times should satisfy thefollowing.

vEdi≤vRdi

PD 6687-2, 7.2.5

BS EN 1992-1-1 6.2.4(4)

BS EN 1992-1-1 6.2.4(6)

BS EN 1992-1-16.2.5

7.3.9

49

Shear

where

vEdi=designvalueoftheshearstressintheinterfaceandisgivenby:

vEdi=b VEd /(zbi)

where VEd= transverseshearforce z = leverarmofthecompositesection bi = widthoftheinterface(seeFigure7.8) b = ratioofthelongitudinalforceinthenewconcreteandthetotallongitudinalforce

eitherinthecompressionortensionzone,bothcalculatedforthesectionconsidered

vRdi=cfctd+μsn+rfyd(μsina +cosa)≤0.5 0.6(1–fck/250) fcd

where

thevaluesofcandμdependontheinterfacesurfaceandareshowninTable7.3 fctd= fctk,0.05/ 1.5

fcd = 1.0 fck/ 1.5 sn= stressnormaltotheinterfacenottobetakengreaterthan0.6fcd

r = As/Ai

As = areaofreinforcementcrossingtheinterfaceincludingordinaryshearreinforcement(ifany),withadequateanchorageatbothsidesoftheinterface

Ai = areaofthejoint a =angleofreinforcementcrossingtheinterface(45°≤a ≤90°)

bi

bi

a) Double-T unit with topping b) I-beam with topping

Figure 7.8Examples of interfaces for shear

Table 7.3Values of m and c for various interfaces

Classification of interface surfaces Friction coefficient, m Shear coefficient, c

Very smooth: surface cast against steel, plastic or smooth wooden moulds

0.5 0.10

Smooth: slipformed or extruded surface or face untreated after vibration

0.6 0.20

Rough: a surface with at least 3 mm roughness at 40 mm spacing

0.7 0.40

Whereasteppeddistributionoftransversereinforcementisused,thetotalresistancewithinanybandofreinforcementshouldbenotlessthanthetotallongitudinalshearinthesamelength and the longitudinal shear stress evaluated at any point should not exceed theresistanceevaluatedlocallybymorethan10%.

BS EN 1992-1-1 fig. 6.8

BS EN 1992-1-16.2.5(2)

PD 6687-2 7.2.6

50

8

8.1

8.1.1

8.1.2

8.2

8.2.1

Punching shear

General

Basis of design

Punching shear is a local shear failure around concentrated loads on slabs and the mostcommonsituationswherethepunchingshearrulesarerelevantinbridgeapplicationsareinthedesignofpilecaps,padfootings,anddeckslabswhicharesubjectedtowheelloadsandaroundsupportsinslabssupportedondiscretebearingsorcolumns.Theresultingstressesareverifiedalongdefinedcontrolperimetersaroundtheloadedarea.Theshearforceactsoveranareaudeff,whereu isthelengthoftheperimeteranddeff istheeffectivedepthoftheslabtakenastheaverageoftheeffectivedepthsintwoorthogonaldirections.

Design procedure

Atthecolumnperimeter,ortheperimeterofthe loadedarea,themaximumpunchingshearstressshouldnotbeexceeded,vEd≤vRd,max.

Punchingshearreinforcementisnotnecessaryif

vEd≤vRd,c

WherevEdexceedsvRd,cforthecontrolsectionconsidered,punchingshearreinforcementshouldbeprovidedaccordingtoSection8.5

where

vEd = designvalueoftheappliedshearstress(seeSections8.2and8.3) vRd,max= designvalueofthemaximumpunchingshearresistance(seeSection8.6)along

thecontrolsectionconsidered vRd,c = designvalueofpunchingshearresistanceofaslabwithout punchingshear

reinforcement,alongthecontrolsectionconsidered(seeSection8.4) vRd,cs = designvalueofpunchingshearresistanceofaslabwith punchingshear

reinforcement,alongthecontrolsectionconsidered(seeSection8.5)

Applied shear stress

General

Where the support reaction is eccentric with regard to the control perimeter, the maximumshearstressshouldbetakenas:

vEd=b VEd /(uid)

where d = meaneffectivedepth

= (dy+dz)/2

ui = lengthofthecontrolperimeterunderconsideration(seeSection8.3)

VEd = designvalueofappliedshearforce

b = factordealingwitheccentricity

dy = effectivedepthiny-direction

dz = effectivedepthinz-direction

BS EN 1992-1-16.4.3(1)

BS EN 1992-1-16.4.3(3)

BS EN 1992-1-16.4.3(2)

BS EN 1992-1-16.4.1

51

Punchingshear

8.2.2

8.2.3

Values of b (conservative values from diagram)

Forbracedstructures,whereadjacentspansdonotdifferbymorethan25%,thevaluesofbshowninFigure8.1maybeused.

Cornercolumn

Edgecolumn Internalcolumn

b =1.5

b =1.4 b =1.15

Figure 8.1Recommended values for b

Values of b (using calculation method)

As an alternative to Section 8.2.2, the values of b can be obtained using the followingmethods.

Internal columnsForinternalrectangularcolumnswithloadingeccentricto■■ oneaxis:

b=1+(kMEd/VEd)(u1/W1)

where k = coefficientdependingontheratioofthecolumndimensionsc1andc2as

showninFigure8.2(seeTable8.1) MEd= designvalueoftheappliedinternalbendingmoment u1 = lengthofthebasiccontrolperimeter(seeFigure8.3) W1 = adistributionofshearasillustratedinFigure8.2andisafunctionofu1 W1 = c1

2/2+c1c2+4c2d+16d2+2pdc1forarectangularcolumn

=ʃui|e|dl forthegeneralcase 0

where

||= theabsolutevalue e = thedistanceofdlfromtheaxisaboutwhichMEdacts dl = alengthincrementoftheperimeter

2d

2d

c1

c2

Figure 8.2Shear distribution due to an unbalanced moment at a slab/ internal column connection

BS EN 1992-1-1 6.4.3(6)

BS EN 1992-1-1 fig. 6.21N & NA

BS EN 1992-1-1 Exp. (6.39)

BS EN 1992-1-1 Exp. (6.40)

BS EN 1992-1-1 fig. 6.19

52

Table 8.1Values for k for rectangular loaded areas

c1/c2 ≤ 0.5 1.0 2.0 ≥ 3.0

k 0.45 0.60 0.70 0.80

Forinternalrectangularcolumnswithloadingeccentricto■■ both axes: b=1+1.8[(ey/bz)2+(ez/by)2]0.5

where eyandez = MEd/VEdalongyandzaxesrespectively byandbz = thedimensionsofthecontrolperimeter(seeFigure8.3)

Forinternalcircularcolumns:■■

b=1+0.6pe/(D+4d)

where D = diameterofthecircularcolumn e = MEd/VEd

u1=basiccontrolperimeter

2d2d

2d

2d

u1

u1u1

by

bz

Figure 8.3Typical basic control perimeters around loaded areas

Edge columns

Foredgecolumns,withloadingeccentricityperpendicularandinteriortotheslabedge,■■

b=u1/u1*

where u1 = basiccontrolperimeter(seeFigure8.4) u1*= reducedcontrolperimeter(seeFigure8.5)

Foredgecolumns,witheccentricitytobothaxesandinteriortotheslabedge■■

b=u1/u1*+keparu1/W1

where k = coefficientdependingontheratioofthecolumndimensionsc1andc2as

showninFigure8.5(seeTable8.2)

epar= eccentricityparalleltotheslabedgeresultingfromamomentaboutanaxisperpendiculartotheslabedge

W1 = c22/4+c1c2+4c1d+8d2+pdc2

where c1andc2areasinFigure8.5

BS EN 1992-1-1 table 6.1

BS EN 1992-1-1 Exp. (6.43)

BS EN 1992-1-1 Exp. (6.42)

BS EN 1992-1-1 fig. 6.13

BS EN 1992-1-1 6.4.3(4)

BS EN 1992-1-1 Exp. (6.44)

53

Punchingshear

2d

u1

u1

u1

2d 2d

2d

2d

2d

u1=basiccontrolperimeter

Figure 8.4Control perimeters for loaded areas at or close to an edge or corner

≤1.5d

≤1.5d

≤1.5d

≤0.5c1

≤0.5c1

≤0.5c2

2d

2d

2d

2d

c1

c1c2

c2

u1*

u1*

a) Edge column b) Corner column

Figure 8.5Equivalent control perimeter u1*

Table 8.2Values for k for rectangular loaded areas at edge of slabs and subject to eccentric loading in both axes

c1/2c2* ≤ 0.5 1.0 2.0 ≥ 3.0

k 0.45 0.60 0.70 0.80

Note

*differsfromTable8.1

Corner columns Forcornercolumnswitheccentricitytowardsinterioroftheslab

b=u1/u1*

where u1 = basiccontrolperimeter(seeFigure8.4) u1*= reducedcontrolperimeter(seeFigure8.5)

BS EN 1992-1-1 fig. 6.15

BS EN 1992-1-1 fig. 6.20

BS EN 1992-1-1 6.4.3(5)

BS EN 1992-1-1 Exp. (6.46)

54

Perimeter columns where eccentricity is exterior to slab

Foredgeandcornercolumns,whereeccentricityisexteriortotheslabtheexpression

b=1+(kMEd/VEd)(u1/W1i

appliesasforinternalcolumnsabove.However,MEd/VEd(=e,eccentricity)ismeasuredfromthecentroidofthecontrolperimeter.

Control perimeters

Basic control perimeter u1 (internal columns)

Thebasiccontrolperimeteru1maybetakentobeatadistanceof2.0dfromthefaceoftheloadedarea,constructedsoastominimiseitslength(seeinFigure8.3).

Openings

Where openings in the slab exist within 6d from the face of the loaded area, part of thecontrolperimeterwillbeineffectiveasindicatedinFigure8.6.

a) Where l1 l2 b) Where l1 > l2

Opening

2d

≤6d

l2

l1≤l2l1>l2

(l1l2)0.5

u1

Ineffective

Figure 8.6Control perimeter near an opening

Perimeter columns

Foredgeorcornercolumns(orloadedareas),thebasiccontrolperimeteru1showninFigure8.4maybeusedforconcentricloading.ThisperimetermustnotbegreaterthantheperimeterobtainedforinternalcolumnsfromusingFigure8.3(seeSection8.3.1).

Whereeccentricityofloadsisinteriortotheslab,thereducedcontrolperimeter,u1*showninFigure8.5shouldbeusedasindicatedinSection8.2.3.

Column heads

Wherecolumnheadsareprovided,distinctionshouldbemadebetweencaseswherelH>2hHandwherelH<2hH

where

lH = projectionofheadfromthecolumn hH = heightofheadbelowsoffitofslab

BS EN 1992-1-1 6.4.3(4)6.4.3(5)

BS EN 1992-1-1 6.4.2

BS EN 1992-1-1 fig. 6.14

BS EN 1992-1-1 6.4.2(5)

BS EN 1992-1-1 6.4.2(9)

8.3

8.3.1

8.3.2

8.3.3

8.3.4

55

Punchingshear

WherelH<2hHpunchingshearneedstobecheckedonlyinthecontrolsectionoutsidethecolumnhead(seeFigure8.7).WherelH>2hHthecriticalsectionsbothwithintheheadandslabshouldbechecked(seeFigure8.8).

LoadedareaAload

Note

y =26.6º,tany=0.5

hH

rcont rcont

hH

d

lH<2.0hH lH<2.0hH

c

Basiccontrolsection

y

y y

y

Figure 8.7Slab with enlarged column head where lH < 2.0 hH

Note

y=26.6º,tany=0.5

lH>2hH lH>2hH

rcont,ext rcont,ext

rcont,ext rcont,ext

LoadedareaAload

Basiccontrolsectionsforcircularcolumns

d d

hHhH

dH dH

c

y

y y

y

Figure 8.8Slab with enlarged column head where lH > 2hH

Punching shear resistance without shear reinforcement

The punching shear resistance of a slab should be assessed for the basic control sectionaccordingtoSection8.3.Thedesignpunchingshearresistancemaybecalculatedasfollows:

Thedesignvaluefortheshearresistanceisgivenby:

vRd,c = (0.18/gC)k(100rlfck)1/3+0.15scp

≥ 0.035k1.5fck0.5 +0.15scp

where k = 1+(200/d)0.5≤2.0(dinmm) gC= 1.5 rl = (rly,rlz)0.5≤0.02

where rly,rlz= reinforcementratiosintheyandzdirectionsrespectively.Thevaluesshould

becalculatedasmeanvalues,takingintoaccountaslabwidthequaltothecolumnwidthplus3deachside

scp = (scy+scz)/2 scy = NEd,y/Acy scz = NEd,z/Acz

BS EN 1992-1-1 fig. 6.17

BS EN 1992-1-1 fig. 6.18

BS EN 1992-1-1 6.4.4

BS EN 1992-1-1 Exp. (6.47) & NA

8.4

56

where NEd,y,NEd,z = longitudinalforcesacrossthefullbayforinternalcolumnsand

thelongitudinalforcesacrossthecontrolsectionforedgecolumns.Theforcemaybefromaloadorprestressingaction

AC = areaofconcretecross-sectionaccordingtothedefinitionofNEd(mm2)

Punching shear resistance with shear reinforcement

WhereshearreinforcementisrequireditshouldbecalculatedinaccordancewiththeExpressionbelow:

vRd,cs=0.75vRd,c+1.5(d/sr)Aswfywd,ef(1/u1d)sina

where Asw = areaofoneperimeterofshearreinforcementaroundthecolumn(mm2)

(forAsw,minseeSection15.4.3)

sr = radialspacingofperimetersofshearreinforcement(mm)

fywd,ef = effectivedesignstrengthofreinforcement(250+0.25d)≤fywd

d = meaneffectivedepthinthetwoorthogonaldirections(mm)

u1 = basiccontrolperimeterat2dfromtheloadedarea(seeFigure8.3)

sina = 1.0forverticalshearreinforcement

a = anglebetweentheshearreinforcementandplaneoftheslab

AssumingverticalreinforcementAsw=(vEd–0.75vRd,c)sru1/(1.5fywd,ef)perperimeter

Punching shear resistance adjacent to columns

Adjacenttothecolumnthepunchingshearresistanceislimitedtoamaximumof:

vEd=bVEd/u0d≤vRd,max

where b = factordealingwitheccentricity(seeSection8.2) VEd = designvalueofappliedshearforce d = meaneffectivedepth u0 = lengthofcolumnperipheryforaninteriorcolumn

=2(c1+c2)forinteriorcolumns = c2+3d≤c2+2c1foredgecolumns = 3d≤c1+c2forcornercolumns where

c1 = columndepth(foredgecolumns,measuredperpendiculartothefreeedge)c2 = columnwidthasillustratedinFigure8.5

vRd,max=0.5vfcd

where v= 0.6[1–(fck/250)]

Control perimeter where shear reinforcement is no longer required, uout

ShearreinforcementisnotrequiredataperimeterwheretheshearstressduetotheeffectiveshearforcedoesnotexceedvRd,c.Theoutermostperimeterofshearreinforcementshouldbeplacedatadistancenotgreaterthan1.5d withintheperimeterwherereinforcementisnolongerrequired.SeeFigures8.9,15.6and15.7.

8.5

8.6

8.7

BS EN 1992-1-1 6.4.5

BS EN 1992-1-1 Exp. (6.52)

BS EN 1992-1-1 6.4.5(3)

BS EN 1992-1-1 6.4.5(4) & NA

57

Punchingshear

Perimeteruout,efPerimeteruout

≤2d

>2d

d

d

1.5d

1.5d

Figure 8.9Control perimeters at internal columns

Distribution of shear reinforcement

TheExpressiongiveninSection8.5assumesaconstantareaofshearreinforcementoneachperimetermovingawayfromtheloadedareaasshowninFigure8.9.Incaseswherethereinforcementareavariesonsuccessiveperimeters,therequiredshearreinforcementmaybedeterminedbycheckingsuccessiveperimeters,uibetweenthebasiccontrolperimeterandtheperimeteruout,toensurethattheshearreinforcementofareaSAswsatisfiesthefollowingexpression:

fywd, ef sin a SAsw

(vEd – 0.75 vRd, c ) ui d=

where SAsw is the total shear reinforcement as shown in Figure 8.10, placed within anarea enclosed between the control perimeter ui chosen and one 2d inside it, except thatshear reinforcement within a distance of 0.3d from the inner perimeter and 0.2d from thecontrolperimetershouldbeignored.FurtherguidanceandbackgroundaregivenbyHendy&Smith[20]

2d

0.2d0.3d

1

Uout

Ui

Notes1 uiisbetweenu1

anduout

2ReinforcementS Aswtoincludeincludeforcheckonperimeterui

Figure 8.10Reinforcement to include in punching shear check

BS EN 1992-1-1 fig. 6.22

PD 6687-2 7.3.2

8.8

PD 6687-2 fig. 4

58

BS EN 1992-1-1 fig. 6.16

8.9 Punching shear resistance of foundation bases

In addition to the verification at the basic control perimeter at 2d from the face of thecolumn, perimeters within the basic perimeter should also be checked for punchingresistance.Incaseswherethedepthofthebasevaries,theeffectivedepthofthebasemaybeassumedtobethatattheperimeteroftheloadedarea.SeeFigure8.11.

Forconcentricloadingthenetappliedforceis

VEd,red=VEd–DVEd

where VEd = appliedshearforce DVEd = netupwardforcewithintheperimeterconsidered,i.e.upwardpressurefromsoil

minusself-weightofbase.

WhenacolumntransmitsanaxialloadVEdandamomentMEd,thepunchingshearstressisgivenbythefollowingexpression:

vEd=(VEd,red/ud)[1+kMEdu/(VEd,redW)]

where u = theperimeterbeingconsidered k = acoefficientdependingontheratioofthecolumndimensionsshowninFigure8.2

andTable8.1 W = W1

Forasquarecolumnandageneralperimeteratriwithlengthui:

2+ 2c2

W1= + ri ric1 c2

c12

c1+ 4 ri 2 + p

ThepunchingshearresistancevRd,cgiveninSection8.4maybeenhancedforcolumnbasesbymultiplyingtheExpressionsby2d/a,whereaisthedistanceoftheperimeterconsideredfromtheperipheryofthecolumn.

Loadedarea

y

d

y≥arctan(0.5)

Figure 8.11Depth of control section in a footing with variable depth

BS EN 1992-1-1 6.4.2(6)

BS EN 1992-1-1 6.4.4(2)

BS EN 1992-1-1 Exp. (6.51)

PD 6687-2 7.3.1

59

Torsion

Torsion

General

Torsionalresistanceshouldbeverifiedinelementsthatrelyontorsionforstaticequilibrium.Instaticallyindeterminatebuildingstructuresinwhichtorsionarisesfromconsiderationofcompatibilityandthestructureisnotdependentontorsionforstability,itwillnormallybesufficienttorelyondetailingrulesforminimumreinforcementtosafeguardagainstexcessivecracking,withouttheexplicitconsiderationoftorsionatULS.

InEurocode2,torsionalresistanceiscalculatedbymodellingallsectionsasequivalentthin-walledsections.Complexsections,suchasT-sectionsaredividedintoaseriesofsub-sectionsandthetotalresistanceistakenasthesumoftheresistancesoftheindividualthin-walledsub-sections.

Thesamestrut inclinationy shouldbeusedformodellingshearandtorsion.The limits forcotynotedinSection7forshearalsoapplytotorsion.

Torsional resistances

Thedesigntorsionalresistancemoment

TRd,max=2vacw fcdAktef,isiny cosy

where v = 0.6[1–(fck/250)] Ak = areaenclosedbythecentrelinesofconnectingwallsincludingtheinnerhollow

area(seeFigure9.1) tef,i = effectivewallthickness(seeFigure9.1).ItmaybetakenasA/ubutshouldnotbe

takenaslessthantwicethedistancebetweenedge (theoutsidefaceofthe member) andcentreofthelongitudinalreinforcement.Forhollowsectionstherealthicknessisanupperlimit

y = angleofthecompressionstrut acw= coefficienttakingaccountofthestateofstressinthecompressionchord(seeTable7.2)

= 1 fornon-prestressedstructures

= (1+scp/fcd)for0<scp≤0.25fcd

= 1.25for0.25fcd<scp≤0.5fcd

= 2.5(1–scp/fcd)for0.5fcd<scp<1.0fcd

where scp=meancompressivestress,measuredpositive,intheconcreteduetothedesign

axialforce.

scp should be obtained by averaging it over the concrete section taking account of thereinforcement.Thevalueofscpneednotbecalculatedatadistancelessthan0.5dcotyfromtheedgeofthesupport.

BS EN 1992-1-1 6.3.1

BS EN 1992-1-1 6.3.2

BS EN 1992-2 6.3.2 (104)

BS EN 1992-26.2.3(103) & NA

9

9.1

9.2

60

Centreline

Cover

Outeredgeofeffectivecross-section,circumference,u

tef

zi

TEd

tef/2

Figure 9.1Notations used in Section 9

ThetorsionalresistanceofasolidrectangularsectionwithshearreinforcementontheouterperipheryTRd,maxmaybededucedfromthegeneralexpression,assumingteff=A/u:

TRd,max=2vacw fcdk2b3sinycosy

where k2 = coefficientobtainedfromTable9.1 b = breadthofthesection(<h,depthofsection)

Table 9.1Values of k2

h/b 1 2 3 4

k2 0.141 0.367 0.624 0.864

Torsionalresistancegovernedbytheareaofclosedlinksisgivenby:

TRd=Asw 2Akcotyfywd/s

where Asw = areaoflinkreinforcement fyw,d = designstrengthofthelinkreinforcement s = spacingoflinks

Therequiredareaoflongitudinalreinforcementfortorsion,SAsl,maybecalculatedfrom:

SAslfyd=TEdukcoty/(2Ak)

where TEd = applieddesigntorsion uk = perimeteroftheareaAk

Incompressivechords,thelongitudinalreinforcementmaybereducedinproportiontotheavailablecompressiveforce.Intensilechords,thelongitudinalreinforcementfortorsionshouldbeaddedtotheotherreinforcement.Thelongitudinalreinforcementshouldgenerallybedistributedoverthelengthofsidezi ,(sidelengthofwallidefinedbythedistancebetweentheintersectionpointswiththeadjacentwalls),butforsmallersectionsitmaybeconcentratedattheendsofthislength.

Bonded prestressing tendons can be taken into account limiting their stress increase toDsp≤500MPa.Inthatcase,SAslfydinExpression(6.28)isreplacedbySAslfyd+ApDsp.

ENV 1992-1-1 Exp. (4.43)[21]

BS EN 1992-2Exp. (6.28)

BS EN 1992-26.3.2(103)

BS EN 1992-1-1 fig. 6.11

61

Torsion

9.3 Combined torsion and shear

Insolidsectionsthefollowingrelationshipshouldbesatisfied:

(TEd/TRd,max)+(VEd/VRd,max)≤1.0

where TRd,max = designtorsionalresistancemoment = 2vacw fcdAktef,isinycosyasinSection9.2.

VRd,max = maximumdesignshearresistance =acwbw z v1 fcd(coty+cota)/(1+cot2y)asinSection7.3.2.

The effects of torsion and shear for both hollow and solid members may be superimposed,assumingthesamevalueforthestrutinclinationy.ThelimitsforygiveninSection7.3.2arealsofullyapplicableforthecaseofcombinedshearandtorsion.

For box sections, each wall should be verified separately, for the combination of shear forcesderivedfromshearandtorsion(Figure9.2).

a) Torsion b) Shear c) Combination

+ =

Figure 9.2Internal actions combination within the different walls of a box section

BS EN 1992-2 Exp. (6.29)

BS EN 1992-2 6.3.2 (102)

BS EN 1992-2 fig. 6.104

62

10

10.1

10.1.1

10.1.2

Strut-and-tie models, bearing zones and partially loaded areas

Design with strut-and-tie models

Struts

The design strength for a concrete strut in a region with transverse compressive stress or notransversestressmaybecalculatedfromthefollowingExpression(seeFigure10.1).

sRd,max=fcd= 0.85 fck / 1.5

Figure 10.1Design strength of concrete

struts without transverse tension

sRd,maxsRd,max

Figure 10.2Design strength of concrete

struts with transverse tension

sRd,maxsRd,max

Thedesignstrengthforconcretestrutsshouldbereducedincrackedcompressionzonesand,unlessamorerigorousapproachisused,maybecalculatedfromthefollowingExpression(seeFigure10.2).

sRd,max=0.6 (1–fck/250) fcd

where fcd= 1.0 fck/ 1.5

Ties

Reinforcementrequiredtoresisttheforcesattheconcentratednodesmaybesmearedoveralength(seeFigure10.3).Whenthereinforcementinthenodeareaextendsoveraconsiderablelength of an element, the reinforcement should be distributed over the length where thecompressiontrajectoriesarecurved(tiesandstruts).Thetensileforce,T,maybeobtainedby:

Forpartialdiscontinuityregions(■■ b ≤H/2)T=(b–a)F/4bForfulldiscontinuityregions(■■ b>H/2)T=(1–0.7a/h)F/4

BS EN 1992-1-16.5.2

BS EN 1992-1-1fig. 6.23

BS EN 1992-1-1fig. 6.24

BS EN 1992-1-16.5.3

63

Strut-and-tiemodels,bearingzonesandpartiallyloadedareas

10.1.3

a) Partial discontinuity b) Full discontinuity

bef

bef = 0.5H + 0.65a; aA h

a

b

z = h/2 h = H/2

F

F

h = bDiscontinuity region

Continuity region

Discontinuity region

H

bef

bef = b

a

b

F

F

Figure 10.3Parameters for the determination of transverse tensile forces in a compression field with smeared reinforcement

Nodes

Therulesfornodesalsoapplytoregionswhereconcentratedforcesaretransferredinamemberandwhicharenotdesignedbythestrut-and-tiemethod.Theforcesactingatnodesshouldbeinequilibrium.Transversetensileforcesperpendiculartoaninplanenodeshouldbeconsidered.

The dimensioning and detailing of concentrated nodes are critical in determining theirloadbearing resistance.Concentrated nodes may develop, for example, where point loads areapplied, at supports, in anchorage zones with concentration of reinforcement or prestressingtendons,atbendsinreinforcingbars,andatconnectionsandcornersofmembers.

Thedesignvaluesforthecompressivestresseswithinnodesmaybedeterminedinthreeways:

Incompressionnodeswherenotiesareanchoredatthenode(seeFigure10.4)■■

sRd,max= 1.0 (1–fck/250) fcd

where sRd,max = maximumstresswhichcanbeappliedattheedgesofthenode fcd = 0.85 fck/ 1.5

sRd,2 sRd,3

sRd,1

s c,0

a2

a3

a1

Fcd,1 = Fcd,1r + Fcd,l

Fcd,2

Fcd,3

Fcd,0

Fcd,1l Fcd,1r

Figure 10.4Compression node without ties

BS EN 1992-1-1 fig 6.25

BS EN 1992-1-1 6.5.4

BS EN 1992-1-1fig. 6.26

64

Incompression–tensionnodeswithanchoredtiesprovidedinonedirection(seeFigure10.5)■■

sRd,max= 0.85 (1–fck/250) fcd

where sRd,maxisthemaximumofsRd,1andsRd,2

fcd= 0.85 fck/ 1.5

sRd,1

sRd,2

s0

su

s0

Ftd

a1

lbd

Fcd,1

Fcd,2

R 2s0

a2

Figure 10.5Compression–tension node with reinforcement provided in one direction

Incompression–tensionnodeswithanchoredtiesprovidedinmorethanonedirection(see■■

Figure10.6),

sRd,max= 0.75 (1–fck/250) fcd

where

fcd= 0.85 fck/ 1.5

sRd,max

Ftd,1

Ftd,2

Fcd

Figure 10.6Compression–tension node with reinforcement provided in two directions

BS EN 1992-1-1fig. 6.27

BS EN 1992-1-1fig. 6.28

65

Strut-and-tiemodels,bearingzonesandpartiallyloadedareas

Theanchorageofthereinforcement incompression-tensionnodesstartsatthebeginningofthenode;inthecaseofasupportanchorage,startingatitsinnerface(seeFigure10.5).Theanchoragelengthshouldextendovertheentirenodelength.Incertaincases,thereinforcementmayalsobeanchoredbehindthenode.

Partially loaded areasForauniformdistributionofloadonanareaAc0(seeFigure10.7)theconcentratedresistanceforcemaybedeterminedasfollows:

FRdu = Ac0 fcd (Ac1 / Ac0)0.5 ≤ 3.0 fcd Ac0

where Ac0= loadedarea, Ac1= maximumdesigndistributionareawithasimilarshapetoAc0

fcd = 0.85 fck/ 1.5

ThedesigndistributionareaAc1requiredfortheresistanceforceFRdushouldcorrespondtothefollowingconditions:

Theheightfortheloaddistributionintheloaddirectionshouldcorrespondtothe■■

conditionsgiveninFigure10.7.Thecentreofthedesigndistributionarea■■ Ac1shouldbeonthelineofactionpassingthroughthecentreoftheloadareaAc0.Ifthereismorethanonecompressionforceactingontheconcretecross-section,the■■

designeddistributionareasshouldnotoverlap.

Reinforcement should be provided to resist the tensile forces due to the effect of actions,therulesforstrutandtiemaybeused.

Transverse tensile forces can arise in the localised area near a concentrated load and alsofrom any further spread of load outside the localised area.The strut-and-tie model usedshould account for both of these potential sources of transverse tensile forces FurtherguidanceandbackgroundaregivenbyHendy&Smith[20].

Line of action

b1

Ac1

Ac0

d1

hR (b2 – b1) and

b2A 3b1

d2A 3d1

R (d2 – d1)

h

Figure 10.7Design distribution for partially loaded areas

10.2 BS EN 1992-1-1 6.7

PD 6687-27.5

BS EN 1992-1-1fig. 6.29

66

10.3 Bearing zones of bridges

Forbearingzonesofbridges,Section10.2forpartiallyloadedareasshouldbeused,notingthefollowing.

ForconcreteclassesequaltoorhigherthanC55/67,theconcentratedresistanceforceshouldbecalculatedusingthefollowingExpression:FRdu = Ac0 fcd (0.46 fck 2/3) / (1 + 0.1 fck) x (Ac1 / Ac0)0.5 ≤ 3.0 Ac0 fcd (0.46 fck) / (1 + 0.1 fck

2/3)

Thedistancefromtheedgeoftheloadedareatothefreeedgeoftheconcretesectionshouldnotbelessthan1/6ofthecorrespondingdimensionoftheloadedareameasuredinthesamedirection.Innocaseshouldthedistancetothefreeedgebetakenaslessthan50mm.

Inordertoavoidedgesliding,uniformlydistributedreinforcementparalleltotheloadedfaceshouldbeprovidedtothepointatwhichlocalcompressivestressesaredispersed.Thispointisdeterminedbydrawingalineatanangle,y(30°),tothedirectionofloadapplicationfromtheedgeofthesectiontointersectwiththeoppositeedgeoftheloadedsurface,asshowninFigure10.8.Thereinforcementprovidedtoavoidedgeslidingshouldbeadequatelyanchored.

Figure 10.8Edge sliding mechanism

FRdu

y

Thereinforcementprovidedinordertoavoidedgesliding(Ar)shouldbecalculatedinaccordancewiththeexpressionArfyd≥FRdu/2.

BS EN 1992-2 fig. J.107

BS EN 1992-2J.104.1 (103)

BS EN 1992-2J.104.1 (102)

BS EN 1992-2J.104.1 (104)

67

Prestressedmembersandstructures

Prestressed members and structures

General

Thesectionprovidesguidancethatisspecifictoprestressedconcreteusingstressedtendons.Ingeneral,prestressisintroducedintheactioncombinationsdefinedinBSEN1990aspartoftheloadingcasesanditseffectsshouldbeincludedintheappliedinternalmomentandaxialforce.

The contribution of the prestressing tendons to the resistance of the section should belimited to their additional strength beyond prestressing.This requirement is most simplyachievedbytreatingthesecondaryeffectsofprestressasanappliedaction(i.e.aload),whilstomittingtheprimaryeffectsofthedesignprestressingforce.Thismaybecalculatedassumingthattheoriginofthestress–strainrelationshipofthetendonsisdisplacedbytheeffectsofprestressing.

Brittle fracture

Brittlefailureofthemembercausedbyfailureofprestressingtendonsshouldbeavoidedbyusingoneofthreemethodsgivenbelow .

Verification

Verifytheloadcapacityusingareducedareaofprestressasfollows:

Calculatetheappliedbendingmomentduetothefrequentcombinationofactions■■ Mfreq .Determinethereducedareaofprestress,■■ Ap,Red,thatresultsinthetensilestressreachingfctmattheextremetensionfibrewhenthesectionissubjecttothebendingmoment

calculatedabove.

Ap,Red=(Mfreq/z–fctm)/[sp(1/Ac+e/z)]

where z = sectionmodulus fctm = meanvalueofconcretecylindercompressivestrength sp = stressintendonsjustpriortocracking Ac = areaofconcrete e = eccentricityofthetendons

FurtherguidanceisgivenbyHendy&Smith[20]

Usingthisreducedareaofprestress,calculatetheultimateflexuralcapacity.Itshouldbe■■

ensuredthatthisexceedsthebendingmomentduetothefrequentcombination.RedistributionofinternalactionswithinthestructuremaybetakenintoaccountforthisverificationandtheultimatebendingresistanceshouldbecalculatedusingthematerialpartialfactorsforaccidentaldesignsituationsgiveninTable2.9.

Assumingthereisnoconventionalreinforcementthen:

Mfreq≥(fctmzs)/[(zs/z)–[sp(1/Ac+e/z)/fp0.1k ]]

where zs = leverarmfortheprestress,whereAp,Redhasbeenusedtodeterminethe

accidentalultimatelimitstate. fctm= meanvalueofconcretecylindercompressivestrength sp = stressintendonsjustpriortocracking

11

11.1

11.2

11.2.1

BS EN 1992-26.1(109)

68

Ac = areaofconcrete e = eccentricityofthetendons

FurtherguidanceisgivenbyHendy&Smith[20]

Minimum provision

The minimum reinforcement area, As,min, is given below. Reinforcing steel provided for otherpurposesmaybeincludedinAs,min.

As,min=Mrep/(zsfyk)

where Mrep= crackingbendingmomentcalculatedusinganappropriatetensilestrength,

fctk,0.05 attheextremetensionfibreofthesection,ignoringanyeffectofprestressing.AtthejointofsegmentalprecastelementsMrepshouldbeassumedtobezero

zs = leverarmattheultimatelimitstaterelatedtothereinforcingsteel

Thisminimumreinforcementsteelareashouldbeprovidedinregionswheretensilestressesoccurintheconcreteunderthecharacteristiccombinationofactions.Inthischeckthesecondaryeffectsofprestressingshouldbeconsideredandtheprimaryeffectsshouldbeignored.

Forpretensionedmembers,Expression(6.101a)shouldbeappliedusingoneofthealternativeapproachesdescribedbelow:

Tendonswithconcretecoveratleast■■ 1.0 timestheminimumspecifiedinFigure4.1areconsideredaseffectiveinAs,min.Avalueofzsbasedontheeffectivestrandsisusedintheexpressionandfykisreplacedwithfp0.1k.

Tendonssubjecttostresseslowerthan0.6■■ fpkafterlossesunderthecharacteristiccombinationofactionsareconsideredasfullyactive.Inthiscasethefollowingrequirementshouldbemet.

As,minfyk+ApDsp≥Mrep/z

where Dsp=smallerof0.4 fptkand500MPa

Toensureadequateductilitytheminimumreinforcingsteelarea■■ As,min,incontinuousbeamsshouldextendtotheintermediatesupportofthespanconsidered.Howeverthisextensionisnot necessary if, at the ultimate limit state, the resisting tensile capacity provided byreinforcingandprestressingsteelabovethesupports, calculated with the characteristicstrength fyk and fp0.1k respectively, is less than the resisting compressive capacity of thebottomflange.Thismeansthatthefailureofthecompressivezoneisnotlikelytooccur,andcanbeassessedasfollows:

Asfyk+ 1.0 Apfp0,1k<tinfb0 1.0 fck

where tinf = thethicknessofthebottomflangeofthesection.IncaseofT-sections,tinfis

takenasequaltob0 b0 = thewidthofthebottomflangeofthesection As = theareaofreinforcedsteelinthetensilezoneattheultimatelimitstate Ap = theareaofprestressingsteelinthetensilezoneattheultimatelimitstate

Inspection

Agreementofanappropriateinspectionregimewiththerelevantnationalauthorityonthebasisofsatisfactoryevidence.

11.2.2

11.2.3

BS EN 1992-2 Exp. (6.101a)

BS EN 1992-2 6.1(110)

BS EN 1992-2 Exp. (6.101b)

BS EN 1992-2 Exp. (6.102)

69

Prestressedmembersandstructures

Prestressing force during tensioning

Maximum stressing force

Theforceappliedtoatendon,Pmax(i.e.theforceattheactiveendduringtensioning)shallnotexceedthefollowingvalue:

Pmax=Apsp,max

where

Ap = cross-sectionalareaofthetendon sp,max = maximumstressappliedtothetendon = MIN{ 0.8 fpk; 0.9 fp0,1k}

Overstressingispermittediftheforceinthejackcanbemeasuredtoanaccuracyof±5%ofthefinalvalueoftheprestressingforce.InsuchcasesthemaximumprestressingforcePmaxmaybeincreasedto 0.95 fp0.1kAp(e.g.fortheoccurrenceofunexpectedlyhighfrictioninlong-line

pretensioning). Forpre-tensioningthisrelaxationisintendedtobeusedonlywherethereare unforeseenproblemsduringconstruction.

Theconcretecompressivestressinthestructureresultingfromtheprestressingforceandotherloadsactingatthetimeoftensioningorreleaseofprestress,shouldbelimitedto:

sc≤0.6fck(t)

where

fck(t) = characteristiccompressivestrengthoftheconcreteattimetwhenitissubjectedtotheprestressingforce

Forpretensionedelementsthestressatthetimeoftransferofprestressmaybeincreasedto0.7 fck(t),ifitcanbejustifiedbytestsorexperiencethatlongitudinalcrackingisprevented.

Ifthecompressivestresspermanentlyexceeds0.45fck(t)thenon-linearityofcreepshouldbetakenintoaccount.

Prestress force

ThevalueoftheinitialprestressforcePm0(x)(attimet=t0)appliedtotheconcreteimmediatelyaftertensioningandanchoring(post-tensioning)oraftertransferofprestressing(pre-tensioning)isobtainedbysubtractingfromtheforceattensioningPmaxtheimmediatelossesDPi(x)andshouldnotexceedthefollowingvalue:

Pm0(x)=Apspm0(x)

where

spm0(x) = stressinthetendonimmediatelyaftertensioningortransfer = MIN{ 0.75 fpk; 0.85 fp0,1k}

Atagiventimetanddistancex(orarclength)fromtheactiveendofthetendonthemeanprestressforcePm,t(x)isequaltothemaximumforcePmaximposedattheactiveend,minustheimmediatelossesandthetimedependentlosses:

Pm,t(x)=Pm0(x)-DPc+s+r(x).

where Pm,t(x) = meanvalueoftheprestressforceatthetimet>t0andshouldbe

determinedwithrespecttotheprestressingmethod DPc+s+r(x) = changeinprestressduetotheresultofcreep,shrinkageoftheconcrete

andthelongtermrelaxationoftheprestressingsteel

Absolutevaluesareconsideredforallthelosses.

11.3

11.3.1

11.3.2

BS EN 1992-1-1 5.10.2.1

BS EN 1992-1-1 5.10.2.2(5)

BS EN 1992-1-1 5.10.3(2)

BS EN 1992-1-1 5.10.3(1)&(4)

70

Immediate losses

WhendeterminingtheimmediatelossesDPi(x)thefollowingimmediateinfluencesshouldbeconsideredforpre-tensioningandpost-tensioningwhererelevant:

Lossesduetoelasticdeformationofconcrete,■■ DPel.

Forpre-tensioning:

DPel(x)=ApEpsc(x)/Ecm(t)

where Ep = modulusofelasticityofprestressingsteel Ecm(t) = modulusofelasticityofconcreteattime,t sc(x) = stressintheconcreteadjacenttothetendonattransfer

Forpost-tensioning:DPel=ApEpS(jDsc(t)/Ecm(t))

where Dsc(t)=variationofstressintheconcreteatthecentreofgravityofthetendonsapplied

attimet j =(n–1)/2nwhenconsideringlossesbeforestressing.Asanapproximationjmaybe

takenas1/2 =1forthevariationsduetopermanentactionsappliedafterprestressing n =numberofidenticaltendonssuccessivelyprestressed.

Lossesduetoshorttermrelaxation,■■ DPr (e.g.lossduetorelaxationoftheprestressing duringtheperiodwhichelapsesbetweenthetensioningofthetendonsandprestressingof theconcrete).

■■■ Lossesduetofriction,DPμ(x),inpost-tensionedtendonsmaybeestimatedfrom:

D Pμ(x)=Pmax(1−e–μ(y+kx))

where y = sumoftheangulardisplacementsoveradistancex(irrespectiveofdirectionorsign) μ = coefficientoffrictionbetweenthetendonanditsduct k = unintentionalangulardisplacementforinternaltendons(perunitlength) x = distancealongthetendonfromthepointwheretheprestressingforceisequalto

Pmax(theforceattheactiveendduringtensioning)

ThevaluesμandkaregivenintherelevantEuropeanTechnicalApproval.Intheabsenceofdatagiven inaEuropeanTechnicalApprovalthevaluesforμgiven inTable11.1maybeassumed.Unintendedangulardisplacementsforinternaltendonswillgenerallybeintherange0.005<k <0.01permetre.

Table 11.1Coefficients of friction, μ, for post-tensioned internal tendons and external unbonded tendons

Tendon type Internal tendonsa

External unbonded tendons

Steel duct: non-lubricated

HDPE duct: non-lubricated

Steel duct: lubricated

HDPE duct: lubricated

Cold drawn wire 0.17 0.25 0.14 0.18 0.12

Strand 0.19 0.24 0.12 0.16 0.10

Deformed bar 0.65 – – – –

Smooth round bar 0.33 – – – –

Key

aFortendonswhichfillabouthalfoftheduct

11.3.3

BS EN 1992-1-1 5.10.3(3)

BS EN 1992-1-1 5.10.5.1(2)

BS EN 1992-1-1 5.10.5.2(1)

BS EN 1992-1-1 5.10.5.2(2)&(3)

BS EN 1992-1-1 table 5.1

71

Prestressedmembersandstructures

Lossesduetoanchorageslip,■■ DPsl, whichareavailablefromtheEuropeanTechnical Approval.Lossesduetofrictionatthebends(inthecaseofcurvedwiresorstrands).■■

Time-dependent losses of prestressAsimplifiedmethodtoevaluatetimedependentlossesatlocationxunderthepermanentloadsisasfollows:

ApDsp,c+s+r DPc+s+r = = Ap

ecsEp+ 0.8Dspr +Ep

Ecm

h (t,t0)sc,QP

(1 + )1 + Ac

zcpIc

Ep Ap

Ecm Ac

2 [1 + 0.8 h (t,t0)]

where Ap = areaofalltheprestressingtendonsatthelocationx Dsp,c+s+r= absolutevalueofthevariationofstressinthetendonsduetocreep, shrinkageandrelaxationatlocationx,attimet ecs = estimatedshrinkagestrain,inabsolutevalue Ep = modulusofelasticityfortheprestressingsteel Ecm = modulusofelasticityfortheconcrete Dspr = absolutevalueofthevariationofstressinthetendonsatlocationx,at timet,duetotherelaxationoftheprestressingsteel.Itisdeterminedfor astressofsp=sp(G +Pm0+c2Q),whichistheinitialstressinthetendons duetoinitialprestressandquasi-permanentactions h (t,t0) = creepcoefficientatatimetandloadapplicationattimet0 sc,QP = stressintheconcreteadjacenttothetendons,duetoself-weightandinitial

prestressandotherquasi-permanentactionswhererelevant.Thevalueofsc,QPmaybetheeffectofpartofself-weightandinitialprestressortheeffectofafullquasi-permanentcombinationofactions(sc(G +Pm0+c2Q)),dependingonthestageofconstructionconsidered

Ac = areaoftheconcretesection Ic = secondmomentofareaoftheconcretesection zcp =distance between the centre of gravity of the concrete section and the

tendons

Compressive stresses and the corresponding strains should be used with a positive sign.ThisExpressionappliesforbondedtendonswhenlocalvaluesofstressesareusedandforunbondedtendonswhenmeanvaluesofstressesareused.Themeanvaluesshouldbecalculatedbetweenstraight sections limited by the idealised deviation points for external tendons or along theentirelengthincaseofinternaltendons.

Effects of prestressing at ultimate limit state

IngeneralthedesignvalueoftheprestressingforcemaybedeterminedfromPd,t(x)=gP, Pm,t(x)

For prestressed members with permanently unbonded tendons, it is generally necessary totakethedeformationofthewholememberintoaccountwhencalculatingtheincreaseofthestressintheprestressingsteel.Ifnodetailedcalculationismade,itmaybeassumedthattheincrease of the stress from the effective prestress to the stress in the ultimate limit state is

100MPaunlessthetendonisoutwithbdfromthetensionface,inwhichcaseDsp,ULS=0.b =0.1ford≥1000mm =0.25ford≤500mmThevalueofbmaybeinterpolatedforthevaluesofdbetween500mmand1000mm.

Ifthestressincreaseinexternaltendonsiscalculatedusingthedeformationstateoftheoverallmember,non-linearanalysisshouldbeused.

11.3.4

11.3.5

BS EN 1992-1-1 5.10.6

BS EN 1992-1-1 5.10.8 & NA

BS EN 1992-2 5.10.8 (103)

72

FatigueVerification conditions

Becauseofthehighliveloadtodeadloadratio,deckslabsarelikelytobeamongsttheelementsmostaffectedbyfatiguecalculations.However,testsshowthattheactualstressrangesinthereinforcementinthesearemuchlowerthantheconventionalelasticcalculationssuggest.Becauseofthis,theNAtoBSEN1992-2identifiescaseswherefatigueassessmentisnotrequiredandprovidesconservativerules.

Afatigueverificationisgenerallynotnecessaryforthefollowingstructuresandstructuralelements:

Footbridges,withtheexceptionofstructuralcomponentsverysensitivetowindaction.■■

Buriedarchandframestructureswithaminimumearthcoverof1mand1.5mforroad■■

andrailwaybridges.Foundations.■■

Piersandcolumnswhicharenotrigidlyconnectedtosuperstructures.■■

Retainingwallsofembankmentsforroadsandrailways.■■

Abutmentsofroadandrailwaybridgeswhicharenotrigidlyconnectedtosuperstructures,■■

excepttheslabsofhollowabutments.Prestressingandreinforcingsteel,inregionswhere,underthefrequentloadcombinationof■■

actionsandPkonlycompressivestressesoccurattheextremeconcretefibres.

Fatigue verification for road bridges is not necessary for the local effects of wheel loadsapplieddirectlytoaslabspanningbetweenbeamsorwebsprovidedthat:

Theslabdoesnotcontainweldedreinforcementorreinforcementcouplers.■■

Theclearspantooveralldepthratiooftheslabdoesnotexceed18.■■

Theslabactscompositelywithitssupportingbeamsorwebs.■■

Either:■■

theslabalsoactscompositelywithtransversediaphragms;or

thewidthoftheslabperpendiculartoitsspanexceedsthreetimesitsclearspan.

Internal forces and stresses for fatigue verification

Thestresscalculationshallbebasedontheassumptionofcrackedcross-sectionsneglectingthetensilestrengthofconcretebutsatisfyingcompatibilityofstrains.

Theeffectofdifferentbondbehaviourofprestressingandreinforcingsteelshallbetakenintoaccountbyincreasingthestressrangeinthereinforcingsteelcalculatedundertheassumptionofperfectbondbythefactor,n,givenby

As + Ap

As + Ap n =

j cfs/fpm

where: As = areaofreinforcingsteel

Ap = areaofprestressingtendonortendons

fs = largestdiameterofreinforcement

fp = diameterorequivalentdiameterofprestressingsteel

= 1.6√−

APforbundles

= 1.75fwireforsingle7-wirestrandswherefwireisthewirediameter

= 1.20fwireforsingle3-wirestrandswherefwireisthewirediameter

j = ratioofbondstrengthbetweenbondedtendonsandribbedsteelinconcrete.ThevalueissubjecttotherelevantEuropeanTechnicalApproval.IntheabsenceofthisthevaluesgiveninTable12.1maybeused.

12 12.1

12.2

BS EN 1992-2 6.8.1(102)

BS EN 1992-2 NA 6.8.1(102)

BS EN 1992-1-1 6.8.2

PD 6687-2 7.6.1

73

Fatigue

Table 12.1Ratio of bond strength, j , between tendons and reinforcing steel

Prestressing steel j

Pre-tensioned Bonded, post-tensioned

≤ C50/60 ≥ C70/85

Smooth bars and wires Notapplicable 0.3 0.15

Strands 0.6 0.5 0.25

Indented wires 0.7 0.6 0.30

Ribbed bars 0.8 0.7 0.35

NoteForintermediatevaluesbetweenC50/60andC70/85interpolationmaybeused.

Inthedesignoftheshearreinforcementtheinclinationofthecompressivestrutsyfatmaybecalculatedusingastrut-and-tiemodelorinaccordancewithtan yfat = tan y ≤ 1.0

where

y = angleofcompressionstrutstothebeamaxisassumedinULSdesign(seeSection7.3.2).

Verification of concrete under compression or shear

S–N curves required to undertake a fatigue verification of concrete under compression orshearareunlikelytobeavailablefromNationalAuthorities.Intheabsenceofsuchdata,thesimplifiedapproachgiveninBSEN1992-2,AnnexNNmaybeusedforrailwaybridges,butnosuchoptionexistsforhighwaybridges.

The fatigue verification for concrete under compression may be assumed tobemet if thefollowingconditionissatisfied:

fcd,fat

sc,max≤ 0.5 + 0.45

fcd,fat

sc,min

where

sc,max= maximum compressive stress at a fibre under the frequent load combination(compressionmeasuredpositive)

sc,min = minimumcompressivestressatthesamefibrewheresc,maxoccurs.Ifsc,minisatensilestress,thensc,minshouldbetakenas0

fcd,fat = designfatiguestrengthofconcrete

fck = 0.85 bcc(t0)fcde1–

250n

fcd = 1.0 fck/ 1.5

bcc(t0)=coefficientforconcretestrengthatfirstloadapplication

■ =

bcc (t0) where = exp s 1 – 28t0

0.5

where t0 = timeofthestartofthecyclicloadingonconcreteindays s = 0.2forcementofstrengthClassesCEM42.5R,CEM52.5NandCEM52.5R(ClassR) = 0.25forcementofstrengthClassesCEM32.5R,CEM42.5(ClassN) = 0.38forcementofstrengthClassCEM32.5(ClassS)

Themaximumvaluefortheratiosc,max/fcd,fatisgiveninTable12.2.

12.3

PD 6687-27.6.2

BS EN 1992-1-1table 6.2

BS EN 1992-1-16.8.7(2)

74

Table 12.2Values for sc,max /fcd, fat

Concrete strength sc,max /fcd, fat

fck≤50MPa ≤0.9

fck>50MPa ≤0.8

For members not requiring design shear reinforcement for the ultimate limit state it may beassumedthattheconcreteresistsfatigueduetosheareffectswherethefollowingapply:

for ≥ 0:

≤ 0.5 + 0.45≤ 0.9 up to C50/60

≤ 0.8 greater than C55/67

VEd,min

VEd,max

VEd,max

VRd,c

VEd,min

VRd,c

for < 0:

≤ 0.5

VEd,min

VEd,max

VEd,max

VRd,c

VEd,min

VRd,c

where VEd,max =designvalueofthemaximumappliedshearforceunderfrequentload

combination VEd,min = isthedesignvalueoftheminimumappliedshearforceunderfrequentload

combinationinthecross-sectionwhereVEd,maxoccurs VRd,c = designvalueforshearresistanceaccordingtoSection7.2.1.

Limiting stress range for reinforcement under tension

Adequate fatigue resistance may be assumed for reinforcing bars under tension if the stressrange under the frequent cyclic load combined with the basic combination does not exceed70MPa forunweldedbarsand 35MPa forweldedbars.

For UK highway bridges, the values in Tables 12.3 and 12.4 may be used for straightreinforcement.ThesearebasedonbarsconformingtoBS4449.ForbarsnotconformingtoBS4449,therulesforbars>16mmdiametershouldbeusedforallsizesunlesstherangesforbars≤16mmdiametercanbejustified.

Table 12.3Limiting stress ranges – longitudinal bending for unwelded reinforcing bars in road bridges, MPa

Span m Adjacent spans loaded Alternate spans loaded

Bars ≤ 16 mm Bars > 16 mm Bars ≤ 16 mm Bars > 16 mm

≤ 3.5 150 115 210 160

5 125 95 175 135

10 110 85 175 135

20 110 85 140 110

30 to 50 90 70 110 85

100 115 90 135 105

≥ 200 190 145 200 155

Notes 1Intermediatevaluesmaybeobtainedbylinearinterpolation.

2ThistableappliestoslabsbutneedonlybeappliedtothoseslabsthatdonotconformtothecriteriagiveninSection12.1.

12.4

PD 6687-2table 2A

BS EN 1992-1-16.8.7(4)

BS EN 1992-1-16.8.6(1)

PD 6687-27.6.3

75

Fatigue

Table 12.4Limiting stress ranges – transverse bending for unwelded reinforcing bars in road bridges, MPa

Span m Bars ≤ 16 mm Bars > 16 mm

≤3.5 210 160

5 120 90

≥10 70 55

Notes1Intermediatevaluesmaybeobtainedbylinearinterpolation.

2ThistableappliestoslabsbutneedonlybeappliedtothoseslabsthatdonotconformtothecriteriagiveninSection12.1.

IfthestressrangelimitsexceedthevaluesgiveninTables12.3and12.4(e.g.forreinforcementoverthepier),fullfatiguechecksaretobecarriedoutusingthe‘damageequivalentstressrange’method,followingtheguidancegiveninAnnexNNofBSEN1992-2.Thestressrangesarecalculatedusing‘FatigueLoadModel3’,whichrepresentsafour-axlevehiclewithanallupweightof48tonnes.AnnexNNfurtherincreasesthisweightto84tonnesforintermediatesupportsand67tonnesforotherareas.

PD 6687-2table 2B

76

ServiceabilityGeneral

Thecommonserviceabilitylimitstatesconsideredare:

Stresslimitation.■■

Crackcontrol.■■

Deflectioncontrol.■■

Inthecalculationofstressesanddeflections,cross-sectionsshouldbeassumedtobeuncrackedprovidedthattheflexuraltensilestressdoesnotexceedfct,eff.Thevalueoffct,effmaybetakenasfctmorfctm,flprovidedthatthecalculationforminimumtensionreinforcementisalsobasedon the same value. For the purposes of calculating crack widths and tension stiffening fctmshouldbeused.

Stress limitation

Longitudinalcracksmayoccurifthestresslevelunderthecharacteristiccombinationofloadsexceedsacriticalvalue.Suchcrackingmayleadtoareductionofdurability.Intheabsenceofothermeasures,suchasanincreaseinthecovertoreinforcementinthecompressivezoneorconfinement by transverse reinforcement, it isrecommendedthat the compressive stress islimitedtoavalue 0.6 fckinareasexposedtoenvironmentsofexposureclassesXD,XFandXS(seeTable4.2).Inthepresenceofconfinementthemaximumstresslimitis 0.66 fck.

Ifthestressintheconcreteunderthequasi-permanentloadsislessthan 0.45 fck,linearcreepmay be assumed. If the stress in concrete exceeds 0.45 fck, non-linear creep should beconsidered(seeSection3.1.2).

For the appearance unacceptable cracking or deformation may be assumed to be avoidedif, under the characteristic combination of loads, the tensile stress in the reinforcement doesnotexceed 0.8 fyk.Wherethestress iscausedbyan imposeddeformation,thetensilestressshould not exceed 1.0 fyk.The mean value of the stress in prestressing tendons should not

exceed 0.75 fpk. Crack control (Section 13.4) and deflection (Section 13.6) should also be

checked.

Calculation of crack widths

Thecrackwidth,wk,maybecalculatedfromfollowingExpression:

wk=sr,max(esm–ecm)

where sr,max = maximumcrackspacing esm = meanstraininthereinforcementundertherelevantcombinationofloads,

includingtheeffectofimposeddeformationsandtakingintoaccounttheeffectsoftensionstiffening.Onlytheadditionaltensilestrainbeyondthestateofzerostrainoftheconcreteatthesamelevelisconsidered

ecm = meanstrainintheconcretebetweencracks

esm–ecmmaybecalculatedfromtheExpression:

fct,eff

rct,effss – kt

Es

(1 + ae rp,eff) ss

Es

0.6esm – ecm =

where ss = stressinthetensionreinforcementassumingacrackedsection.For

pretensionedmembers,ssmaybereplacedbyDsp,whichisthestressvariationinprestressingtendonsfromthestateofzerostrainoftheconcreteatthesamelevel

13 13.1

13.2

13.3

BS EN 1992-1-17.1

BS EN 1992-27.2(102) & NA

PD 6687-28.1.1

PD 6687-28.1.2

BS EN 1992-1-17.3.4

BS EN 1992-1-17.2(3)

BS EN 1992-1-17.2(5), NA

77

Serviceability

kt = factordependentonthedurationoftheload

= 0.6forshorttermloading

= 0.4forlongtermloading

ae = ratioEs/Ecm

rp,eff = (As+j12Ap' )/Ac,eff

where

Ap' = areaofpre-orpost-tensionedtendonswithinAc,eff.

Ac,eff = effectiveareaofconcreteintensionsurroundingthereinforcementorprestressingtendonsofdepth,hc,ef,wherehc,efisthelesserof2.5(h – d),(h – x)/3orh/2(seeFigure13.3).

j1 = adjustedratioofbondstrengthtakingintoaccountthedifferentdiametersofprestressingandreinforcingsteel:

= (j fs/fp)0.5

j = ratioofbondstrengthofprestressingandreinforcingsteel,accordingtoTable12.1

Ifonlyprestressingsteelisusedtocontrolcracking,j1=j 0.5

fs = largestbardiameterofreinforcingsteel

fp = equivalentdiameteroftendonaccordingtoSection12.2

Insituationswherebondedreinforcementisfixedatreasonablyclosecentreswithinthetensionzone(spacing≤5(c +f/2),themaximumfinalcrackspacingmaybecalculatedfromfollowingExpression(seeFigure13.1):

sr,max=k3c + k1k2k4f/rp,eff

where f = bar diameter.Where a mixture of bar diameters is used in a section, an equivalent

diameter,feq,shouldbeused where feq = (n1f1

2+n2f2)/(n1f1+n2f2) n1 = numberofbarsofdiameterf1 n2 = numberofbarsofdiameterf2 k3 = 3.4 c = covertothelongitudinalreinforcement. Thenominalcover,cnom,maybeused. k1 = coefficientwhichtakesaccountofthebondpropertiesofthebonded

reinforcement = 0.8forhighbondbars = 1.6forbarswithaneffectivelyplainsurface(e.g.prestressingtendons)

f

Concretetension surface

Crack spacing predictedby Expression (7.14)

Crack spacing predicted byExpression (7.11)

Actual crack width

Neutral axis

(h – x)

5(c + f/2)

c

w

Figure 13.1Crack width, w, at concrete surface relative to distance from bar

BS EN 1992-1-1fig. 7.2

BS EN 1992-1-1Exp. (7.11)

78

k4 = 0.425 k2 = coefficientwhichtakesaccountofthedistributionofstrain = 0.5forbending = 1.0forpuretension Forcasesofeccentrictensionorforlocalareas,intermediatevaluesofk2should

beusedwhichmaybecalculatedfromtherelation: k2 = (e1+e2)/(2e1) e1 = greatertensilestrainattheboundariesofthesectionconsidered,assessedon

thebasisofacrackedsection e2 = lessertensilestrainattheboundariesofthesectionconsidered,assessedonthe

basisofacrackedsection

Wherethespacingofthebondedreinforcementexceeds5(c+f/2)(seeFigure13.1)orwherethereisnobondedreinforcementwithinthetensionzone,anupperboundtothecrackwidthmaybefoundbyassumingamaximumcrackspacing:

sr,max=1.3(h – x)

Wheretheanglebetweentheaxesofprincipalstressandthedirectionofthereinforcement,formembersreinforcedintwoorthogonaldirections,issignificant(>15°),thenthecrackspacingsr,maxmaybecalculatedfromthefollowingexpression:

sr,max=1/(cosy/sr,max,y+siny/sr,max,z)

where y = anglebetweenthereinforcementinthe ydirectionandthedirectionofthe

principaltensilestress sr,max,y= crackspacingcalculatedinthey-direction sr,max,z= crackspacingcalculatedinthez-direction

Alimitingcalculatedcrackwidth wmax ,takingaccountoftheproposedfunctionandnatureofthestructureandthecostsoflimitingcracking,shouldbeestablished.Duetotherandomnatureof the cracking phenomenon, actual crack widths cannot be predicted. However, if the crackwidths calculated in accordance with the models given in BS EN 1992-2 are limited to thevaluesgiveninTable13.1,theperformanceofthestructureisunlikelytobeimpaired.

The decompression limit requires that all concrete within a certain distance of bondedtendons or their ducts should remain in compression under the specified loading. Thedistancewithinwhichallconcreteshouldremainincompressionshouldbetakenasthevalueofcmin,dur.WherethemosttensilefaceofasectionisnotsubjecttoXDorXSexposurebutanother face is, the decompression limit should require all tendons within 100 mm of asurface subject toXD orXS exposure to have a depth cmin,dur of concrete in compressionbetweenthemandsurfacessubjecttoXDorXSexposure.

Sincethedecompressionlimitof100mmislikelytobegreaterthanthecoverrequiredfordurability,thisintroducesananomaly.Forexample,only50mmofconcreteincompressionmight be deemed adequate to protect the tendons, whereas 60 mm of concrete incompressionplus40mmnotincompressionwouldnot,whichisclearlyillogical.Changingthedistancefromtherecommendedvalueof100mmtothecoverrequiredfordurability,cmin,dur,ismorelogical.

In some situations, such as structures cast against the ground, cnom will be significantlygreaterthanthecoverrequiredfordurability.Wheretherearenoappearancerequirementsitisreasonabletodeterminethecrackwidthatthecoverrequiredfordurabilityandverifythatitdoesnotexceedtherelevantmaximumcrackwidth.Thismaybedonebymultiplyingthecrackwidthdeterminedatthesurfaceby(cmin,dur,+Dcdev)/cnomtogivethecrackwidthat the cover required for durability, and verifying that it is not greater than wmax. Thisapproach assumes that the crack width varies linearly from zero at the bar. Given theaccuracyofcrackcalculationmethodsthissimplificationisconsideredreasonable.

BS EN 1992-2NA. NA.2.2

BS EN 1992-27.3.1(105) & NA

BS EN 1992-1-1Exp. (7.14)

PD 6687-2 8.2.1b)

PD 6687-2 8.2.2

79

Serviceability

13.4

Table 13.1Recommended values of wmax and relevant combination rules

Exposure classa Reinforced members and prestressed members without bonded tendons

Prestressed members with bonded tendons

Quasi-permanent load combinationb (mm)

Frequent load combinationb (mm)

X0, XC1 0.3c 0.2

XC2, XC3, XC4 0.3 0.2d

XD1, XD2, XD3 XS1, XS2, XS3

0.3 0.2e anddecompression

KeyaTheexposureclassconsidered,includingattransfer,appliestothemostsevereexposurethesurface

willbesubjecttoinservice.

bForthecrackwidthchecksundercombinationswhichincludetemperaturedistribution,theresultingmemberforcesshouldbecalculatedusinggrosssectionconcretepropertiesandself-equilibrating thermalstresseswithinasectionmaybeignored.

cForX0,XC1exposureclasses,crackwidthhasnoinfluenceondurabilityandthislimitissettoguaranteeacceptableappearance.Intheabsenceofappearanceconditionsthislimitmayberelaxed.

dFortheseexposureclasses,inaddition,decompressionshouldbecheckedunderthequasipermanentcombinationofloads.

e0.2appliestothepartsofthememberthatdonothavetobecheckedfordecompression.

Control of cracking

WheretheminimumreinforcementgivenbySection13.5isprovided,crackwidthsareunlikelytobeexcessiveif:

Forcrackingcausedpredominantlybyrestraint,thebarsizesgiveninTable13.2arenot■■

exceededwherethesteelstressisthevalueobtainedimmediatelyaftercracking(i.e.ssinSection13.5).Forcrackscausedmainlybyloading,eithertheprovisionsofTable13.2ortheprovisionsof■■

Table13.3arecompliedwith.Thesteelstressshouldbecalculatedonthebasisofacrackedsectionundertherelevantcombinationofactions.

Forpre-tensionedconcrete,wherecrackcontrolismainlyprovidedbytendonswithdirectbond,Tables13.2and13.3maybeusedwithastressequaltothetotalstressminusprestress.Forpost-tensionedconcrete,wherecrackcontrolisprovidedmainlybyordinaryreinforcement,thetablesmaybeusedwiththestressinthisreinforcementcalculatedwiththeeffectofprestressingforcesincluded.

Themaximumbardiametershouldbemodifiedasfollows:

Bending(atleastpartofsectionincompression):

fs = f*s ( fct,eff/2.9)kchcr

2 (h – d)

Tension(uniformaxialtension):

fs = f*s ( fct,eff/2.9) hcr/(8(h – d))

where fs = adjustedmaximumbardiameter fs = maximumbarsizegivenintheTable13.2 h = overalldepthofthesection hcr = depthofthetensilezoneimmediatelypriortocracking,consideringthe

characteristicvaluesofprestressandaxialforcesunderthequasi-permanentcombinationofactions

d = effectivedepthtothecentroidoftheouterlayerofreinforcement

BS EN 1992-2 &NA, table NA.2

BS EN 1992-1-1 7.3.3(2)

80

Whereallthesectionisundertensionh–distheminimumdistancefromthecentroidofthelayer of reinforcement to the face of the concrete (consider each face where the bar is notplacedsymmetrically).

Table 13.2Maximum bar diameters for crack control

Steel stress (MPa) Maximum bar size (mm) for crack widths of

0.4 mm 0.3 mm 0.2 mm

160 40 32 25

200 32 25 16

240 20 16 12

280 16 12 8

320 12 10 6

360 10 8 5

400 8 6 4

450 6 5 —

Table 13.3Maximum bar spacing for crack control

Steel stress (MPa) Maximum bar spacing (mm) for maximum crack widths of

0.4 mm 0.3 mm 0.2 mm

160 300 300 200

200 300 250 150

240 250 200 100

280 200 150 50

320 150 100 —

360 100 50 —

Minimum reinforcement areas of main bars

Ifcrackcontrolisrequired,aminimumamountofbondedreinforcementisrequiredtocontrolcrackinginareaswheretensionisexpected.TherequiredminimumareasofreinforcementAs,minmaybecalculatedasfollows.Inprofiledcross-sectionslikeT-beamsandboxgirders,minimumreinforcementshouldbedeterminedfortheindividualpartsofthesection(webs,flanges).

As,min=kckfct,effAct/ss

where Act = areaofconcretewithintensilezone.Thetensilezoneisthatpartofthesection

whichiscalculatedtobeintensionjustbeforeformationofthefirstcrack ss = absolutevalueofthemaximumstresspermittedinthereinforcement

immediatelyafterformationofthecrack.Thismaybetakenastheyieldstrengthofthereinforcement,fyk.Alowervaluemay,however,beneededtosatisfythecrackwidthlimitsaccordingtothemaximumbarsizeorspacingindicatedinTables13.2and13.3.

fct,eff = meanvalueofthetensilestrengthoftheconcreteeffectiveatthetimewhenthecracksmayfirstbeexpectedtooccur.

= fctmorlower( fctm(t))ifcrackingisexpectedearlierthan28days

Aminimumvalueof2.9MPashouldbetaken k = coefficientwhichallowsfortheeffectofnon-uniformself-equilibratingstresses,

whichleadtoareductionofrestraintforces = 1.0forwebswithh≤300mmorflangeswithwidthslessthan300mm,

intermediatevaluesmaybeinterpolated

13.5

BS EN 1992-1-1table 7.3N

BS EN 1992-1-17.3.2(1)

BS EN 1992-27.3.2(102)

BS EN 1992-1-1table 7.2N

BS EN 1992-1-1Exp. (7.1)

BS EN 1992-27.3.2(105)

81

Serviceability

= 0.65forwebswithh≥800mmorflangeswithwidthsgreaterthan800mm,intermediatevaluesmaybeinterpolated

kc = coefficientwhichtakesaccountofthestressdistributionwithinthesectionimmediatelypriortocrackingandofthechangeoftheleverarm:

= 1.0forpuretension. = 0.4forpurebending. = 0.4[1–(sc/(k1(h/h*)fct,eff))]≤1forrectangularsectionsandwebsofbox

sectionsandT-sections. = 0.9Fcr/(Actfct,eff)≥0.5forflangesofboxsectionsandT-sections. sc = meanstressoftheconcreteactingonthepartofthesectionunderconsideration. = NEd/bh NEd = axialforceattheserviceabilitylimitstateactingonthepartofthecross-section

underconsideration(compressiveforcepositive).NEdshouldbedeterminedconsideringthecharacteristicvaluesofprestressandaxialforcesundertherelevantcombinationofactions

h* = MIN{h;1.0} k1 = coefficientconsideringtheeffectsofaxialforcesonthestressdistribution: = 1.5ifNEdisacompressiveforce = 2h*/3hifNEdisatensileforce Fcr = absolutevalueofthetensileforcewithintheflangeimmediatelypriortocracking

duetothecrackingmomentcalculatedwithfct,eff

SeealsoSection15.2.1forasimplifiedmethodofcalculatingminimumareaofsteel.

Inflangedcross-sectionslikeT-beamsandboxgirders,thedivisionintopartsshouldbeasindicatedinFigure13.2.

sc, web

sc, flange

fct,eff fct,eff

Flange Flange

Web

Sflange

Sm

Sweb

Web Flange

a) Components b) Stresses

Figure 13.2Example for a division of a flanged cross-section for analysis of cracking

Bondedtendonsinthetensionzonemaybeassumedtocontributetocrackcontrolwithinadistance≤150mmfromthecentreofthetendon.Thismaybetakenintoaccountbyincludingthetermj1Ap

' DpintheExpressionabovetogive:

As,min=(kckfct,effAct–j1Ap' Dsp)/ss

where Ap

' = areaofpre-orpost-tensionedtendonswithinAc,eff Ac,eff = effectiveareaofconcreteintensionsurroundingthereinforcementor

prestressingtendonsofdepth,hc,ef hc,ef = MIN{2.5(h – d);(h – x)/3;h/2}(seeFigure13.3) j1 = adjustedratioofbondstrengthtakingintoaccountthedifferentdiametersof

prestressingandreinforcingsteel =(j fs/fp)0.5

= j 0.5ifonlyprestressingsteelisusedtocontrolcracking j = ratioofbondstrengthofprestressingandreinforcingsteel,accordingto

Table13.4

BS EN 1992-2fig. 7.101

BS EN 1992-1-1 7.3.2(3)

82

fs = largestbardiameterofreinforcingsteel fp = equivalentdiameteroftendon = 1.6Ap

0.5forbundles = 1.75fwireforsingle7wirestrandswherefwireisthewirediameter = 1.20fwireforsingle3wirestrandswherefwireisthewirediameter Dsp = stressvariationinprestressingtendonsfromthestateofzerostrainofthe

concreteatthesamelevel

Level of steel centroid

Effective tension area, Ac,eff

Effective tension area, Ac,eff

Effective tension area for upper surface, Act,eff

Effective tension area for lower surface, Acb,eff

e2 = 0

e2 = 0

a) Beam

b) Slab

c) Member in tension

e1

e1

e2

e1

hc,ef

hc,ef

hc,ef

hc,ef

h

h d

h d d

x

d

x

Figure 13.3Effective tension area (typical cases)

In prestressed members no minimum reinforcement is required in sections where, under thecharacteristic combination of loads and the characteristic value of prestress, the concrete iscompressedortheabsolutevalueofthetensilestressintheconcreteisbelow fct,eff .

Table 13.4Ratio of bond strength, j , between tendons and reinforcing steel

Prestressing steel j

Pre-tensioned Bonded, post-tensioned

≤ C50/60 ≥ C70/85

Smooth bars and wires Notapplicable 0.3 0.15

Strands 0.6 0.5 0.25

Indented wires 0.7 0.6 0.30

Ribbed bars 0.8 0.7 0.35

NoteForintermediatevaluesbetweenC50/60andC70/85interpolationmaybeused.

BS EN 1992-1-1 Fig 7.1

BS EN 1992-1-1 7.3.2 (4)

BS EN 1992-1-1table 6.2

83

Serviceability

Control of deflection

The calculation method adopted shall represent the true behaviour of the structure underrelevantactionstoanaccuracyappropriatetotheobjectivesofthecalculation.

Memberswhicharenotexpectedtobeloadedabovethelevelwhichwouldcausethetensilestrengthoftheconcretetobeexceededanywherewithinthemembershouldbeconsideredtobeuncracked.Memberswhichareexpectedtocrack,butmaynotbefullycracked,willbehaveinamannerintermediatebetweentheuncrackedandfullycrackedconditionsand,formemberssubjected mainly to flexure, an adequate prediction of behaviour is given in the followingexpression:

a = z aII + (1 – z) aI

where a = deformationparameterconsideredwhichmaybe,forexample,astrain,a

curvature,orarotation.(Asasimplification,amayalsobetakenasadeflection–seebelow)

aI, aII = thevaluesoftheparametercalculatedfortheuncrackedandfullycrackedconditionsrespectively

z = distributioncoefficient(allowingfortensioningstiffeningatasection) = 1– b(ssr /ss)2

= 0foruncrackedsections b = coefficienttakingaccountoftheinfluenceofthedurationoftheloadingorof

repeatedloadingontheaveragestrain = 1.0forasingleshort-termloading = 0.5forsustainedloadsormanycyclesofrepeatedloading ss = stressinthetensionreinforcementcalculatedonthebasisofacrackedsection ssr = stressinthetensionreinforcementcalculatedonthebasisofacrackedsection

undertheloadingconditionscausingfirstcracking

Note:ssr /ssmaybereplacedbyMcr/MforflexureorNcr/Nforpuretension,whereMcristhecrackingmomentandNcristhecrackingforce.

Deformations due to loading may be assessed using the tensile strength and the effectivemodulusofelasticityoftheconcrete.

Table3.1indicatestherangeoflikelyvaluesfortensilestrength.Ingeneral,thebestestimateofthe behaviour will be obtained if fctm is used.Where it can be shown that there are no axialtensilestresses(e.g.thosecausedbyshrinkageorthermaleffects)theflexuraltensilestrength,fctm,fl,maybeused.

fctm,fl = MAX{(1.6– h/1000)fctm;fctm }

where h = totalmemberdepthinmm fctm = meanaxialtensilestrengthfromTable3.1

Forloadswithadurationcausingcreep,thetotaldeformationincludingcreepmaybecalculatedbyusinganeffectivemodulusofelasticityforconcreteaccordingtothefollowingExpression

Ec,eff = Ecm / (1 + h (∞,t0))

where h (∞,t0)=creepcoefficientrelevantfortheloadandtimeinterval(seeSection3.1.2)

Shrinkagecurvaturesmaybeassessedfromthefollowing:

1/rcs=easaeS/I

where 1/rcs = curvatureduetoshrinkage

13.6

BS EN 1992-1-1 7.4.3(2)

BS EN 1992-1-1 7.4.3(3)

BS EN 1992-1-1Exp. (7.18)

BS EN 1992-1-1 7.4.3(4)

BS EN 1992-1-1 3.1.8

BS EN 1992-1-1 7.4.3(5)

BS EN 1992-1-1 7.4.3(6)

84

ecs = freeshrinkagestrain(seeSection3.1.3) S = firstmomentofareaofthereinforcementaboutthecentroidofthesection I = secondmomentofareaofthesection ae = effectivemodularratio = Es/Ec,eff

Sand Ishouldbecalculatedfortheuncrackedconditionandthefullycrackedcondition,thefinalcurvaturebeingassessedusingtheExpressionforaabove.

Themostrigorousmethodofassessingdeflectionsusingthemethodgivenaboveistocomputethe curvatures at frequent sections along the member and then calculate the deflection bynumerical integration. In most cases it will be acceptable to compute the deflection twice,assumingthewholemembertobe in theuncrackedandfullycrackedcondition inturn,andtheninterpolateusingtheExpressionforaabove.

BS EN 1992-1-1 7.4.3(7)

85

Detailing–generalrequirements

Detailing – general requirementsGeneral

The rules given in this section apply to ribbed reinforcement, welded mesh and prestressingtendonsusedinstructuressubjectpredominantlytostaticloading.

Unlessotherwisestated,therulesforindividualbarsalsoapplyforbundlesofbarsforwhichanequivalentdiameterfn=f(nb)0.5shouldbeusedinthecalculations.InthisExpression,nbisthenumberofbarsinthebundle.Avaluefornbshouldbelimitedtofourverticalbarsincompressionandinlappedjoints,andtothreeinallothercases.Thevalueoffnshouldbelessthanorequalto55mm.

Thecleardistancebetween(andthecoverto)bundledbarsshouldbemeasuredfromtheactualexternalcontourofthebundledbars.Barsareallowedtotouchoneanotheratlapsandtheyneednotbetreatedasbundledbarsundertheseconditions.

Spacing of bars

Thespacingofbarsshouldbesuchthatconcretecanbeplacedandcompactedsatisfactorilyforthedevelopmentofbond.

Thecleardistancebetweenindividualparallelbarsorbetweenhorizontallayersofparallelbarsshouldnotbelessthanthe bardiameter, theaggregatesize+ 5mm, or20mm,whicheveristhegreatest.

Wherebarsarepositionedinseparatehorizontallayers,thebarsineachlayershouldbelocatedverticallyaboveeachother.Thereshouldbesufficientspacebetweentheresultingcolumnsofbarstoallowaccessforvibratorstogivegoodcompactionoftheconcrete.

Mandrel sizes for bent bars

Thediametertowhichabarisbentshouldbesuchastoavoiddamagetothereinforcementandcrushingofconcreteinsidethebendofthebar.Toavoiddamagetoreinforcementthemandrelsizeisasfollows: 4f, forbardiameterf≤16mm 7f, forbardiameterf>16mm 20f, formeshbentafterweldingwheretransversebarisonorwithin4fofthebend.

Otherwise 4f, or 7f, asabove.WeldingmustcomplywithISO/FDIS17660-2[22].

Themandreldiameterfmtoavoidcrushingofconcreteinsidethebendneednotbecheckedif:Anchorageofthebardoesnotrequirealengthmorethan5■■ fpasttheendofthebend;andThebarisnotpositionedatanedgeandthereisacrossbar(ofdiameter≥■■ f)insidethebend,andDiametersnotedaboveareused.■■

Otherwisethefollowingminimummandreldiameterfm,minshouldbeused:

fm,min≥Fbt((1/ab)+1/(2f))/fcd

where Fbt = tensileforceinthebaratthestartofthebendcausedbyultimateloads ab = halfthecentretocentrespacingofbars(perpendiculartotheplaneofthe

bend).Forbarsadjacenttothefaceofthemember,ab=cover+0.5f fcd = 0.85 fck/ 1.5

ThevalueoffcdshouldnotbetakengreaterthanthatforconcreteclassC55/67

where fck = characteristiccylinderstrength

14 14.1

14.2

14.3

BS EN 1992-1-1 8.1(1)

BS EN 1992-1-1 8.9.1(1) & (2)

BS EN 1992-1-1 8.9.1(3) & (4)

BS EN 1992-1-1 8.2

BS EN 1992-1-1 8.3(1) & (2)

BS EN 1992-1-1 table 8.1N & NA

BS EN 1992-1-1 8.3(3)

BS EN 1992-1-1 Exp. (8.1)

BS EN 1992-1-13.1.6(1) & NA to BS EN 1992-2

86

Anchorage of bars

General

Allreinforcementshouldbesoanchoredthattheforcesinthemaresafelytransmittedtothesurroundingconcretebybondwithoutcausingcracksorspalling.ThecommonmethodsofanchorageoflongitudinalbarsandlinksareshowninFigures14.1and14.2.

a) Basic anchorage length lb,rqd, for any shape measured along the centreline

lb,rqd

f

lbd

b) Equivalent anchorage length for standard bend 90º a < 150º where lb,eq = a1 lb,rqd

lb,eq

≥5f

a

e) Welded transverse bar where lb,eq = a4 lb,rqd

lb,eq

≥5ff≥0.6f

c) Equivalent anchorage length for standard hook where lb,eq = a1 lb,rqd

lb,eq

≥150º

≥5f

d) Equivalent anchorage length for standard loop where lb,eq = a1 lb,rqd

lb,eq

Keylbd = designanchoragelengthlb,req = basicanchoragelengthlb,eq = equivalentanchoragelength

Figure 14.1Methods of anchorage other than by a straight bar

c) Two welded transverse bars

d) Single welded transverse bar

f f f f

5f,but≥50mm

10f,but≥70mm

≥0.7f

≥2f ≥1.4f≥10mm

≥10mm

≥20mm

≤50mm

Figure 14.2Anchorage of links

14.4

14.4.1

BS EN 1992-1-1 8.4(1) & (2)

BS EN 1992-1-1 fig. 8.1

BS EN 1992-1-1 fig. 8.5

87

Detailing–generalrequirements

Design anchorage length lbd

Thedesignanchoragelengthlbdis

lbd =(a1a2a3a4a5)lb,rqd≥lb,min

where a1 = factordealingwiththeformofbarassumingadequatecover

=0.7forbentbarsintensionwherecd>3f,wherecdisdefinedinFigure14.3=1.0otherwiseforbarsintension=1.0forbarsincompression

a2 = factordealingwitheffectofconcreteminimumcover

=1–0.15(cd–f)/f≥0.7forstraightbarsintensionbut≤1.0=1–0.15(cd–3f)/f≥0.7forbentbarsintensionbut≤1.0=1.0otherwiseforbarsintension=1.0forbarsincompression

a3 = factordealingwitheffectofconfinementbytransversereinforcement

=1.0generally

a4 = factordealingwiththeeffectofinfluenceofweldedtransversebars

=0.7foraweldedtransversebarconformingwithFigure14.1e)=1.0otherwise

a5 = factordealingwiththeeffectofpressuretransversetotheplaneofsplittingalongthedesignanchoragelength

=1.0generally

lb,rqd = basicanchoragelength(seeSection14.4.3) lb,min = theminimumanchoragelength ≥ MAX{0.3lb,rqd;10f;100mm}intensionbars;and ≥ MAX{0.6lb,rqd;10f;100mm}incompressionbars.

Theproduct(a2a3a5)≥ 0.7

Figure 14.3Values of

cd for beams and slabs

a) Straight bars cd = minimum of a/2, c or c1

b) Bent or hooked bars cd = minimum of a/2 or c1

c1

c1

c

a a

Note

candc1aretakentobenominalcovers

Basic anchorage length lb,rqd

lb,rqd = basicanchoragelengthrequired=(f/4)(ssd/fbd)

where f = diameterofthebar ssd= designstressinthebaratthepositionfromwheretheanchorageismeasured fbd = ultimatebondstress(seeSection14.5)

Theanchoragelengthshouldbemeasuredalongthecentrelineofthebarinbentbars.

14.4.2

14.4.3

BS EN 1992-1-1 8.4.4(1) & table 8.2

BS EN 1992-1-1 fig. 8.3

BS EN 1992-1-1 8.4.3

88

Equivalent anchorage length lb,eq

Asasimplification

FortheshapesshowninFigure14.1b)tod)anequivalentanchoragelength■■ lb,eqmaybeusedwherelb,eq=a1lb,rqd.

ForthearrangementshowninFigure14.1e)■■ lb,eq=a4lb,req.

Ultimate bond stress

Theultimatebondstress,fbd,forribbedbarsmaybetakenas(seealsoTable14.1)

fbd=2.25n1n2fctd

where n1 = coefficientrelatedtothequalityofthebondconditionandthepositionofthebar

duringconcreting = 1.0for‘good’bondconditions(seeFigure14.4fordefinition) = 0.7forallothercasesandforbarsinstructuralelementsbuiltusingslipforms n2 = coefficientrelatedtobardiameter = 1.0forbardiameter≤32mm = (132–f)/100forbardiameter>32mm fctd = (actfctk,0.05/gC)isthedesignvalueoftensilestrengthusingthevalueoffctk,0.05

obtainedfromTable3.1,act= 1.0 andgC= 1.5. Duetothebrittlenessofhigherstrengthconcretefctk,0.05shouldbelimitedheretothevalueforC60/75,unlessitcanbeverifiedthattheaveragebondstrengthincreasesabovethislimit

Directionofconcreting Directionofconcreting

Directionofconcreting

Directionofconcreting

Key

b) h 250 mm d) h > 600 mm

hh

300

c) h > 250 mm

250

a) 45º a 90º

a

‘good’bondconditions

‘poor’bondconditions

Figure 14.4Description of bond conditions

14.4.4

14.5

BS EN 1992-1-1 8.4.4(2)

BS EN 1992-1-1 8.4.2(2)

BS EN 1992-2 3.1.6(102) & NA

BS EN 1992-1-1 fig. 8.2

89

Detailing–generalrequirements

Table 14.1 Design bond stress for different bond conditions

Design bond stress f bd (N/mm2)

C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75

Good bond & f ≤ 32 mm

2.7 3.0 3.3 3.8 4.1 4.4 4.5 4.7

Good bond & f = 40 mm

2.5 2.8 3.0 3.5 3.7 4.0 4.1 4.3

Poor bond & f ≤ 32 mm

1.9 2.1 2.3 2.6 2.8 3.0 3.2 3.3

Poor bond & f = 40 mm

1.7 1.9 2.1 2.4 2.6 2.8 2.9 3.0

Anchorage of tendons at ULS

The anchorage of tendons should be checked in sections where the concrete tensile stressexceeds fctk,0.05 ( fctk,0.05 should not exceed the value for class C60/75 concrete). The total

anchoragelengthforatendonwithastressspdis:

lbpd=lpt2+(a2f(spd–spm,∞)/fbpd)

where lpt2=1.2(a1a2fspm,0/fbpt)

where a1 = 1.0forgradualreleaseofprestressand1.25forsuddenrelease spm,0 = stressinthetendonjustafterrelease fbpt = np1n1fctd(t) np1 = 2.7forindentedwiresand3.2for3-and7-wirestrands n1 = 1.0forgoodbondconditionsand0.7otherwise fctd(t) = designtensilevalueofstrengthatthetimeofrelease = 1.0 0.7fctm(t)/ 1.5

fctm(t) = (bcc(t))afctm

bcc(t) = coefficientwhichdependsontheageofloading

=exp {s[1–( 0.5]}28t

)

s = coefficientwhichdependsontypeofcement(seeSection3.1.2) = 0.20forcementstrengthclassesCEM42.5R,CEM52.5NandCEM52.5R(ClassR) = 0.25forcementstrengthclassesCEM32.5R,CEM42.5N(ClassN) = 0.38forcementstrengthclassCEM32.5(ClassS) t = ageofconcreteindays fctm = meanvalueofaxialtensilestrengthofconcrete(seeTable3.1) a =1fort <28 =2/3fort ≥28 a2 = 0.25forcirculartendonsand0.19for3-and7-wirestrands f = nominaldiameterofthetendon spd = tendonstresscorrespondingtotheforcecalculatedforacrackedsection spm,∞ = prestressafteralllosses fbpd = np2n1fctd,wherenp2=1.4forindentedwiresand1.2for7-wirestrands.

n1isdescribedinSection14.5

14.6

BS EN 1992-1-1 8.10.2.3

BS EN 1992-1-1 Exp. (8.21)

90

Anchorage of tendons at transfer of prestress

Thebasicvalueofthetransmissionlengthatthereleaseoftendons,lpt,isgivenby:

lpt=a1a2fspm,0/fbpt

where a1 = 1.0forgradualrelease = 1.25forsuddenrelease a2 = 0.25fortendonswithcircularcross-section = 0.19for3-and7-wirestrands f = nominaldiameteroftendon spm,0 = tendonstressjustafterrelease fbpt = bondstress = np1n1fctd(t)

where np1 = coefficientthattakesintoaccountthetypeoftendonandthebond

situationatrelease = 2.7forindentedwires = 3.2for3-and7-wirestrands n1 =1.0forgoodbondconditions = 0.7otherwise,unlessahighervaluecanbejustifiedwithregardtospecial

circumstancesinexecution fctd(t) = designtensilevalueofstrengthattimeofrelease(seeSection14.6)

Thedesignvalueofthetransmissionlengthshouldbetakenasthelessfavourableoftwovalues,dependingonthedesignsituation:

lpt1 =0.8lpt

orlpt2=1.2lptNormallythelowervalueisusedforverificationsoflocalstressesatrelease,thehighervalueforultimatelimitstates(shear,anchorageetc.).

Laps

General

Forces are transmitted from one bar to another by lapping, welding or using mechanicaldevices.

Lapsbetweenbarsshouldnormallybestaggeredandnot located inareasofhighmoments/forces.Allbarsincompressionandsecondaryreinforcementmaybelappedatoneplace.

Lapping bars

LapsofbarsshouldbearrangedasshowninFigure14.5.

Thedesignlaplengthl0is:

l0=a1a2a3a4a5a6lb,rqd≥l0,min

where a6 = (r1/25)0.5.1<a6<1.5(seeTable14.2) r1 = percentageofreinforcementlappedwithin0.65l0fromthecentre lineofthelap

beingconsidered l0,min≥ MAX{0.3a6lb,rqd;15h;200mm}

a1,a2,a3,a4anda5aredescribedinSection14.4.2

14.7

14.8

14.8.1

14.8.2

BS EN 1992-1-1 8.7

BS EN 1992-1-1 8.7.2(2) & 8.7.3

BS EN 1992-1-1 Exp. (8.10)

BS EN 1992-1-1 8.10.2.2(2)

BS EN 1992-1-1 Exp. (8.16)

91

Detailing–generalrequirements

Table 14.2Values of coefficient a6

r1, % lapped bars relative to total cross-sectional area

< 25% 33% 50% > 50%

a6 1.0 1.15 1.4 1.5

Fs

Fs

Fs

Fs

Fs

Fs

l0≥0.3l0

f

a

≤50mm

≥20mm

≤4f

≥2f

Figure 14.5Arranging adjacent lapping bars

Lapping fabric

LapsoffabricshouldbearrangedasshowninFigure14.6.

Whenfabricreinforcementislappedbylayering,thefollowingshouldbenoted:

Calculatedstressinthelappedreinforcementshouldnotbemorethan80%ofthe■■

designstrength;ifnot,themomentofresistanceshouldbebasedontheeffectivedepthtothelayerfurthestfromthetensionfaceandthecalculatedsteelstressshouldbeincreasedby25%forthepurposesofcrackcontrol.Permissiblepercentageoffabricmainreinforcementthatmaybelappedinanysectionis:■■

100%if(As/s)≤1200mm2/m(wheresisthespacingofbars)60%ifAs/s>1200mm2/m.Allsecondaryreinforcementmaybelappedatthesamelocationandtheminimumlap■■

lengthl0,minforlayeredfabricisasfollows:

≥150mmforf≤6mm≥250mmfor6mm<f<8.5mm≥350mmfor8.5mm<f<12mm

Thereshouldgenerallybeatleasttwobarpitcheswithinthelaplength.Thiscouldbereducedtoonebarpitchforf≤6mm.

Figure 14.6Lapping of

welded fabric

a) Intermeshed fabric (longitudinal section)

b) Layered fabric (longitudinal section)

Fs

Fs

Fs

Fs

l0

l0

14.8.3BS EN 1992-1-1 8.7.5

BS EN 1992-1-1 fig. 8.10

BS EN 1992-1-1 8.7.5.1(7)8.7.5.2(1)

BS EN 1992-1-1 fig. 8.7

92

14.8.4

14.8.5

Transverse reinforcement

Transversereinforcementisrequiredinthelapzonetoresisttransversetensionforces.

Wherethediameterofthelappedbarislessthan20mmorthepercentageofreinforcementlappedatanysectionislessthan25%,thenanytransversereinforcementorlinksnecessaryforother purposes may be deemed sufficient for the transverse tensile forces without furtherjustification.

Whentheaboveconditionsdonotapply,transversereinforcementshouldbeprovidedasshowninFigure14.7.Wheremorethan50%ofbarsarelappedatonesectionandthespacingbetweenadjacentlaps(dimensionainFigure14.5)<10f,thetransversereinforcementshouldbeintheformoflinksorUbarsanchoredintothebodyofthesection.

InFigure14.7,thetotalareaoftransversereinforcementatlapsSAst>Asofonelappedbar.

Figure 14.7Transverse

reinforcement for lapped splices

a) Bars in tension

b) Bars in compression

Fs

Fs

FsFs

l0

l0

l0/3 l0/3

l0/3 l0/3

SAst/2 SAst/2

SAst/2 SAst/2

4f 4f

≤150mm

≤150mm

Lapping large bars

Forbarslargerthan 40mm indiameterthefollowingadditionalrequirementsapply:

Barsshouldbeanchoredusingmechanicaldevices.Asanalternativetheymaybeanchored■■

asstraightbars,butlinksshouldbeprovidedasconfiningreinforcement.■■■ Barsshouldnotbelappedexceptinsectionswithaminimumdimensionof1morwherethestressisnotgreaterthan80%oftheultimatestrength.

Intheabsenceoftransversecompression,transversereinforcement,inadditiontothat■■

requiredforotherpurposes,shouldbeprovidedintheanchoragezoneatspacingnotexceeding5timesthediameterofthelongitudinalbar.ThearrangementshouldcomplywithFigure14.8.

BS EN 1992-1-1 fig. 8.9

BS EN 1992-1-1 8.8

BS EN 1992-1-1 8.7.4

93

Detailing–generalrequirements

BS EN 1992-1-1 fig. 8.11

Figure 14.8Additional

reinforcement in an anchorage for

large diameter bars where there

is no transverse compression

Anchoredbar Continuingbar

a) n1 = 1, n2 = 2 b) n1 = 2, n2 = 2

SAsh≥0.5As1SAsh≥0.25As1

SAsv≥0.5As1 SAsv≥0.5As1

As1 As1

Note

n1=numberoflayers,n2=numberofbars

94

15 15.1

15.2

15.2.1

Detailing – particular requirementsGeneral

Thissectiongivesparticular requirements fordetailingofstructuralelements.Theseare inadditiontothoseoutlinedinSections13and14.

Beams

Longitudinal bars

TheareaoflongitudinalreinforcementshallnotbetakenaslessthanAs,min

As,min=0.26(fctm/fyk)btd≥0.0013btd

where fctm = meanaxialtensilestrengthofconcrete(seeTable3.1) fyk = characteristicyieldstrengthofreinforcement bt = meanwidthofthetensionzone;foraT-beamwiththeflangeincompression,only

thewidthofthewebistakenintoaccountincalculatingthevaluebt d = effectivedepthValuesofAs,minforvariousstrengthclassesareprovidedinTable15.1

Thecross-sectionalareaoftensionorcompressionreinforcementis 0.04Ac outsidelaplocations.

Any compression longitudinal reinforcement which is included in the resistance calculationshouldbeheldbytransversereinforcementwithspacingnotgreaterthan15timesthediameterofthelongitudinalbar.

Wherethedesignofasectionhasincludedthecontributionofanylongitudinalcompressionreinforcement in the resistance calculation, such longitudinal compression reinforcementshould be effectively restrained by transverse reinforcement. Effective restraint may beachievedbysatisfyingallofthefollowingconditions.

Linksshouldbesoarrangedthateverycornerandalternatebarorgroupinanouter■■

layerofcompressionreinforcementisheldinplacebyalinkanchoredinaccordancewithFigure14.2a)orb).Allothercompressionreinforcementshouldbewithin150mmofabarheldinplaceby■■

alink.Theminimumsizeofthetransversereinforcementandlinks,wherenecessary,shouldbe■■

notlessthan6mmoronequarterofthediameterofthelongitudinalbars,whicheverisgreater.

Table 15.1Minimum area of longitudinal reinforcement as a proportion of btd

Strength class

C25/30 C28/35 C30/37 C32/40 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75 C70/85

As,min as a % of btd

0.13 0.14 0.15 0.16 0.17 0.18 0.20 0.21 0.22 0.23 0.24

For members prestressed with permanently unbonded tendons or with external prestressingcables,itshouldbeverifiedthattheultimatebendingcapacityislargerthantheflexuralcrackingmoment.Acapacityof1.15timesthecrackingmomentissufficient.

BS EN 1992-1-1 9.1

BS EN 1992-1-1 9.2.1.1

BS EN 1992-1-1 9.2.1.2(3)

PD 6687-210.2

BS EN 1992-1-1 9.2.1.1(4)

95

Detailing–particularrequirements

Curtailment

Sufficientreinforcementshouldbeprovidedatallsectionstoresisttheenvelopeoftheactingtensileforce.Theresistanceofbarswithintheiranchoragelengthsmaybetakenintoaccountassuminglinearvariationofforce.

Thelongitudinaltensileforcesinthebarsincludethosearisingfrombendingmomentsandthosefromthetrussmodelforshear.AsmaybeseenfromFigure15.1,thoseforcesfromthetrussmodelforshearmaybeaccommodatedbydisplacingthelocationwhereabarisnolongerrequiredforbendingmomentbyadistanceofalwhere

al=z(coty–cota)/2

where y = strutangleusedforshearcalculations(seeFigure7.3) a = angleoftheshearreinforcementtothelongitudinalaxis(seeFigure7.3)

Forallbuthighshearcoty=2.5;forverticallinkscota=0;sogenerallyal=1.25z.

Hoggingreinforcement

EnvelopeofMEd/z +NEd

ActingtensileforceFs

ResistingtensileforceFRs

Saggingreinforcement

lbd

lbd

lbd

lbd

lbd

lbd

lbd

lbd

al

al

DFtd

DFtd

Figure 15.1Illustration of the curtailment of longitudinal reinforcement, taking into account the effect of inclined cracks and the resistance of reinforcement within anchorage lengths

Top reinforcement in end supports

In monolithic construction, (even when simple supports have been assumed in design) thesectionatsupportsshouldbedesignedforbendingmomentarisingfrompartialfixityofatleast25%ofthemaximumbendingdesignmomentinspan.

15.2.2

15.2.3

BS EN 1992-1-1fig. 9.2

BS EN 1992-1-1 9.2.1.3

BS EN 1992-1-19.2.1.2(1) & NA

96

Bottom reinforcement in end supports

Theareaofbottomreinforcementprovidedatendswithlittleornofixityassumedinthedesignshould be at least 25% of the area of the steel provided in the span.The bars should beanchoredtoresistaforce,FEd,of

FEd=( |VEd| al /z)+NEd

where

|VEd|= absolutedesignvalueofshearforce NEd = axialforce, al,isasdefinedinSection15.2.2

Theanchorageismeasuredfromthelineofcontactbetweenthebeamandthesupport.

Intermediate supports

Atintermediatesupportsofcontinuousbeams,thetotalareaoftensionreinforcement,As,ofaflanged cross-section should be spread over the effective width of the flange (as defined inFigure15.2).Partofitmaybeconcentratedoverthewebwidth.

beff

beff1 beff2

As

bw

hf

Figure 15.2Placing of tension reinforcement in flanged cross-section

Shear reinforcement

Whereacombinationoflinksandbentupbarsisusedasshearreinforcement,atleast50%ofthereinforcementrequiredshouldbeintheformoflinks.Thelongitudinalspacingofshearassemblies should not exceed 0.75d(1+cota) , and spacing of bent-up bars should notexceed 0.6d(1+cota) where a is the inclination of the shear reinforcement to thelongitudinalaxisofthebeam.Thetransversespacingofthelegsofshearlinksshouldnotexceed0.75d≤600mm .

A minimum area of shear reinforcement should be provided to satisfy the followingExpression:

Asw/(s bwsina)≥0.08fck0.5/fyk

where s = longitudinalspacingoftheshearreinforcement bw= breadthofthewebmember a = angleoftheshearreinforcementtothelongitudinalaxisofthemember. Forverticallinkssina=1.0.

15.2.4

15.2.5

15.2.6

BS EN 1992-1-1 9.2.1.2(2)

BS EN 1992-1-1 fig. 9.1

BS EN 1992-1-1 9.2.2(4),(6)&(7)

BS EN 1992-1-1 9.2.2(5) & NA

97

Detailing–particularrequirements

15.2.7

15.2.8

Torsion reinforcement

Wherelinksarerequiredfortorsion,theyshouldcomplywiththeanchorageshowninFigure15.3.Themaximumlongitudinalspacingofthetorsionlinkssl,maxshouldbe:

sl,max≤MIN{u/8;0.75d(1+cota);h;b}

where u = circumferenceofouteredgeofeffectivecross-section(seeFigure9.1) d = effectivedepthofbeam h = heightofbeam b = breadthofbeam

Thelongitudinalbarsrequiredfortorsionshouldbearrangedsuchthatthereisatleastonebarateachcornerwiththeothersbeingdistributeduniformlyaroundthe innerperipheryofthelinksataspacingnotexceeding350mm.

a1) a2) a3)

a) Recommended shapes b) Shape not recommendedNoteThesecondalternativefora2)shouldhaveafulllaplengthalongthetop

or

Figure 15.3Examples of shapes for torsion links

Indirect supports

Whereabeamissupportedbyabeam,insteadofawallorcolumn,reinforcementshouldbeprovided to resist the mutual reaction.This reinforcement is in addition to that required forother reasons. The supporting reinforcement between two beams should consist of linkssurroundingtheprincipalreinforcementofthesupportingmember.Someoftheselinksmaybedistributedoutsidethevolumeofconcretecommontothetwobeams.SeeFigure15.4.

Figure 15.4Plan section

showing supporting

reinforcement in the intersection

zone of two beams

Supportedbeamwithheighth2(h1≥h2)

Supportingbeamwithheighth1

≤h2/3

≤h2/2

≤h1/3

≤h1/2

BS EN 1992-1-1fig. 9.6

BS EN 1992-1-19.25

BS EN 1992-1-1fig. 9.7

BS EN 1992-1-1 9.2.3

98

15.3

15.3.1

15.3.2

15.3.3

15.3.4

15.4

15.4.1

15.4.2

One-way and two-way spanning slabs

Main (principal) reinforcement

TheminimumandmaximumsteelpercentagesinthemaindirectioninSection15.2.1apply.

The spacing of main reinforcement should not exceed 3h (but not greater than 400mm),wherehisthetotaldepthoftheslab.Inareaswithconcentratedloadsorareasofmaximummomenttheseprovisionsbecomerespectively 2hand ≤250mm .

Secondary (distribution) reinforcement

Secondary reinforcement of not less than 20% of the principal reinforcement should beprovidedinone-wayslabs.

The spacing of secondary reinforcement should not exceed 3.5h (but not greater than450mm).Inareaswithconcentratedloads,orinareasofmaximummoment,theseprovisions

becomerespectively 3h(butnotgreaterthan 400mm).

Reinforcement in slabs near supports

In simply supported slabs, half the calculated span reinforcement should continue up to thesupportandbeanchoredthereininaccordancewithSection14.4.2.

Wherepartialfixityoccursalonganedgeofaslabbutisnottakenintoaccountintheanalysis,thetopreinforcementshouldbecapableofresistingatleast25%ofthemaximummomentinthe adjacent span. This reinforcement should extend at least 0.2 times the length of theadjacentspanmeasuredfromthefaceofthesupport.Atanendsupportthemomenttoberesistedmaybereducedto15%ofthemaximummomentintheadjacentspan.

Shear reinforcement

Aslabinwhichshearreinforcementisprovidedshouldhaveadepthofatleast200mm.

Whereshearreinforcementisprovidedtherulesforbeamsmaybefollowed.

Flat slabs

Details at internal columns

Atinternalcolumns,unlessrigorousserviceabilitycalculationsarecarriedout,topreinforcementwithanareaof0.5Atshouldbeplacedoverthecolumninawidthequaltothesumof0.125times the panel width on either side of the column. At represents the area of reinforcementrequiredtoresistfullnegativemomentfromthesumofthetwohalfpanelsoneachsideofthecolumn. Bottom bars (≥ 2 bars) in each orthogonal direction should be provided at internalcolumnsandthisreinforcementshouldpassthroughthecolumn.

Details at edge and corner columns

ReinforcementperpendiculartoafreeedgerequiredtotransmitbendingmomentsfromtheslabtoanedgeorcornercolumnshouldbeplacedwithintheeffectivewidthbeshowninFigure15.5.

BS EN 1992-1-19.3

BS EN 1992-1-19.3.1.1(1)

BS EN 1992-1-19.3.1.1(3) & NA

BS EN 1992-1-19.3.1.1(3) & NA

BS EN 1992-1-1 9.3.1.2

BS EN 1992-1-1 9.3.2

99

Detailing–particularrequirements

15.4.3

a) Edge column b) Corner column

Noteyisthedistancefromtheedgeoftheslabtotheinnermostfaceofthecolumn

Slabedge

Slabedge

Slabedge

ycanbe>cy zcanbe>cxandycanbe>cy

be=cx+ybe=z+y/2

cycy

cxcx

y

y

z

Figure 15.5Effective width, be, of a flat slab

Punching shear reinforcement

Wherepunchingshearreinforcementisrequired,itshouldbeplacedbetweentheloadedarea /columnand 1.5dinsidethecontrolperimeteratwhichreinforcementisnolongerrequired.

The spacing of link legs around a perimeter should not exceed 1.5d within the first controlperimeter(2dfromtheloadedarea)andshouldnotexceed2dforperimetersoutsidethefirstcontrolperimeter(seeFigure15.6).

Outerperimeterofshearreinforcement

Outercontrolperimeteruout

≤1.5d a1.5d

0.5d

≤0.75d

st

sr

A A

Notes1ForsectionA–A

refertoFigure15.72Nationalvalueshavebeenused

Keya≤2.0dif>2d

fromcolumn

Figure 15.6Layout of flat slab shear reinforcement

BS EN 1992-1-1fig. 9.9

BS EN 1992-1-1 9.4.1(2) & (3)

BS EN 1992-1-1 9.4.2(1)

BS EN 1992-1-1 9.4.3

100

BS EN 1992-1-19.5.3(1) & NA

BS EN 1992-1-1 9.4.3(2)

BS EN 1992-1-1 9.5.2 & NA

15.5

15.5.1

15.5.2

Outercontrolperimeterrequiringshearreinforcement

Outercontrolperimeternotrequiringshearreinforcement,uout

≤1.5d

>0.3d≤0.5d

sr≤0.75d

Figure 15.7Section A – A from Figure 15.6: spacing of punching shear reinforcing links

Theintentionistoprovideanevendistribution/densityofpunchingshearreinforcementwithinthezonewhereitisrequired(seeSection8.8).

Thecontrolperimeteratwhichshearreinforcementisnotrequired,Uout,shouldbecalculatedfromthefollowingExpression:Uout=bVEd/(VRd,cd)

Theoutermostperimeterofshearreinforcementshouldbeplacednotgreaterthan1.5dwithinUout.

Whereshearreinforcementisrequired,theareaofalinkleg,Asw,minisgivenbythefollowingExpression:

Asw,min(1.5sina+cosa)/(srst)≥0.08fck0.5/fyk

where srandst = spacing of shear reinforcement in radial and tangential directions respectively

(seeFigure15.6)

Columns

Longitudinal reinforcement

Longitudinalbarsshouldhaveadiameterofnotlessthan 12mm.

ThetotalamountoflongitudinalreinforcementshouldnotbelessthanAs,min:

As,min≥MAX{0.1NEd/fyd;0.002Ac}

where NEd= designaxialcompressionforce fyd = designyieldstrengthofthereinforcement Ac = cross-sectionalareaofconcrete

The area of longitudinal reinforcement should not exceed 0.04Acoutside lap locations.Thislimitshouldbeincreasedto0.08Acatlaps.

Transverse reinforcement (links)

Thediameterofthetransversereinforcement(links,loopsorhelicalspiralreinforcement)shouldnotbelessthan6mmoronequarterofthediameterofthelongitudinalbars,whicheverisgreater.

BS EN 1992-1-1 6.4.5(4) & NA

BS EN 1992-1-1 fig. 9.10

101

Detailing–particularrequirements

15.6

15.6.1

15.6.2

15.6.3

Thespacingofthetransversereinforcementalongthecolumnshouldnotexceed:

20timesthediameterofthelongitudinalbar,or■■

thelesserdimensionofthecolumn,or■■

400mm.■■

Themaximumspacingrequiredaboveshouldbereducedbyafactorof0.6:

Insectionswithinadistanceequaltothelargerdimensionofthecolumncross-section■■

aboveandbelowabeamorslab.Nearlappedjoints,ifthemaximumdiameterofthelongitudinalbarsisgreaterthan14mm.■■

Aminimumof3barsevenlyplacedinthelaplengthisrequired.

Wherethedirectionofthelongitudinalbarschanges,thespacingoftransversereinforcementshouldbecalculatedtakingintoaccountthetransverseforces involved.Theseeffectsmaybeignoredifthechangeofdirectionislessthanorequalto1in12.

Wherethedesignofasectionhasincludedthecontributionofanylongitudinalcompressionreinforcement in the resistance calculation, such longitudinal compression reinforcementshould be effectively restrained by transverse reinforcement. Effective restraint may beachievedbysatisfyingallofthefollowingconditions:

Linksshouldbesoarrangedthateverycornerandalternatebarorgroupinanouter■■

layerofcompressionreinforcementisheldinplacebyalinkanchoredinaccordancewithFigure14.2a)orb).

Allothercompressionreinforcementshouldbewithin150mmofabarheldinplaceby■■

alink.Theminimumsizeofthetransversereinforcementandlinks,wherenecessary,shouldbenot■■

lessthan6mmoronequarterofthediameterofthelongitudinalbars,whicheverisgreater.

For circular columns, where the longitudinal reinforcement is located round the peripheryadequatelateralsupportisprovidedbyacirculartiepassingroundthebarsorgroups.

Walls

Vertical reinforcement

The area of vertical reinforcement should lie between 0.002Ac and 0.04Ac outside lapslocations.Thislimitmaybedoubledatlaps.

Thedistancebetweentwoadjacentbarsshouldnotexceed3timesthewallthicknessor400mm,whicheveristhelesser.

Horizontal reinforcement

Horizontalreinforcementrunningparalleltothefacesofthewallshouldbeprovidedateachsurface. It should not be less than either 25% of the vertical reinforcement or 0.001Ac,whicheverisgreater.

Thespacingbetweentwoadjacenthorizontalbarsshouldnotbegreaterthan400mm.

Transverse reinforcement

Inanypartofawallwherethetotalareaofthevertical reinforcement inthetwofacesexceeds0.02Ac,transversereinforcementintheformoflinksshouldbeprovidedinaccordancewiththerulesforcolumns.

BS EN 1992-1-19.5.3(3) & (4)

BS EN 1992-1-19.5.3(5)

PD 6687-210.2

BS EN 1992-1-19.6.2 & NA

BS EN 1992-1-19.6.3 & NA

BS EN 1992-1-19.6.4

102

PD 6687-2 fig. 6

15.7

Where the main reinforcement is placed nearest to the wall faces, transverse reinforcementshould also be provided in the form of links with at least 4 per m2 of wall area.Transversereinforcementneednotbeprovidedwhereweldedmeshandbarsofdiameterf ≤16mmareusedwithconcretecoverlargerthan2f.

Pile caps

Thedistancefromtheouteredgeofthepiletotheedgeofthepilecapshouldbesuchthatthetieforcescanbeproperlyanchored.Theexpecteddeviationofthepileonsiteshouldbetakenintoaccount.

Reinforcement in a pile cap should be calculated either by using strut-and-tie or flexuralmethodsasappropriate.Themaintensilereinforcementtoresisttheactioneffectsshouldbeconcentrated in stress zones between the tops of the piles.The minimum diameter of barsshouldbe 12mm.

Wherethedistancebetweentheedgeofapileandapierislessthan2d,someoftheshearforceinthepilecapwillbetransmitteddirectlybetweenthepierandthepileviaastruttingaction.Thebasicpunchingperimetercannotbeconstructedwithoutencompassingapartofthesupportasshownforthe2dperimeterinFigure15.8.Insuchcases,itisrecommendedthatthetensionreinforcementisprovidedwithafullanchoragebeyondthelineofthepilecentres and that the shear design takes into consideration of the following in addition tootherverificationsrequiredbyBSEN1992-2:2005.

Flexural shear on plane passing across the full width of the pile cap■■ .Flexuralshearshouldbecheckedonplanespassingacrossthefullwidthofthepilecap,suchastheflexuralshearplaneinFigure15.8.Shearenhancementshouldbetakenintoaccountbyanincreasetotheconcreteresistanceandnotbyareductionintheshearforce.Wherethespacingofthepilecentresislessthanorequalto3pilediameters,theshortshearspanenhancementmaybeappliedoverthewholesection.Wherethespacingisgreaterthanthis,theenhancementmayonlybeappliedonstripsofwidth3pilediameterscentredoneachpile.Theshearspanavshouldbetakenasthedistancebetweenthefaceofthecolumnorwallandtheneareredgeofthepilesplus20%ofthepilediameter.

Maximum permissible shear stress for punching■■ .ThemaximumpermissibleshearstressatthefaceofthepilesandpiersshouldbecheckedinaccordancewithSection8.6.Theshearperimeterforcornerpilesshouldbethepileperimeter,oraperimeterpassingpartiallyaroundthepileandextendingouttothefreeedgesofthepilecap,whicheverisless.

Punching resistance of corner piles.■■ Cornerpilesshouldbecheckedforpunchingresistanceata2dperimeter(withoutsupportenhancement)ignoringthepresenceofthepierorsupportandanyverticalreinforcementwithinit.

FurtherguidanceisgiveninHendy&Smith[20].

Figure 15.8Corner piles

within 2d of a column base

2d perimeterFlexural shear plane across cap

BS EN 1992-2 9.8.1 (103) & NA

PD 6687-2 10.4

103

Detailing–particularrequirements

15.8

15.9

15.9.1

15.9.2

15.9.3

15.9.4

Bored piles

BoredpilesshouldhavetheminimumreinforcementshowninTable15.2. Aminimumofsixlongitudinalbarswithdiameterofatleast16mmshouldbeprovidedwithamaximumspacing of 200 mm around the periphery of the pile.The detailing should comply withBSEN1536[23].

Table 15.2Recommended minimum longitudinal reinforcement in cast-in-place bored piles

Area of cross-section of the pile (Ac) Ac ≤ 0.5 m2 0.5 m2 ≤ 1.0 m2 Ac > 1.0 m2

Minimum area of longitudinal reinforcement (As,bpmin)

≥0.005Ac ≥25cm2 ≥0.0025Ac

Requirements for voided slabs

PD6687-2givesthefollowingguidanceforthedesignofvoidedslabbridgedeckscastinsitu.

Transverse shear

Theeffectsofcelldistortionduetotransverseshearshouldbeconsidered.Inparticular:

Theincreasedstressesinthetransversereinforcementandshearlinksduetocell■■

distortionresultingfromtransverseshearshouldbecalculatedbyanappropriateanalysis(e.g.ananalysisbasedontheassumptionthatthetransverseactionactsinamannersimilartoaVierendeelframe).Theresistanceoftheflangesandwebstothelocalmomentsproducedbythetransverse■■

sheareffectsshouldbeverified.

Thetopandbottomflangesshouldbedesignedassolidslabs,eachtocarryapartoftheglobaltransverseshearforceproportionaltotheflangethickness.

Longitudinal shear

Thelongitudinalribsbetweenthevoidsshouldbedesignedasbeamstoresisttheshearforcesinthelongitudinaldirection,includinganyshearduetotorsionaleffects.

Punching

Punching of wheel loads through the top flange of decks with circular voids will generallyneedtobeconsideredforunusuallythinflanges,typicallythosewithvoiddiametertoslabdepthratiosofgreaterthan0.75.

Transverse reinforcement

Intheabsenceofadetailedanalysis,theminimumtransversereinforcementprovidedshouldbeasfollows:

Inthepredominantlytensileflangeeither1500mm■■ 2/mor1%oftheminimumflangesection,whicheveristhelesser.Inthepredominantlycompressiveflangeeither1000mm■■ 2/mor0.7%oftheminimumflangesection,whicheveristhelesser.

BS EN 1992-1-19.85

BS EN 1992-1-1table 9.6.N

PD 6687-210.5.2

PD 6687-210.5.3

PD 6687-210.5.4

PD 6687-210.5.5

104

BS EN 1992-1-1 fig. 8.14

BS EN 1992-1-1 fig. 8.15

BS EN 1992-1-1 8.10.1.3 (3)

PD 6687-29.2

15.10

15.10.1

15.10.2

The spacing of the transverse reinforcement should not exceed twice the minimumflangethickness.

Inskewvoidedslabs,itispreferableforthetransversesteeltobeplacedperpendiculartothevoidsandthelongitudinalsteeltobeplacedparalleltothevoids.

Prestressing

Arrangement of pre-tensioned tendons

Theminimumclearhorizontalandverticalspacingofindividualpre-tensionedtendonsshouldbeinaccordancewiththatshowninFigure15.9.

f≥dg

≥2f

≥dg+5

≥2f

≥20 mm

≥f≥40 mm

≥dg+5

≥f≥50 mm

≥dg

≥f≥40 mm

NoteWherefisthediameterofpre-tensionedtendonanddgisthemaximumsizeofaggregate

Figure 15.9Minimum clear spacing between pre-tensioned tendons

Arrangement of post-tensioned ducts

The minimum clear spacing of between ducts should be in accordance with that shown inFigure15.10.

Intheabsenceoftheprovisionofreinforcementbetweenductstopreventsplittingoftheconcrete,designedinaccordancewiththestrutandtierules(seeSection10),theminimumcentretocentreductspacingsshouldbeasgiveninTable15.3.ThesespacingsaregiveninBS5400-4:1990[24].

f≥dg

≥2f

≥dg+5

≥2f

≥20 mm

≥f≥40 mm

≥dg+5

≥f≥50 mm

≥dg

≥f≥40 mm

NoteWherefisthediameterofpost-tensionedductanddgisthemaximumsizeofaggregate

Figure 15.10Minimum clear spacing between post-tensioned ducts

BS EN 1992-1-1 8.10.1.2(1)

105

Detailing–particularrequirements

Table 15.3Minimum spacing of post-tensioning ducts (mm)

Radius of curvature of duct (m)

Duct internal diameter (mm)

19 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

Tendon force (kN)

296 387 960 1337 1920 2640 3360 4320 5183 6019 7200 8640 9424 10336 11248 13200

2 110 140 350 485 700 960

4 55 70 175 245 350 480 610 785 940 Radiinotnormallyused

6 38 60 120 165 235 320 410 525 630 730 870 1045

8 90 125 175 240 305 395 470 545 655 785 855 940

10 80 100 140 195 245 315 375 440 525 630 685 750 815

12 160 205 265 315 365 435 525 570 625 680 800

14 140 175 225 270 315 375 450 490 535 585 785

16 160 195 235 275 330 395 430 470 510 600

18 180 210 245 290 350 380 420 455 535

20 200 220 265 315 345 375 410 480

22 240 285 310 340 370 435

24 265 285 315 340 400

26 260 280 300 320 370

28 345

30 340

40 38 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

Notes

1Thetendonforceshownisthemaximumnormallyavailableforthegivensizeofduct(takenas80%ofthecharacteristicstrengthofthetendon).

2Valueslessthan2×ductinternaldiameterarenotincluded.

Connections

Connections transmitting compression

Connections without bedding material (dry connections) should only be used where anappropriate quality of workmanship can be achieved.The average bearing stress should notexceed0.3fcdwhere

fcd= 0.85fck/1.5

Intheabsenceofotherspecificationsthefollowingvaluecanbeusedforthebearingstrengthofotherconnections

fRd=fbed≤0.85fcd

where fcd = lowerofthedesignstrengthsforsupportedandsupportingmember

= 0.85fck/1.5

fbed= designstrengthofthebeddingmaterial

15.11

15.11.1

PD 6687-2 table 3

BS EN 1992-1-1 10.9.4.3(3)

BS EN 1992-1-1 10.9.5.2(2)

106

15.12

BS EN 1992-1-1 10.9.5.1(4)

BS EN 1992-1-1 10.9.5.2(1)

BS EN 1992-1-1 10.9.4.7(1)

BS EN 1992-1-1 10.9.5.2(3)

BS EN 1992-1-1 fig. 10.6

Bearings

Bearingsshallbedesignedanddetailedtoensurecorrectpositioningtaking intoaccounttheproductionandassemblingdeviations.

Thenominallength,a,ofasimplebearingasshowninFigure15.11maybecalculatedas:

++= Da22a a1 +a2 +a3 Da3

2

where a1 = netbearinglengthwithregardtobearingstressa1=FEd/(b1 fRd)butnotlessthan

minimumvaluesinTable15.4 FEd = designvalueofsupportreaction b1 = netbearingwidth(seebelow) fRd = designvalueofbearingstrength(seeSection15.11.1) a2 = distanceassumedineffectivebeyondouterendofsupportingmember,seeFigure

15.11andTable15.5 a3 = similardistanceforsupportedmember,seeFigure15.11andTable15.6 Da2 = allowancefordeviationsforthedistancebetweensupportingmembers,seeTable

15.7 Da3 = allowancefordeviationsforthelengthofsupportingmember = ln/2500 ln = lengthofmember

Theeffectivebearinglengtha1iscontrolledbyadistance,d,(seeFigure15.12)fromtheedgeoftherespectiveelements

where di = ci+Daiwithhorizontalloopsorotherwiseend-anchoredbars di = ci+Dai+riwithverticallybentbars

where ci = concretecover Dai = deviation ri = bendradius

Ifmeasuresaretakentoobtainauniformdistributionofthebearingpressure,e.g.withmortar,neopreneorsimilarpads,thedesignbearingwidthb1maybetakenastheactualwidthofthebearing.Otherwise,and intheabsenceofamoreaccurateanalysis,b1shouldnotbegreaterthanto600mm.

a) Elevation b) Plan

Da3a3

b1

a1

a1

a+ Da2a2+

Figure 15.11Example of bearing with definitions

107

Detailing–particularrequirements

Figure 15.12Example of

detailing of reinforcement

in support

di ci

ri

ri

> a1 + Da3

ci di> a1 + Da2

Table 15.4Minimum value of

a1 (mm)

Relative bearing stress, sEd / fcd ≤0.15 0.15 – 0.4 >0.4

Line supports (floors, roofs) 25 30 40

Ribbed floors and purlins 55 70 80

Concentrated supports (beams) 90 110 140

Table 15.5Distance a2 (mm) assumed ineffective from outer end of supporting member

Support material and type Relative bearing stress, sEd / fcd

≤0.15 0.15 – 0.4 >0.4

Steel line

concentrated

0

5

0

10

10

15

Reinforced concrete ≥ C30 line

concentrated

0

10

10

15

15

25

Plain concrete and reinforced concrete < C30 line

concentrated

10

15

15

25

25

35

Brickwork line

concentrated

10

20

15

25

a

a

KeyaConcretepadstoneshouldbeusedinthesecases

Table 15.6Distance a3 (mm) assumed ineffective beyond outer end of supported member

Detailing of reinforcement Support

Line Concentrated

Continuous bars over support (restrained or not) 0 0

Straight bars, horizontal, close to end of member 5 15,butnotlessthanendcover

Tendons or straight bars exposed at end of member

5 15

Vertical loop reinforcement 15 Endcover+innerradiusofbending

BS EN 1992-1-1fig.10.5

BS EN 1992-1-1table 10.2

BS EN 1992-1-1table 10.3

BS EN 1992-1-1table 10.4

108

BS EN 1992-1-1table 10.5

Table 15.7 Allowance Da2 for tolerances for the clear distance between the faces of the supports

Support material Da2

Steel or precast concrete 10≤l/1200≤30mm

Brickwork or cast in-situ concrete 15≤l/1200+5≤40mm

Notel=spanlength

109

Designfortheexecutionstages

16 Design for the execution stages

Forbridgesbuilt instages,accountoftheconstructionprocedureshouldbeconsideredatserviceabilityandultimatelimitstates.

Serviceabilitycriteriaforthecompletedstructureneednotbeappliedtointermediateexecutionstages,providedthatdurabilityandfinalappearanceofthecompletedstructurearenotaffected(e.g. deformations). Even for bridges or elements of bridges in which the limit-state ofdecompressionischeckedunderthequasi-permanentorfrequentcombinationofactionsonthe completed structure, tensile stresses less than 1.0 fctm(t) under the quasi-permanentcombinationofactionsduringexecutionarepermitted.Forbridgesorelementsofbridges inwhich the limit-state of cracking is checked under frequent combination on the completedstructure,thelimitstateofcrackingshouldbeverifiedunderthequasi-permanentcombinationofactionsduringexecution.

BS EN 1992-2113

BS EN 1992-2113.3.2

110

Design aids

Thefollowingtext,tablesandfigureshavebeenderivedfromEurocode2andareprovidedasanaidtodesignersintheUK.

Design for bending

Determinewhether■■ K ≤K’ornot(i.e.whetherunder-reinforcedornot). where K = MEd/(bd2fck)

where d= effectivedepth=h–cover–flink–f/2 b= widthofsection

ForrectangularsectionsK'maybedeterminedfromTable17.1or,forslabsonly,Table17.2maybeused.K'isdependentontheconcretestrengthandtheredistributionratioused.

Fornon-rectangularsectionx/dlimitsgiveninTable17.1maybeused.

If■■ K≤K',sectionisunder-reinforced.

Forrectangularsections:

As1=MEd/fydz

where As1 = areaoftensilereinforcement MEd= designmoment fyd = fyk/gS=500/1.15=434.8MPa z = d[0.5+0.5(1–3.53K/n)0.5]≤0.95d n = factordefiningeffectivestrength = 1.0–( fck–50)/200(seeTable6.1)

Forflangedbeamswherex<1.25hf,

As1= MEd/fydz x = depthtoneutralaxis hf = thicknessofflange For flanged beams where x ≥ 1.25hf, refer to How to design concrete structures using

Eurocode 2: Beams [25]

If■■ K>K',sectionisover-reinforced andrequirescompressionreinforcement.

As2=(MEd–M'Ed)/fsc(d–d2)

where As2 = compressionreinforcement M'Ed = K'bd2fck fsc = 700(xu–d2)/xu≤fyd

where d2 = effectivedepthtocompressionreinforcement xu = (d–l/z)d d = redistributionratio

Whenfyk=500MPa,fsc=fydunlessd2/xu≥0.379.

TotalareaoftensionsteelAs1=M'Ed /(fydz)+As2fsc/fyd

17

17.1

Section 4

111

Designaids

Table 17.1Limiting values of K' and xu/d

Percentage redistribution

d ( Redistribution ratio)

fck 50 55 60 70

n 1.000 0.975 0.950 0.900

l 0.800 0.788 0.775 0.750

ecu2 0.0035 0.0031 0.0029 0.0027

k1 or k3 0.44 0.54 0.54 0.54

k2 = k4 1.251 1.310 1.357 1.409

0 1.00 K' 0.167 0.132 0.123 0.110

xu /d 0.448 0.351 0.339 0.326

5 0.95 K' 0.155 0.119 0.111 0.099

xu /d 0.408 0.313 0.302 0.291

10 0.90 K' 0.142 0.107 0.099 0.088

xu/d 0.368 0.275 0.265 0.256

15 0.85 K' 0.129 0.093 0.087 0.077

xu /d 0.328 0.237 0.228 0.220

Table 17.2Limiting values of K' and xu/d for slabs

Percentage redistribution

d ( Redistribution ratio)

fck 50 55 60 70

n 1.000 0.975 0.950 0.900

l 0.800 0.788 0.775 0.750

ecu2 0.0035 0.0031 0.0029 0.0027

k1 or k3 0.4 0.4 0.4 0.4

k2 = k4 1.000 1.048 1.086 1.127

0 1.00 K' 0.207 0.193 0.181 0.163

xu /d 0.600 0.573 0.553 0.532

5 0.95 K' 0.194 0.181 0.170 0.152

xu /d 0.550 0.525 0.507 0.488

10 0.90 K' 0.181 0.169 0.158 0.141

xu/d 0.500 0.477 0.461 0.444

15 0.85 K' 0.167 0.155 0.145 0.130

xu /d 0.450 0.429 0.415 0.399

20 0.80 K' 0.152 0.141 0.132 0.118

xu /d 0.400 0.382 0.368 0.355

25 0.75 K' 0.136 0.126 0.118 0.105

xu /d 0.350 0.334 0.322 0.311

30 0.70 K' 0.120 0.111 0.103 0.092

xu /d 0.300 0.286 0.276 0.266

112

17.2

17.2.1

17.2.2

17.2.3

Design for beam shear

Requirement for shear reinforcement

IfvEd>vRd,cthenshearreinforcementisrequired

where vEd = VEd/bwd,forsectionswithoutshearreinforcement(i.e.slabs) vRd,c = shearresistancewithoutshearreinforcement,fromTable17.3

Table 17.3Shear resistance without shear reinforcement, vRd,c (MPa)

rl = Asl/bwd Effective depth d (mm)

≤ 200 225 250 275 300 350 400 450 500 600 750

0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.43 0.41 0.40 0.38 0.36

0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.45

0.75% 0.68 0.66 0.64 0.63 0.62 0.59 0.58 0.56 0.55 0.53 0.51

1.00% 0.75 0.72 0.71 0.69 0.68 0.65 0.64 0.62 0.61 0.59 0.57

1.25% 0.80 0.78 0.76 0.74 0.73 0.71 0.69 0.67 0.66 0.63 0.61

1.50% 0.85 0.83 0.81 0.79 0.78 0.75 0.73 0.71 0.70 0.67 0.65

1.75% 0.90 0.87 0.85 0.83 0.82 0.79 0.77 0.75 0.73 0.71 0.68

≥2.00% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71

Notes1 TablederivedfromBSEN1992-1-1andUKNationalAnnex.

2 Tablecreatedforfck=30MPaassumingverticallinks.

3 Forrl≥0.4%and fck = 25MPa,applyfactorof0.94 fck = 40MPa,applyfactorof1.10 fck ≥ 50MPa,applyfactorof1.19

fck = 35MPa,applyfactorof1.05 fck = 45MPa,applyfactorof1.14

Section capacity check

IfvEd,z>vRd,maxthensectionsizeisinadequate

where vEd,z = VEd/bwz=VEd/bw0.9d,forsectionswithshearreinforcement vRd,max = capacityofconcretestrutsexpressedasastressintheverticalplane = VRd,max/bwz = VRd,max/bw0.9d

vRd,maxcanbedeterminedfromTable17.4,initiallycheckingatcoty=2.5.Shoulditberequired,agreaterresistancemaybeassumedbyusingalargerstrutangle,y.

Shear reinforcement design

Asw/s≥vEd,zbw/fywdcoty

where Asw = areaofshearreinforcement(verticallinksassumed) s = spacingofshearreinforcement vEd,z = VEd/bwz,asbefore bw = breadthoftheweb fywd = fywk/gS=designyieldstrengthofshearreinforcement

Alternatively,Asw/spermetrewidthofbwmaybedeterminedfromFigure17.1a)or17.1b)asindicatedbythebluearrowsinFigure17.1a).Thesefiguresmayalsobeusedtoestimatethevalueofcoty.

Section 7.3.2

Section 7.3.3

Section 7.2

113

Designaids

Beamsaresubjecttoaminimumshearlinkprovision.Assumingverticallinks,Asw,min/sbw≥0.08fck

0.5/fyk(seeTable17.5).

Table 17.4Capacity of concrete struts expressed as a stress, vRd,max, where z = 0.9d

fck vRd,max (MPa) v

cot y 2.50 2.14 1.73 1.43 1.19 1.00

y 21.8º 25º 30º 35º 40º 45º

25 3.10 3.45 3.90 4.23 4.43 4.50 0.540

30 3.64 4.04 4.57 4.96 5.20 5.28 0.528

35 4.15 4.61 5.21 5.66 5.93 6.02 0.516

40 4.63 5.15 5.82 6.31 6.62 6.72 0.504

45 5.09 5.65 6.39 6.93 7.27 7.38 0.492

≥50 5.52 6.13 6.93 7.52 7.88 8.00 0.480

Notes1 TablederivedfromBSEN1992-1-1andUKNationalAnnexassumingverticallinks,i.e.cota=0

2 v=0.6[1–(fck/250)]

3 vRd,max=vfcd(coty+cota)/(1+cot2y)

Table 17.5Values of Asw,min/sbw × 103 for beams for vertical links and fyk = 500 MPa

Concrete class C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 ≥C50/60

Asw,min /sbwx103 0.72 0.80 0.88 0.95 1.01 1.07 1.13

4.0

3.0

2.0

5.0

6.0

7.0

8.0

0 2 4 6 8 10 12 14

C35/45

C40/50

C45/55

0.0

1.0

2.14 1.73 1.43

1.19

1.00

SeeFig.17.1b)

Asw/srequired per metre width of bw

fywk= 500 MPa

vRd,maxforcoty=2.5

v Ed,z

(M

Pa)

C30/37

C20/25

C25/30

≥C50/60

Figure 17.1a)Diagram to determine Asw/s required (for beams with high shear stress)

Section 15.2.6

114

C20/25C25/30C30/37

C30/37

C35/45C40/50C45/55C50/60

4.0

3.0

2.0

1.0

0.00 1 2 3 4

fywk = 500 MPa

Asw,min/sforbeams

RangeofvRd,cforranged=200mm,r=2.0%tod=750mm,r=0.5%

C25/30

Asw/srequired per metre width of bw

v Ed,z

(M

Pa)

C20/25

Figure 17.1b)Diagram to determine Asw/s required (for slabs and beams with low shear stress)

Design for punching shear

Determine if punching shear reinforcement is required, initially at u1, then if necessary atsubsequentperimeters,ui.IfvEd>vRd,cthenpunchingshearreinforcementisrequired

where vEd = bVEd/uid

where b = factordealingwitheccentricity(seeSection8.2) VEd = designvalueofappliedshearforce ui = lengthoftheperimeterunderconsideration(seeSections8.3,8.7and15.4.3) d = meaneffectivedepth vRd,c = shearresistancewithoutshearreinforcement(seeTable17.3)

Forverticalshearreinforcement

(Asw/sr)=u1(vEd–0.75vRd,c)/(1.5fywd,ef)

where Asw = areaofshearreinforcementinoneperimeteraroundthecolumn. ForAsw,minseeSection15.4.3 sr = radialspacingofperimetersofshearreinforcement u1 = basiccontrolperimeter(seeFigures8.3and8.4) fywd,ef = effectivedesignstrengthofreinforcement=(250+0.25d)≤fywd.ForClass500

shearreinforcementseeTable17.6

Table 17.6Values of fywd, ef for Class 500 reinforcement

d 150 200 250 300 350 400 450

fywd,ef 287.5 300 312.5 325 337.5 350 362.5

17.3

Section 8.21

Section 8.5

Section 15.4.3

115

Designaids

17.4

17.4.1

17.4.2

Design for axial load and bending

General

Incolumns,designmomentsMEdanddesignappliedaxialforceNEdshouldbederivedfromanalysis,considerationofimperfectionsand,wherenecessary,2ndordereffects(seeSection5.6).

Design by calculation

Assumingtwolayersofreinforcement,As1andAs2,thetotalareaofsteelrequiredinacolumn,As,maybecalculatedasshownbelow.

Foraxialload■■

AsN/2 = (NEd–accnfckbdc/gC)/(ssc–sst)

where AsN= totalareaofreinforcementrequiredtoresistaxialloadusingthismethod. AsN= As1+As2andAs1=As2

where As1(As2) = areaofreinforcementinlayer1(layer2)(seeFigure6.3) NEd= designvalueofaxialforce acc = 0.85 n = 1for≤C50/60(seeTable6.1whenfck>50) b = breadthofsection dc = effectivedepthofconcreteincompression=lx≤h

where l = 0.8for≤C50/60(seeTable6.1whenfck>50) x = depthtoneutralaxis h = heightofsection gC = 1.5 ssc,(sst)= stressincompression(andtension)reinforcement

Formoment■■

AsM=

MEd–accnfckbdc(h/2–dc/2)/gC

2 (h/2–d2)(ssc+sst)

where AsM = totalareaofreinforcementrequiredtoresistmomentusingthismethod AsM = As1+As2andAs1=As2

Solution:iterate■■ xsuchthatAsN=AsM.

Section 5.6

Section 6.2.2

116

17.4.3 Column charts

AlternativelyAsmaybeestimatedfromcolumncharts.

Figures17.2a)toe)givenon-dimensionaldesignchartsforsymmetricallyreinforcedrectangularcolumnswherereinforcementisassumedtobeconcentratedinthecorners.

Inthesecharts:acc = 0.85fck ≤ 50MPa

Simplifiedstressblockassumed.

As = totalareaofreinforcementrequired = (As fyk/bh fck)bh fck/fykwhere (As fyk/bh fck) is derived from the appropriate design chart interpolating as necessary

betweenchartsforthevalueofd2/hforthesection.

Wherereinforcementisnotconcentratedinthecorners,aconservativeapproachistocalculateaneffectivevalueofd2asillustratedinFigures17a)toe).d2=effectivedepthtosteelinlayer2.

Figures17.3a)toe)givenon-dimensionaldesignchartsforcircularcolumns.

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

0

0.10.2

0.3

0.40.5

0.60.7

0.8

0.91.0

Af

bhf

syk

c k

/

K r = 0.2

Figure 15.5(a)Rectangular columns / = 0.05d h2

h/2

h

d 2

Centroid of bars inhalf section

Ratio d2/h = 0.05

N/ Ed

/bhf

ck

MEd/bh2fck

Figure 17.2a)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.05

117

Designaids

h/2

h

d 2

Centroid of bars inhalf section

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

K r =1

K r = 0.2

0

0.10.2

0.3

0.40.5

0.6

0.7

0.80.9

1.0

Figure 15.5(b)Rectangular columns / = 0.10d h2

Af

bhf

syk

/ck

Ratio d2/h = 0.10

NEd

/bhf

ck

MEd/bh2fck

Figure 17.2b)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.10

h/2

h

d 2

Centroid of bars inhalf section

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

0.10.2

0.30.4

0.5

0.7

0.9

1.0

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Af

bhf

syk

c k

/

K r =1

K r = 0.2

Figure 15.5(c)Rectangular columns / = 0.15d h2

0.6

0.8

Ratio d2/h = 0.15

MEd/bh2fck

N/ Ed

/bhf

ck

Figure 17.2c)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.15

118

h/2

h

d 2

Centroid of bars inhalf section

0 0.05 0.10 0.15 0.20 0.25 0.30 0.350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.1

1.3

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Af

bhf

syk

c k

/

Ratio d2/h = 0.20

Figure 15.4(d)Rectangular columns / = 0.20d h2

K r = 1

K r = 0.2

00.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1.0

N/ Ed

/bhf

ck

MEd/bh2fck

Figure 17.2d)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.20

Af

bhf

syk

c k

/

Figure 15.5(e)Rectangular columns / = 0.25d h2

K r = 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.05 0.10 0.15 0.20 0.25 0.30

1.00.9

0. 80.7

0.60.5

0.40.3

0.20.1

0

K r = 1

h/2

h

d 2

Centroid of bars inhalf section

N/ Ed

/bhf

ck

MEd/bh2fck

Ratio d2/h = 0.25

Figure 17.2e)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.25

119

Designaids

Kr =1

0.9

0.8

0.7

0.6

0.5

0.4

0.31.0

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.2

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

0.9

dh

File Concise EurocodeCircular Columns 0.6v1 10.11.08

As fyk/h2fck Ratio d/h = 0.6

NEd

/h2

f ck

MEd / h3fck

Figure 17.3a)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.6

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.02 0.04 0.06 0.08 0.10 0.12

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0

0.10.2

0.3

File Concise Eurocode

d h

Ratio d/h = 0.7

NEd

/h2

f ck

MEd / h3fck

Kr =1

As fyk/h2fck

Figure 17.3b)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.7

120

d h

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Ratio d/h = 0.8As fyk/h2fck

Kr =1

NEd

/h2

f ck

MEd / h3fck

Figure 17.3c)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.8

d h

0.2

0.31.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0

0.4

0.5

0.6

0.7

0.8

0.9

0 0.05 0.10 0.15 0.20 0.25

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.1

File Concise EurocodeCircular Columns 0.85

Ratio d/h = 0.85

Kr =1

As fyk/h2fck

NEd

/h2

f ck

MEd / h3fck

Figure 17.3d)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.85

121

Designaids

d h

0.05 0.10 0.15 0.20 0.25 0.30

0.7

0.2

0.3

0.4

0.5

0.6

0.8

0.9

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00

File Concise EurocodeCircular Columns 0.9v1 10.11.08

Ratio d/h = 0.9

Kr =1

As fyk/h2fck

NEd

/h2

f ck

MEd / h3fck

Figure 17.3e)Rectangular columns (fck ≤ 50 MPa, fyk = 500 MPa) d2/h = 0.9

122

18 References

1 BRITISHSTANDARDSINSTITUTION.BSEN1992-1-1,Eurocode2–Design of concrete structures Part1-1: General rules and rules for buildings. BSI,2004,incorporatingcorrigendumdated12-11-2007.1a NationalAnnextoEurocode2–Part1-1.BSI,2005.

2 BRITISHSTANDARDSINSTITUTION.BSEN1992-2,Eurocode2–Design of concrete structures Part2: Concrete bridges – Design and detailing rules. BSI,2005,incorporatingcorrigendumdated12-11-2007.2a NationalAnnextoEurocode2–Part2.BSI,2007.

3 BRITISHSTANDARDSINSTITUTION.PD6687-2Recommendations for the design of structures to BS EN 1992-2: 2005.BSI,2008.

4 WOOD,RH.Thereinforcementofslabsinaccordancewithapre-determinedfieldofmoments. Concrete, 1968,No.2,pp.69–76.

5 DENTON,SR&BURGOYNE,CJ.Theassessmentofreinforcedconcreteslabs. The Structural Engineer,7thMay1996,Vol.74,No.9,pp.147–152.

6 BRITISHSTANDARDSINSTITUTION.PD6687Background paper to the UK National Annexes BS EN 1992-1.BSI,2006.

7 BRITISHSTANDARDSINSTITUTION.BSEN1990,Eurocode:Basis of structural design. BSI,2002,incorporatingamendmentNo.1.7a NationalAnnextoEurocode.BSI,2004,incorporatingamendmentNo.1.

8 BRITISHSTANDARDSINSTITUTION.BS8500-1:Concrete –Complementary British Standard to BS EN 206-1 – Part 1: Method of specifying and guidance to the specifier. BSI,2006.

9 BRITISHSTANDARDSINSTITUTION.BSEN1991,Eurocode1:Actions on structures (10parts).BSI,2002–2006.9a NationalAnnexestoEurocode1.BSI,2005 –2009andinpreparation.

10 BRITISHSTANDARDSINSTITUTION.ENV13670-1:2008:Execution of concrete structures: Common.BSI,2000.

11 BRITISHSTANDARDSINSTITUTION.BSEN13670.Execution of concrete structures.BSI,due2009.

12 BRITISHSTANDARDSINSTITUTION.BSEN1997,Eurocode7:Geotechnical design – Part 1. General rules.BSI,2004.12a NationalAnnextoEurocode7–Part1.BSI,2007.

13 BRITISHSTANDARDSINSTITUTION.PD6694-1Recommendations for the design of structures subject to traffic loading to BS EN 1997-1:2004.BSI,due2009.

14 BRITISHSTANDARDSINSTITUTION.BSEN206-1.Concrete – Part 1: Specification, performance, production and conformity. BSI,2000.

15 BRITISHSTANDARDSINSTITUTION.BSEN197-1Cement – Composition, specifications and conformity criteria for common cements.BSI,2000.

16 BRITISHSTANDARDSINSTITUTION.BS4449:Steel for the reinforcement of concrete – Weldable reinforcing steel – Bar, coil and decoiled product – Specification. BSI,2005.

17 BRITISHSTANDARDSINSTITUTION.BSEN10080:Steel for the reinforcement of concrete – Weldable reinforcing steel – General. BSI,2005.

18 BRITISHSTANDARDSINSTITUTION.BS5896.High tensile steel wire and strand for the prestressing of concrete. BSI,1980,incorporatingamendmentNo.1.

19 BUILDINGRESEARCHESTABLISHMENT.Concrete in aggressive ground. BRESpecialDigest1.BRE,2005.

123

References

20 HENDY,CR&SMITH,DA.Designers guide to EN 1992–2. ThomasTelford,2007.

21 ENV1992-1-1:Eurocode2:Design of concrete structures - Part 1-1: General rules and rules for buildings.BSI,1992(supersededbyreference1).

22 INTERNATIONALSTANDARDSORGANISATION,ISO/FDIS.17660-2:Welding – Welding of reinforcing steel – Part 2: Non load-bearing welded joints.ISO,2005.

23 BRITISHSTANDARDSINSTITUTION.BSEN1536:Execution of special geotechncial work – Bored piles.BSI,2000.

24 BRITISHSTANDARDSINSTITUTION.BS5400:Steel, concrete and composite bridges – Part 4: Code of Practice for design of concrete bridges.BSI,1990.

25 BROOKER,Oetal.How to design concrete structures using Eurocode 2. TheConcreteCentre,2006.

3

Guide to presentation

Grey shaded text, tables and figures

Modified Eurocode 2 text and additional text, derived formulae, tables and illustrations not from Eurocode 2

Yellow shaded text, tables and figures

Additional text from PD 6687[6] or PD 6687-2[3]

BS EN 1992-1-1 6.4.4

Relevant code and clauses or figure numbers

BS EN 1992-1-1 NA From the relevant UK National Annex

BS EN 1992-1-1 6.4.4 & NA From both Eurocode 2-1-1 and UK National Annex

Section 5.2 Relevant parts of this publication

1.0 Nationally Determined Parameter. UK values have been used throughout

4

Concise Eurocode 2 for Bridges

This publication summarises the material that will be commonly used in the design of reinforced and prestressed concrete bridges using Eurocode 2.

With extensive clause referencing, readers are guided through Eurocode 2, other relevant European standards and non-contradictory complementary information. The publication, which includes design aids, aims to help designers with the transition to design using Eurocodes.

Concise Eurocode 2 for Bridges is part of a range of resources available from the cement and concrete industry to assist engineers with the design of a variety of concrete bridges. For more information visit www.concretecentre.com

Owen Brooker is senior structural engineer for The Concrete Centre. He is author of several publications, including the well received series How to design concrete structures using Eurocode 2. He regularly lectures and provides training to structural engineers, particularly on the application of Eurocode 2.

Paul Jackson is a technical director of Gifford, which he joined from BCA in 1988. He has worked on bridge design, assessment, construction, strengthening and research. He has contributed extensively to codes of practice and is currently a member of the BSI committee for bridges and convenor of its working group for concrete bridges. He served on the project team for EN 1992-2.

Stephen Salim is a senior engineer with Gifford. He has worked on bridge assessment, feasibility studies, design, construction supervision and research. He was also involved in the calibration work of BS EN 1992-2; some of the proposals arising from this work were adopted in the UK National Annex.

CCIP-038Published 2009ISBN 978-1-904818-82-3Price Group P© MPA – The Concrete Centre

Riverside House, 4 Meadows Business Park,Station Approach, Blackwater, Camberley, Surrey, GU17 9ABTel: +44 (0)1276 606800 Fax: +44 (0)1276 606801www.concretecentre.com