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Dr. Naveed Anwar
International Bridge Design Standards and Approaches
Topic 4Day 2
Naveed Anwar
Dr. Naveed Anwar2
• Origins of the Code
• Intent of the Code• Explicit
• Implicit
• Spirit of the Code
• Letter of the Code
Dr. Naveed Anwar3
Structural Design
3
“Structural Design is the process of proportioning the structure to safely
resist the applied forces in the most cost effective and friendly manner”
A systematic investigation of the stability, strength and rigidity of structures
Where Safety is a prime concern
Dr. Naveed Anwar4
Ensuring Safety through Factor of Safety!
4
Capacity > Demand
𝑪
𝑫= 𝑭𝒐𝑺 𝐶 = 𝐷 𝑥 𝐹𝑜𝑆
𝐶
𝐹𝑜𝑆= 𝐷
𝐶
𝐹𝑜𝑆1= 𝐷 𝑥 𝐹𝑜𝑆2
Dr. Naveed Anwar5
Capacity side: :Working Stress Design
5
StrainSt
ress
fy
0.5fy
Unused Strength and Ductility
𝐶
𝐹𝑜𝑆= 𝐷
Dr. Naveed Anwar6
Capacity Side > “Real Behavior”
6
Dr. Naveed Anwar7
Ultimate Strength Design
7
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Strain
Stresses fo
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f1
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• The Strain becomes the primary concern, • Full “Strengths” of the materials at “ultimate”
strains are utilized with appropriate “other” factors
Dr. Naveed Anwar8
Considering Interaction of Actions
8
Nz
Mx
My
• Shear-Torsion Interaction
• Shear – Flexure interaction
• Torsion-Flexure Interaction
• Shear-Torsion-Flexure Interaction
The realization that “Envelop Results” can not be used for design
Dr. Naveed Anwar9
The Strut and Tie Approaches – Post Crack Strength
9
An RC Beam and “Hidden” Truss
A Real Truss
Dr. Naveed Anwar10
The Strut and Tie Approaches
• Extensively used for• “D” regions of all members
• Shear Design
• Torsion Design
• “Deep” Beams
• Brackets
• Corbels
• Joints
• Pipecaps
• Shear walls
• Transfer girders
• …
Dr. Naveed Anwar11
Approach 3 - Limit State Design
• Limit State Design concept is an advancement over both Working Stress and Ultimate Strength design approaches.
• Attempts to ensures safety at ultimate loads and serviceability at working loads.
• The basic idea involves the identification of all potential modes of failure (i.e. identify significant limit states and determination of acceptable levels of safety against occurrence of each limit state.
• This philosophy uses more than one safety factors attempting to provide adequate safety
11
Dr. Naveed Anwar12
Limit State Design
12
Types of Limit State Description
Ultimate Limit states • Loss of equilibrium
• Rupture
• Progressive Collapse
• Formation of plastic mechanism
• Instability
• Fatigue
Serviceability limit states • Excessive deflections
• Excessive crack width
• Undesirable Vibration
Special limit states Due to abnormal conditions and abnormal loading such as
• Damage or collapse in extreme earthquakes
• Structural effects of fire, explosion
• Corrosion or deterioration
Dr. Naveed Anwar13
Partial Factors of Safety
13
Characteristic value of
material basic strength Design Strength
Design member
capacity
Characteristic value of
LoadDesign load
Design member
capacity
Ym Yb
Yf Ya
Verification
Yi
Material safety
Factor
Member Factor
Load Factor Structural Analysis
Factor
Structure
Factor
The value of Safety Factor tells how much confidence we have on our knowledge.
Dr. Naveed Anwar14
Eurocode - ULS
Dr. Naveed Anwar15
Euro Code - SLS
Dr. Naveed Anwar16
Improving Factors of Safety
16
Factors Example
Structure Level Importance Factors (1.0 to 1.5)Structure type “R” factors
Member Level Over strength Factors
Action Level Different “fi” factors for flexure, shear, …
Material Level Different gamma factors for concrete and steel
Load Factors Different for different loads, based on probability of variance
Load Combination Factors Deferent for various probability of simultaneousoccurrence
Dr. Naveed Anwar
The Development and Role of Building Codes
Dr. Naveed Anwar18
The First Building Code: Code of Hammurabi
18
• The earliest known written building code was
the Babylonian law of ancient Mesopotamia
• Also known as the code of King Hammurabi
(who ruled Babylon from 1792 BC to 1750 BC).
• Found in 1901 in Khuzestan, Iran
• Contains detailed accounts of laws pertaining
to builders as well as construction conflicts.
Dr. Naveed Anwar19
Code of Hammurabi
19
Clause 229:
If a builder builds a house for someone, and does not construct it
properly, and the house which he built falls in and kills its owner,
then that builder shall be put to death.
Dr. Naveed Anwar20
Ancient Building Code: Laws of Moses
20
“In case you build a newhouse, you must also makea parapet for your roof, thatyou may not place bloodguiltupon your house becausesomeone falling might fallfrom it”.
- The Bible, Book of Deuteronomy, Chapter 22, Verse 8
Dr. Naveed Anwar21
The Modern Codes
21
(ACI 318 – 11)
Extremely Detailed prescriptions and equations using seemingly arbitrary, rounded limits with implicit meaning
(IS 456-2000)
Dr. Naveed Anwar22
Are All Codes Correct ?
• If they differ, can all of them be correct ?
• Did we inform the structures to follow which code when earthquake or ship strikes ?
• Codes change every 3 or years, should be upgrade our structures every 3 or 5 years to conform ?
22
Dr. Naveed Anwar23
Prescriptive Codes – A Shelter
• Public: • Is my structure safe ?
• Structural Engineer:• Not sure, but I did follow the “Code”
As long as engineers follow the code, they can be sheltered by its provisions
23
Dr. Naveed Anwar
Newer Design ApproachesPrimarily geared towards Earthquakes and Extreme Events
Dr. Naveed Anwar25
Design for Seismic Resistance and Extreme Events
• Force/stress based design• Assume reduced forces, limit the stresses
• Displacement based design• Allow force D/C to exceed, as long as displacements can be limited
• Capacity based design• Put “fuses” in the structure limit the force capacity, hence the demand
• Energy based design• Total energy input is collectively resisted by kinetic energy, the elastic strain
energy and energy dissipated through plastic deformations and damping
25
Dr. Naveed Anwar26
Progression of Seismic Resistance Design
26
Historical Approach:Earthquake forces proportional tobuilding mass (Vdes = 5 - 10% of Wt), Traditional Codes:
Elastic earthquake forces reduced forlinear design (Vdes = Vmax /R)
Lack of Knowledge on Earthquake Demand and
Building Capacity
Linear Elastic Building Response
V
Vdes
Yield Max
V
Vdes
Elastic Forces reduced for Design by R
Inelastic Response
Dr. Naveed Anwar27
Performance Based Design (PBD)
• Explicitly link the performance with earthquake hazard
• Why it was needed?• Traditional codes not suitable/adequate
• Explicit verification not specified or required in most codes
• Public does not care about the code, or theories or procedures, they care about “safety” and ‘performance”
27
Dr. Naveed Anwar28
Prescriptive Vs Performance
2
Approach Procdure Outcome
Prescriptive(emphasis on procedures)
Specify “what, and how to do”
Make Concrete: 1:2:4
Implicit Expectation
(a strength of 21 MPA is expected)
Performance Based Approach(emphasis on KPI)
What ever it takes
(within certain bounds)
Explicit Performance
Concrete less than 21 MPA is rejected
Dr. Naveed Anwar29
Define Performance Levels
29
Restaurant Restaurant
Resta
uran
t
Operational (O)Immediate Occupancy
(IO)
Life Safety (LS) Collapse Prevention (CP)
Ref: FEMA 451 B
Dr. Naveed Anwar30
Link the Damage to Performance Levels
30
Structural Displacement
Lo
adin
g S
ever
ity
Resta
urant
Resta
urant
Resta
uran
t
Haz
ard
Vulnerability
Consequences
Dr. Naveed Anwar31
Link Performance other Indicators
31
Restaurant Restaurant
Resta
uran
t
Operational (O) Immediate Occupancy (IO) Life Safety (LS) Collapse Prevention (CP)
0 % Damage or Loss 99 %
Ref: FEMA 451 B
CasualtiesLowest Highest
Rehab Cost to Restore after eventLowest Highest
Retrofit Cost to Minimize ConsequencesHighest Lowest
Downtime for RehabLowest Highest
Dr. Naveed Anwar32
Demand to Capacity Ratio – An Important indicator
• This could apply to• Forces, actions (Moment, shear, etc) • Ductility• Deformations (drift, deflection)
• Indicates the “safety”, “acceptability” as well as “efficiency” of design
D/C > 1 <Not acceptable, in many cases)
D<C < 1 <Acceptable in most cases
D/C =1 <Ideal design, not practical>
0.5 < D/C < 0.9 <Efficient design>
32
Dr. Naveed Anwar33
Consequence Based Engineering
• It is not enough to say “Cracking and non-structural damge is acceptable, as long as structure does not collapse”
• A natural extension of the performance-based design approach
• Structural consequences can be defined in terms of repair costs, casualties and loss of use duration (dollars, deaths and downtime) (Porter, 2003).
• Other types of consequences which result from the inherent function of a structure, are addressed using importance factors for various occupancy categories in design codes (Yuxian 2013).
33
Dr. Naveed Anwar34
Consequence Based Engineering
• “Structural consequence and non-structural effects” determined entirely from the analysis of structural member as well as overall system behavior.
• The consequence-based structural design approach proceeds through the analysis of expected system consequences, irrespective of the event triggering these consequences.
• This philosophy requires the structural members to be designed for variable reliability levels, depending upon their contribution in causing adverse system consequences.
34
Dr. Naveed Anwar
Comparing Codes
Dr. Naveed Anwar36
Codes
• Most modern international codes, if used and applied consistently will yield nearly similar structural performance expectations
• For bridge design codes consideration should be given to• Local loading and traffic patterns
• Local materials
• Local construction practices
• Local regulations and controls
Dr. Naveed Anwar37
Code Comparison
Material Properties (AASHTO LRFD, BS and EN Standards)
Load Combinations (AASHTO LRFD, BS and EN Standards)
Load Factors (AASHTO LRFD, BS and EN Standards)
Flexural Design Based on AASHTO LRFD Standards
Flexural Design Based on British Standards
Flexural Design Based on European Standards
Dr. Naveed Anwar38
Presentation Contents
Shear and Torsion Design based on AASHTO LRFD Standards
Shear and Torsion Design based on British Standards
Shear and Torsion Design based on European Standards
Seismic Design of Bridges based on AASHTO LRFD Standards
Seismic Design of Bridges based on European Standards
Dr. Naveed Anwar39
A Sample Code Comparisons
Footing design AASHTO Code Chinese Code
Dimensions (5×6)m, thickness = 1.5m (5×6)m, thickness = 1.5m
Number of piles4-bored piles with Dia. = 1m,with depth = 62.7m
4-bored piles with Dia. =1m, withdepth = 62.7m
Pile cap design
25 bars #9 (2.8cm) in the bottom mats Number of bars = 29 bars (2.8cm) ineach direction in the bottom mats
21 bars #9 (2.8cm) in the topmats
Number of bars = 25 bars (2.8cm) ineach direction in the top mats
Pile design
16 bars #8 (2.5cm) in the bottom Number of bars = 20 bars (2.5cm) ineach direction in the bottom
24 bars #8 (2.5cm) in the top Number of bars = 29 bars (2.8cm) ineach direction in the top
Design of Substructure Bridge with Different Codes and Analysis the Data for Settlement and Bearing Capacity Manually and by Using Plaxiz 3D Program of Finite ElementsPosted in Project Reports, Research Papers
Dr. Naveed Anwar40
CE 72.32 - Design of Tall Buildings, Dr. Naveed Anwar
BS Standard Title Superseded By Euro
BS 5400-1:1988 Steel, concrete and composite bridges. General statement EN 1990, EN 1991
BS 5400-2: 2006 Steel, concrete and composite bridges. Specification for loads EN 1990, EN 1991
BS 5400-3:2000 Steel, concrete and composite bridges. Code of practice for design of steel bridges EN 1993
BS 5400-4: 1990 Steel, concrete and composite bridges. Code of practice for design of concrete bridges EN 1992
BS 5400-5:2005 Steel, concrete and composite bridges. Code of practice for design of composite bridges EN 1994
BS 5400-6: 1999 Steel, concrete and composite bridges. Specification for materials and workmanship, steel
EN 1090-2
BS 5400-7:1978 Steel, concrete and composite bridges. Specification formaterials and workmanship, concrete, reinforcement and prestressing tendons
EN 1992
BS 5400-8: 1978 Steel, concrete and composite bridges. Recommendationsfor materials and workmanship, concrete, reinforcement and prestressing tendons
EN 1992
BS 5400-9.1 and 9.2 Bearings not affected
BS 5400-10C: 1999 teel, concrete and composite bridges. Charts for classification of details for fatigue not affected
From 1 April 2010 the UK design standard for concrete bridges is BS EN 1992-2 (aka Eurocode 2, part 2),
Dr. Naveed Anwar
Material Properties
Dr. Naveed Anwar42
Compressive Strength based on AASHTO LRFD
Class Applicability Compressive Strength
A All Elements of Structure 4.0
A(AE) 4.0
B Footings, Pedestals, Massive Pier Shafts, and Gravity Walls
2.4
B(AE) 2.4
C Reinforced Railings less than 4.0 in. thick, Steel Grid Floors
4.0
C(AE) 4.0
P Pre-Stressed Concrete Members As Specified
P(HPC) As Specified
S Cofferdams -
Dr. Naveed Anwar43
Concrete Strength based on BS Codes
Design Stress-Strain Curve for Normal Weight Concrete
Dr. Naveed Anwar44
Concrete Strength based on EN Codes
The strength classes (C) in this code are denoted by the characteristic cylinder strength determined at 28 days.
The value of the design compressive strength is defined as
fc = α𝑐𝑐𝑓𝑐𝑘/γ𝑐
The value of the design tensile strength is defined as
Where;
α = coefficient of taking long term effects ; γ = partial safety factor
ft = α𝑐𝑐𝑓𝑐𝑘/γ𝑐
Dr. Naveed Anwar45
Modulus of Elasticity
Where;
K1= correction factor for source of aggregate to be taken as 1.0 unless determined by physical test.
wc =unit weight of concrete
fci=Specified Compressive Strength
AASHTO LRFD British Standards
Dr. Naveed Anwar46
Coefficient of Thermal Expansion
AASHTO LRFD
Normal weight concrete 6.0 × 10–6/°F Lightweight concrete 5.0 × 10–6/°F
British Standards
Normal weight concrete 12.0 × 10–6/°F Lightweight concrete 7.0 × 10–6/°F
Dr. Naveed Anwar47
Creep
Based on AASHTO LRFD creep coefficient may be taken as:
Where;
Ks = 1.45 – 0.13 (V/S) > 1Khc = 1.56 – 0.008 HKf = 5/ (1 + fci)Ktd = t/ (61 – 4 fci + t)H = Relative humidityt = Maturity of concretefci = Specified Compressive StrengthV/S = Volume to Surface Ratio
Dr. Naveed Anwar48
Creep
Based on British Standards creep coefficient may be taken as:
Where;
E28 = secant modulus of elasticity of the concrete at the ageof 28 days
kL = depends on the environmental conditionsKM = depends on the hardening (maturity) of the
concretekC = depends on the composition of the concretekE = depends on the effective thickness of the memberKj = defines the development of the time-dependent
deformation with time
ψ = (𝑓𝑐/E28) * kL KM kC kE Kj
Dr. Naveed Anwar49
Creep
Based on European Standards creep coefficient may be taken as:
Where;
kϬ = Stress-Strain ratiot0 = age of concrete
Dr. Naveed Anwar50
Creep
ψ = (𝑓𝑐/E28) * kL KM kC kE Kj
US
BS
EU
Dr. Naveed Anwar51
Shrinkage
Based on AASHTO LRFD the strain due to shrinkage, εsh, at time, t, may be taken as:
Where;
Ks = 1.45 – 0.13 (V/S) > 1Khs = 2.00 – 0.014 HKf = 5/ (1 + fci)Ktd = t/ (61 – 4 fci + t)H = Relative humidityt = Maturity of concretefci = Specified Compressive StrengthV/S = Volume to Surface Ratio
Dr. Naveed Anwar52
Shrinkage
Based on British Standards the strain due to shrinkage, εss for RC sections at time, t, may be taken as:
Where;
εsh = Shrinkage of plain concreteρ = Area of steel relative to concreteK = Factor taken as 25 for internal exposure and 15 for
external exposure
Dr. Naveed Anwar53
Shrinkage
Based on European Standards the strain due to drying shrinkage,εcs at any time can be taken as:
Dr. Naveed Anwar54
Shrinkage
US
BS
EU
Dr. Naveed Anwar
Loads Patterns
Dr. Naveed Anwar56
General
In all international codes, loads are categorized into two categories.
Permanent Load: Dead Load, Superimposed Dead Loads, Load due to material infill
Transient Load: All other loads except permanent loads
Dr. Naveed Anwar57
Load Patterns (AASHTO LRFD)
Load Patterns for Permanent Loads
Dr. Naveed Anwar58
Load Patterns(AASHTO LRFD)
Load Patterns for Transient Loads
Dr. Naveed Anwar59
Load Patterns (EUROPEAN)
Load Patterns for Permanent Loads
Dr. Naveed Anwar60
Load Patterns (EUROPEAN)
Load Patterns for Transient Loads
Dr. Naveed Anwar61
Load Patterns (EUROPEAN)
Load Patterns for Transient Loads
Dr. Naveed Anwar
Loads Combinations
Dr. Naveed Anwar63
Load Combination
AASHTO LRFD specifies load combinations for strength,fatigue, service and extreme limits states.
British standards specifies load combinations fordifferent bridges and for service and ultimate limitstates.
European codes specifies load combination rules fordifferent types of bridges (Road bridge, foot bridge,railway bridge) and for service and ultimate limit statesonly.
Dr. Naveed Anwar64
Load Combinations for Strength Limit State (AASHTO LRFD)
Strength I Basic load combination relating to the normal vehicularuse of the bridge without wind.
Strength II Load combination relating to the use of the bridge byOwner-specified special design vehicles, evaluationpermit vehicles, or both without wind
Strength III Load combination relating to the bridge exposed towind velocity exceeding 55 mph
Strength IV Load combination relating to very high dead load to liveload force effect ratios
Strength V Load combination relating to normal vehicular use ofthe bridge with wind of 55 mph velocity
Dr. Naveed Anwar65
Load Combinations Extreme Event Limit State (AASHTO LRFD)
Extreme Event I Load combination relating to the use of thebridge by Owner-specified special designvehicles, evaluation permit vehicles, or bothwithout wind
Extreme Event II Load combination relating to ice load, collisionby vessels and vehicles, check floods, andcertain hydraulic events with a reduced liveload other than that which is part of thevehicular collision load,
Dr. Naveed Anwar66
Load Combinations for Service Limit State (AASHTO LRFD)
Service I Load combination relating to the normal operationaluse of the bridge with a 55 mph wind and all loadstaken at their nominal values. Also related to deflectioncontrol in buried metal structures, tunnel liner plate,and thermoplastic pipe, to control crack width inreinforced concrete structures, and for transverseanalysis relating to tension in concrete segmentalgirders. This load combination should also be used forthe investigation of slope stability.
Service II Load combination intended to control yielding of steelstructures and slip of slip-critical connections due tovehicular live load
Dr. Naveed Anwar67
Load Combinations for Service and Fatigue Limit State (AASHTO LRFD)
Service III Load combination for longitudinal analysis relating totension in prestressed concrete superstructures withthe objective of crack control and to principal tension inthe webs of segmental concrete Girders.
Service IV Load combination relating only to tension inprestressed concrete columns with the objective ofcrack control.
Fatigue I Fatigue and fracture load combination related to infiniteload induced fatigue life.
Fatigue II Fatigue and fracture load combination related to finiteload induced fatigue life.
Dr. Naveed Anwar68
Load Combinations for Service and Ultimate Limit State (British Standards)
Combination 1: For highway and foot/cycle track bridges, the loads tobe considered are the permanent loads, together withthe appropriate primary live loads, and, for railwaybridges, the permanent loads, together with theappropriate primary and secondary live loads.
Combination 2: For all bridges, the loads to be considered are the loadsin combination 1, together with those due to wind, and,where erection is being considered, temporary erectionloads.
Combination 3: For all bridges, the loads to be considered are the loadsin combination 1, together with those arising fromrestraint due to the effects of temperature range anddifference, and, where erection is being considered,temporary erection loads
Dr. Naveed Anwar69
Load Combinations for Service and Ultimate Limit State (British Standards)
Combination 4 Combination 4 does not apply to railway bridges exceptfor vehicle collision loading on bridge supports. Forhighway bridges, the loads to be considered are thepermanent loads and the secondary live loads, togetherwith the appropriate primary live loads associated withthem. Secondary live loads shall be consideredseparately and are not required to be combined. Eachshall be taken with its appropriate associated primarylive load.
Combination 5 For all bridges, the loads to be considered are thepermanent loads, together with the loads due to frictionat bearings
Dr. Naveed Anwar70
Load Models (European Standards)
Load Model 1
A double-axle load (calledthe Tandem System) isapplied in each traffic lane inconjunction with auniformly distributed load
Load Model 2
A single-axle load is appliedanywhere on thecarriageway
Dr. Naveed Anwar71
Load Models (European Standards)
Load Model 3
If the structure is to bedesigned for abnormal loadthen vehicles from LoadModel 3 will need to beconsidered.
Load Model 4
A uniformly distributed loadof 5kN/m2 used to representcrowd loading and may beapplied to both road bridgesand footway/cyclewaybridges
Dr. Naveed Anwar72
Load Combinations (European Standards)
Combination Group 1 (gr1a)
Load Model 1 is combined with footway loading. The footway loading isreduced to 3kN/m2
Combination Group 1 (gr1b)
This consists of the 400kN axle shown in Load Model 2 and is notcombined with any other load model
Combination Group 2 (gr2)
The 'Frequent' value of Load Model 1 is combined with Braking &Acceleration Forces and Centrifugal &Transverse Forces
Dr. Naveed Anwar73
Load Combinations (European Standards)
Combination Group 3 (gr3)This consists of Load Model 4 and is applied to the footways only; it is notcombined with any other load model. The UDL may be applied to one or both ofthe footways so as to achieve the worst load effect.
Combination Group 4 (gr4)This consists of Load Model 4 and is applied to the footways, carriageways andcentral reserve; it is not combined with any other load model.
Combination Group 5 (gr5)The 'Frequent' value of Load Model 1 (LM1) is combined with Load Model 3(LM3).
Combination Group 6 (gr6)Load Model 3 is combined with Braking and Acceleration Forces and Centrifugaland Transverse Forces
Dr. Naveed Anwar74
Load Combinations (AASHTO LRFD)
Dr. Naveed Anwar75
Load Combinations (British Standards)
Load Combination for Ultimate Limit State
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Load Combinations (British Standards)
Load Combination for Service Limit State
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Load Combinations (European Standards)
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Load Combinations (European Standards)
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Load Combinations (European Standards)
Dr. Naveed Anwar
Loads Factors (AASHTO LRFD, BS & EN Standards)
Dr. Naveed Anwar81
Load Factors for Permanent Loads (AASHTO LRFD)
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Load Factors for Permanent Loads due to Superimposed Deformations (AASHTO LRFD)
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Load Factors (British Standards)
Dr. Naveed Anwar84
Load Factors (British Standards)
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Load Factors (European Standards)
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Load Factors (European Standards)
Dr. Naveed Anwar
Flexure Design(AASHTO LRFD)
Dr. Naveed Anwar88
Design Process
The natural relationship between concrete stress and strain may beconsidered satisfied by an equivalent rectangular concretecompressive stress block of 0.85f ′c over a zone bounded by the edgesof the cross-section and a straight line located parallel to the neutralaxis at the distance a = β1c from the extreme compression fiber.
The distance c shall be measured perpendicular to the neutral axis.
β1 = 0.85 for concrete strengths not exceeding 4.0 ksi.
For concrete strengths exceeding 4.0 ksi, β1 shall be reduced at a rateof 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β1shall not be taken to be less than 0.65.
Dr. Naveed Anwar89
Flexural Resistance
Factored Flexural Resistance ,
Mn = Nominal ResistanceΦ = Resistance Factor
Mr = ϕMn
For rectangular and flanged sections:
For rectangular sections Mn can be computed by necessaryapproximations as specified by the standards and codes.
Dr. Naveed Anwar90
Minimum Reinforcement Criteria
fr = Modulus of rupture of concrete specified
fcpe = Compressive stress in concrete due to effective prestress forces only
Mdnc = Total unfactored dead load moment
Sc = Section modulus for the extreme fiber of the composite section wheretensile stress is caused by externally applied loads
Snc = Section modulus for the extreme fiber of the monolithic ornoncomposite section where tensile stress is caused by externallyapplied loads
Dr. Naveed Anwar91
Crack Control Criteria
The provisions specified herein shall apply to the reinforcement of allconcrete components, except that of deck slabs design.
Class 1 exposure condition applies when cracks can be tolerated dueto reduced concerns of appearance and/or corrosion. Class 2exposure condition applies to transverse design of segmentalconcrete box girders for any loads applied prior to attaining fullnominal concrete strength and when there is increased concern ofappearance and/or corrosion.
Spacing,
Dr. Naveed Anwar
Flexure Design(British Standards)
Dr. Naveed Anwar93
Design Process
Rectangular stress block of maximum depth of 0.5 d and uniformcompression stress of 0.4 fcu is assumed to evaluate moments.
Stresses in Concrete in Compression with m = 1.5
Stresses in Reinforcements in m = 1.15
Dr. Naveed Anwar94
Flexural Resistance
Ultimate resistance of flanged sections
Ultimate resistance of rectangular sections
As = Area of Tension Reinforcement As. = Area of Compression Reinforcementd = width of sections; d. = effective depth to tension reinforcement b = width of sections z = lever arm
Dr. Naveed Anwar95
Minimum Reinforcement Criteria
Minimum area of tension reinforcement > 0.15 % of bad(grade 460)
Minimum area of tension reinforcement > 0.25 % of bad(grade 250)
For columns cross-sectional area of longitudinal barsshould not be less than 1 % of the total area.
For Walls, vertical reinforcement should be more than0.4 % of gross sectional area of concrete.
Dr. Naveed Anwar96
Crack Control Criteria
Maximum spacing should not be greater than 300 mm .
For solid rectangular sections, design crack width at surface shouldbe calculated as
For flanges in overall tension including tensile zone of box beamsand voided slabs, the design crack width at surface is calculated as
Design Crack Width = 3 acr X .m
Spacing of transverse bars in slab with circular voids should not betwice the minimum flange thickness.
Dr. Naveed Anwar
Flexure Design(European Standards)
Dr. Naveed Anwar98
Design Process
Rectangular design stress strain relationship to determine stress
λ = 0.8 for fck < 50 Mpa ; η = 1.0 for fck < 50 Mpaλ = 0.8 - (fck – 50)/400 for 50<fck< 90 Mpa ; η = 1.0-(fck–50)/200 for 50<fck< 90 Mpa
Dr. Naveed Anwar99
Design Process
Calculation of Stresses
Stress-Strain Diagram for Reinforcing Steel for Tension & Compression
Stress-Strain Diagram for Prestressing Steel
Dr. Naveed Anwar100
Flexural Resistance
Verification of the load capacity using reduced area of pre-stressfollowing steps mentioned below:
Calculate the applied bending moment due to the frequentcombination of actions.
Determine the reduced area of prestress that results in thetensile stress reaching fctm at the extreme tension fibre whenthe section is subject to the bending moment calculated.
Using this reduced area of prestress, calculate the ultimateflexural capacity. It should be ensured that this exceeds thebending moment due to the frequent combination
Dr. Naveed Anwar101
Flexural Resistance
Providing minimum reinforcing steel area calculatedfrom the equation:
As(min) = 𝑀 𝑟𝑒𝑝
𝑧𝑓𝑦
Agreeing an appropriate inspection regime with therelevant National Authority on the basis of satisfactoryevidence
Dr. Naveed Anwar
Shear & Torsion Design(AASHTO LRFD)
Dr. Naveed Anwar103
Factored Torsional and Shear Resistance
Factored torsional resistance shall be taken as
Tr = ϕ Tn
Vr = ϕ Vn
Factored shear resistance shall be taken as
Where;
Tn = nominal torsional resistance Vn = nominal torsional resistance φ = resistance factor specified
Dr. Naveed Anwar104
Shear Stress on Concrete
where:φ = resistance factor for shear specified inbv= effective web widthdv = effective shear depth; it need not be taken to be less than the greater of0.9 de or 0.72h (in.)
Dr. Naveed Anwar105
Torsional Effects
For normal weight concrete, torsional effects shall be investigated where
where:Tu = factored torsional momentTcr = torsional cracking momentAcp = total area enclosed by outside perimeter of concrete cross-sectionpc = the length of the outside perimeter of the concrete section fpc = compressive stress in concrete after prestress losses have occurred φ = resistance factor
Dr. Naveed Anwar106
Factored Shear Force
For Solid Sections:
Factored Shear Force, Vu
For Box Sections:
Where:ph = Perimeter of the centerline of the closed transverse torsion
reinforcement Tu = Factored torsional moment
Dr. Naveed Anwar107
Transverse Reinforcements
Except for slabs, footings, and culverts, transverse reinforcement shallbe provided either consideration of torsion is required or where:
Where;
Vu = factored shear force (kip)Vc = nominal shear resistance of the concrete (kip)Vp = component of prestressing force in direction of the shear forceφ = resistance factor
Dr. Naveed Anwar108
Minimum Transverse Reinforcements
Minimum Transverse Reinforcement is calculated as
where:Av = Area of a transverse reinforcement within distance sbv = Width of web adjusted for the presence of ductss = Spacing of transverse reinforcementfy = Yield strength of transverse reinforcement
For segmental post-tensioned concrete box girder minimum transverse reinforcement is given by
Dr. Naveed Anwar109
Spacing of Transverse Reinforcements
The spacing of the transverse reinforcement shall not exceed themaximum permitted spacing, smax, determined as:
If vu < 0.125 f ′c, then: smax = 0.8dv ≤ 24.0 in. If vu ≥ 0.125 f ′c, then: 0.4 12.0 Smax = dv ≤ 12.0 in.
where:vu = the shear stress calculateddv = effective shear depth
For segmental post-tensioned concrete box girder bridges,spacing of closed stirrups or closed ties required to resist sheareffects due to torsional moments shall not exceed one-half of theshortest dimension of the crosssection, nor 12.0 in.
Dr. Naveed Anwar110
Design and Detailing Requirements
The design yield strength of nonprestressed transverse reinforcement shallbe taken equal to the specified yield strength when the latter does not exceed60.0 ksi.
For nonprestressed transverse reinforcement with yield strength in excess of60.0 ksi, the design yield strength shall be taken as the stress correspondingto a strain of 0.0035, but not to exceed 75.0 ksi.
The design yield strength of prestressed transverse reinforcement shall betaken as the effective stress, after allowance for all prestress losses, plus 60.0ksi, but not greater than fpy When welded wire reinforcement is used astransverse reinforcement, it shall be anchored at both ends in
Components of inclined flexural compression and/or flexural tension invariable depth members shall be considered when calculating shearresistance
Dr. Naveed Anwar
Shear & Torsion Design(British Standards)
Dr. Naveed Anwar112
Shear Resistance and Reinforcement
The shear stress, ʋ at any cross section should be calculated from
ʋ =V
bd
Incase ʋ exceeds 0.75 fc or 4.75N
mm2shear reinforcement is provided.
Value of ʋ Area of Vertical Shear Reinforcement
ʋ = ʋc Asv = 0.4 bsv 0.87f𝑦𝑣
ʋ > ʋc Asv = bsv (ʋ + 0.4 − 𝑠ʋc ) 0.87f𝑦𝑣
Where;
Dr. Naveed Anwar113
Enhancement of Shear Strength
At any cross section additional longitudinal reinforcement, Asa isrequired in the tensile zone.
An enhancement of shear strength may be allowed for sectionswithin a distance av < 2d from the face of a support, front edge of arigid bearing or center line of a flexible bearing.
This enhancement should take the form of an increase in theallowable shear stress and under such cases the main reinforcementat the section considered should continue to the support and beprovided with an anchorage equivalent to 20 times the bar size
Dr. Naveed Anwar114
Torsional Shear Stress and Reinforcement
Box Sections
Torsional shear stress
Torsion Reinforcement Criteria
Rectangular Sections
Torsional shear stress
Torsion Reinforcement Criteria
Dr. Naveed Anwar115
Longitudinal Shear
The longitudinal shear force, V1 per unitlength of a composite member, whethersimply supported or continuous, shouldbe calculated at the interface of theprecast unit and the in situ concrete andat any vertical planes which may becritical in longitudinal shear
V1 should not exceed lesser of thefollowing: Potential Shear Planes
Dr. Naveed Anwar116
Minimum Transverse Reinforcement Criteria
The amount of transverse reinforcement should exceedlesser of the following:
In the bottom, or predominantly tensile, flangeeither 1 500 mm2/m or 1 % of the minimum flangesection.
In the top, or predominantly compressive, flangeeither 1 000 mm2/m or 0.7 % of the minimumflange section
Dr. Naveed Anwar117
Detailing Requirements
Care should be taken in detailing to prevent diagonal compressiveforces in adjacent faces of beam spalling.
Longitudinal reinforcements should be positioned uniformly suchthat there is bar at each corner of the links.
In detailing the longitudinal reinforcement to cater for torsionalstresses account may be taken of those areas of the cross sectionsubjected to simultaneous flexural compressive stresses, and alesser amount of reinforcement provided.
In the case of beams, the depth of the compression zone used tocalculate the area of section subject to flexural compression shouldbe taken as twice the cover to the closed links.
Dr. Naveed Anwar
Shear & Torsion Design(European Standards)
Dr. Naveed Anwar119
Design Shear Resistance
Shear resistance is taken smaller of the following
V Rds = Asw
sz fywd cot θ
V Rdmax = αcwbwzv1fcd/(Cot θ + tan θ)
Where;
αcw = coefficient taking account of stress state.Asw = Cross-sectional area of shear reinforcementfywd = Design Yield Strengthv1 = Strength Reduction Factors
Dr. Naveed Anwar120
Design Shear Resistance
Recommended values of v1
V1 = 0.6 fck < 60 Mpa
V1 = 0.9- fck /200 > 0.5 fck < 60 Mpa
Recommended values of αcw
αcw = 1 + σcp/ fcd 0 < σcp < 0.25 fcd
αcw = 1.25 0.25 fcd < σcp < 0.50 fcd
αcw = 2.5(1 - σcp/ fcd ) 0.50 fcd < σcp < 1.00 fcd
σcp = Mean Compressive Stress
Dr. Naveed Anwar121
Design Shear Resistance
Maximum effective cross-sectional area of shear reinforcement Asw is given by
Area of Shear Reinforcement is evaluated from the followingequation:
Dr. Naveed Anwar122
Design Shear Resistance
For straight tendons, a high level of prestress ({σcp / fcd > 0,5) andthin webs, if the tension and the compression chords are able tocarry the whole prestressing force and blocks are provided at theextremity of beams to disperse the prestressing force it may beassumed that the prestressing force is distributed between thechords. Hence, the compression field due to shear only should beconsidered in the web (αcw= 1).
Dr. Naveed Anwar123
Design Shear Resistance
For bonded prestressing, located within the tensile chord, theresisting effect of prestressing may be taken into account forcarrying the total longitudinal tensile force.
In the case of inclined bonded prestressing tendons in combinationwith other longitudinal reinforcement/tendons the shear strengthmay be evaluated, by a simplification, superimposing two differenttruss models with different geometry and weighted mean valuebetween θ1 and θ2 may be used for concrete stress field verification.
Dr. Naveed Anwar124
Design Shear Resistance
In the case of segmental constructionwith precast elements and no bondedprestressing in the tension chord, theeffect of opening of the joint should beconsidered. The force in the tensionchord should be assumed to remainunchanged after the joints haveopened. In consequence, as the appliedload increases and the joints open theconcrete stress field inclination withinthe web increases. The shear capacitycan be evaluated by
V Rds = Asw
sz fywd cot θ
Dr. Naveed Anwar125
Shear between Web and Flanges
The longitudinal shear stress, VEd at the junction between one side of aflange and the web is determined by the change of the normal(longitudinal) force in the part of the 'flange considered, according to:
VEd = ΔFd /(hf . Δx)
Dr. Naveed Anwar126
Design for Torsion
The effects of torsion and shear for both hollow and solid members maybe superimposed, assuming the same value for the strut inclination θ.
Dr. Naveed Anwar127
Longitudinal Reinforcement for Torsion Design
The required area of the longitudinal reinforcement for torsion ΣAsl
may be calculated as:
In compressive chords, the longitudinal reinforcement may bereduced in proportion to the available compressive force.
In tensile chords the longitudinal reinforcement for torsion shouldbe added to the other reinforcement.
The longitudinal reinforcement should generally be distributedover the length of side. but for smaller sections it may beconcentrated at the ends of this length
Dr. Naveed Anwar128
Max. Resistance to Torsion and Shear
Solid SectionsTEd /TRdmax + VEd /Vrdmax <1.0
TEd = Design Torsional Moment
VEd = Design Transverse Force
Vrdmax = Max. Design Shear Resistance
TRdmax = Design Torsional Resistance=2 vαcwfcdAktefi Sin θ Cos θ
Box Sections
Each wall should be designed separately for combined effects of shear andtorsion. The ultimate limit state for concrete should be checked with referenceto the design shear resistance, Vrdmax
Dr. Naveed Anwar
Seismic Design (AASHTO LRFD)
Dr. Naveed Anwar130
CE 72.32 - Design of Tall Buildings, Dr. Naveed Anwar
Seismic Design Flowchart
(AASHTO LRFD)
Dr. Naveed Anwar131
Seismic Hazard
The seismic hazard at a bridge site shall be characterized by theacceleration response spectrum for the site and the site factors forthe relevant site class.
The acceleration spectrum shall be determined using either theGeneral Procedure specified the Site Specific Procedure.
The General Procedure shall use the peak ground accelerationcoefficient (PGA) and the short- and long period spectralacceleration coefficients.
The site-specific probabilistic ground-motion analysis should beperformed to generate a uniform-hazard acceleration responsespectrum considering a seven percent probability of exceedance in75 yr for spectral values over the entire period range of interest.
Dr. Naveed Anwar132
Site Classification
Dr. Naveed Anwar133
Site Factors and Spectral Acceleration Coefficients
Values of Site Factor at Zero-Period on Acceleration Spectrum
Values of Site Factor for long Period Range of Acceleration Spectrum
Dr. Naveed Anwar134
Seismic Performance Zones
Each bridge shall be assigned to one of the four seismic zones using the value of SD1 calculated from the expression:
SD1 = Fv S1
Dr. Naveed Anwar135
Response Modification Factors
Response Modification Factors—Substructures
Response Modification Factors—Connections
Dr. Naveed Anwar136
Earthquake Analysis for Bridges
Minimum analysis Requirements for Multispan Bridges
* No Seismic Analysis RequiredSM Single Mode Elastic MethodUL Ultimate Load Elastic MethodMM Multimode Elastic MethodTH Time History Method
Dr. Naveed Anwar137
Single Mode Method
The single-mode method of spectral analysis shall be based on thefundamental mode of vibration in either the longitudinal ortransverse direction.
For regular bridges, the fundamental modes of vibration in thehorizontal plane coincide with the longitudinal and transverseaxes of the bridge structure.
This mode shape may be found by applying a uniform horizontalload to the structure and calculating the corresponding deformedshape.
The natural period may be calculated by equating the maximumpotential and kinetic energies associated with the fundamentalmode shape.
Dr. Naveed Anwar138
Single Mode Method
Calculate the static displacements vs(x) due to an assumed uniform loading po
Calculate factors α, β, and γ as:
α = ʃ vs(x) dxβ = ʃ w(x) dxγ = ʃ w (x) vs
2dx
Calculate time period of bridge as:
Calculate the equivalent static earthquake loading pe(x)
Dr. Naveed Anwar139
Uniform Load Method
The uniform load method shall be based on thefundamental mode of vibration in either thelongitudinal or transverse direction of the basestructure.
The period of this mode of vibration shall be taken asthat of an equivalent single mass-spring oscillator.
The stiffness of this equivalent spring shall becalculated using the maximum displacement thatoccurs when an arbitrary uniform lateral load isapplied to the bridge
Dr. Naveed Anwar140
Uniform Load Method
Calculate the static displacements vs(x) due to an assumed uniformloading po
Calculate the bridge lateral stiffness, K, and total weight, W, from thefollowing expressions
Calculate the period of the bridge, Tm, using the expression
Calculate the equivalent static earthquake loading pe from theexpression
Dr. Naveed Anwar141
Multimode Method
The multimode spectral analysis method shall be used for bridgesin which coupling occurs in more than one of the three coordinatedirections within each mode of vibration.
As a minimum, linear dynamic analysis using a three-dimensionalmodel shall be used to represent the structure.
The number of modes included in the analysis should be at leastthree times the number of spans in the model.
The member forces and displacements may be estimated bycombining the respective response quantities (moment, force,displacement, or relative displacement) from the individual modesby the Complete Quadratic Combination (CQC) method
Dr. Naveed Anwar142
Time History Analysis
Developed time histories shall have characteristics that arerepresentative of the seismic environment of the site and the localsite conditions
Where recorded time histories are used, they shall be scaled to theapproximate level of the design response spectrum in the periodrange of significance.
Each time history shall be modified to be response-spectrumcompatible using the time-domain procedure.
At least three response-spectrum-compatible time histories shallbe used for each component of motion in representing the designearthquake (ground motions having seven percent probability ofexceedance in 75 yr).
Dr. Naveed Anwar143
Time History Analysis
All three orthogonal components (x, y, and z) of design motionshall be input simultaneously when conducting a nonlinear time-history analysis.
The design actions shall be taken as the maximum responsecalculated for the three ground motions in each principaldirection.
If a minimum of seven time histories are used for each componentof motion, the design actions may be taken as the mean responsecalculated for each principa l direction.
Dr. Naveed Anwar144
Determine Design Displacements
P-Δ Requirements
The displacement of any column or pier in the longitudinal or transverse direction shall satisfy:
Δ Pu = 0.25 ϕMn
Where,Δ = Rd Δe
If T< 1.25Ts then Rd = (1-1/R)*1.25Ts/T + 1/RIf T> 1.25Ts then Rd = 1.0
Δ = displacement of the point of contraflexure in the column Δe = displacement calculated from elastic seismic analysisT = period of fundamental mode of vibrationTS = corner period Pu = axial loadφ = flexural resistance factor for column specified
Dr. Naveed Anwar
Seismic Design (European Standards)
Dr. Naveed Anwar146
Design Requirements
No-Collapse (Ultimate Limit
State)
Minimisation of damage
(serviceability limit state)
• Flexural Yielding of Specific Sections are Allowed
• No damage to Brick Damage
• Minor Damage to Secondary Components
Dr. Naveed Anwar147
Intended Behaviour
The bridge shall be designed so that its behaviour under the designseismic action is either ductile, or limited ductile/essentially elastic,depending on the seismicity of the site.
Q = Behaviour FactorIE = Ideal ElasticE = Essentially ElasticLD = Limited DuctileD = Ductile
Dr. Naveed Anwar148
Seismic Analysis Methods
Linear Dynamic Analysis
Fundamental Mode Analysis
Alternative Linear Methods
Non-Linear Dynamic Time
History Analysis
Pushover Analysis
Dr. Naveed Anwar149
Linear Dynamic Analysis (Response Spectrum Analysis)
The Response Spectrum Analysis is an elastic calculation of the peakdynamic responses of all significant modes of the structure, usingthe ordinates of the site dependent design spectrum.
The overall response is obtained by statistical combination of themaximum modal contributions. Such an analysis may be applied inall cases in which a linear analysis is allowed.
The earthquake action effects shall be determined from anappropriate discrete linear model (Full Dynamic Model), idealised inaccordance with the laws of mechanics and the principles ofstructural analysis, and compatible with an associated idealisation ofthe seismc action. In general this model is a space model.
Dr. Naveed Anwar150
Fundamental Model Method (FMM)
Fundamental mode method, equivalent static seismic forces are derivedfrom the inertia forces corresponding to the fundamental mode andnatural period of the structure in the direction under consideration, usingthe relevant ordinate of the site dependent design spectrum
Rigid Deck Model
Flexible Deck
Model
Individual Pier Model
Dr. Naveed Anwar151
Rigid Deck Model
This model is only be applied, when deformation of the deck within ahorizontal plane is negligible compared to the horizontal displacements ofthe pier tops under seismic action.
The earthquake effects shall be determined by applying a horizontal equivalent static force at the deck given by the expression
F= MSDT
M = Total effective mass of structureSD = Spectral AccelerationT = Fundamental Time Period
Dr. Naveed Anwar152
Flexible Deck Model
The fundamental period of the structure in the horizontal directionconsidered, may be estimated via the Rayleigh quotient, using ageneralised single-degree-of-freedom system:
The earthquake effects shall be determined by applying horizontal forcesFi at all nodal points given by:
Dr. Naveed Anwar153
Individual Pier Model
In some cases the seismic action in the transverse direction of the bridgeis resisted mainly by the piers, without significant interaction betweenadjacent piers. In such cases the seismic action effects acting in the i-thpier may be approximated by applying on it an equivalent static force as:
Fi= MiSDiTi
Where;
Dr. Naveed Anwar154
Alternative Linear Method
Time series analysis is an alternative linear method, the design Seismic action shall be taken as theaverage of the extreme response computed for eachaccelerogram in a set of time-histories considered.
Dr. Naveed Anwar155
Nonlinear Dynamic Time History Analysis
The time dependent response of the structure shall be obtained throughdirect numerical integration of its non-linear differential equations ofmotion.
The seismic input shall consist of ground motion time-histories
The effects of gravity loads and of the other quasi-pern1anent actions in theseismic design situation, as well as second order effects, shall be taken intoaccount.
This method can be used only in combination with a standard responsespectrum analysis to provide insight into the post -elastic response andcomparison between required and available local ductility den1ands.
Generally, the results of the non-linear analysis shall not be used to relaxrequirements resulting from the response spectrum analysis
Dr. Naveed Anwar156
Pushover Analysis
Pushover analysis is a static non-linear analysis of thestructure under constant vertical (gravity) loads andmonotonically increased horizontal loads, representing theeffect of a horizontal Seismic component. Second order effectsshall be accounted for.
The horizontal loads are increased until a target displacementis reached at a reference point.
The method may be applied to the entire bridge structure orto individual components
Dr. Naveed Anwar157
Pushover Analysis
The main objectives of the analysis are:
The estimation of the sequence and the final patternof plastic hinge formulation;
The estimation of the redistribution of forcesfollowing the formulation of plastic hinges.
The assessment of the force-displacement curve ofthe structure (capacity curve) and of the deformationdemands of the plastic hinges up to the targetdisplacement.
Dr. Naveed Anwar158
Capacity Design Approach
For structures designed for ductile behaviour, capacity designeffects Fc (Vc, Mc, Nc) shall be calculated by analysing theintended plastic mechanism under:
The non-seismic actions in the design seismic situationand
The level of seismic action in the direction underconsideration at which all intended flexural hinges havedeveloped bending moments equal to an upper fractile oftheir flexural resistance, called the over strength moment,Mo.
Dr. Naveed Anwar159
Capacity Design Approach
The over strength moment of a section shall be calculated as:
Mo = γo MRD
Where; Yo is the overstrength factor;MRD is the design flexural strength of the section.
The value of the overstrength factor should reflect the variability ofmaterial strength properties, and the ratio of the ultimate strengthto the yield strength.
Yo = 1.35 for concrete membersYo = 1.25 for steel members
Dr. Naveed Anwar160
Capacity Design Approach
In the case of reinforced concrete sections with special confiningreinforcement and with the value of the normalized axial forceexceeding 0.1, the value of the overstrength factor shall bemultiplied by 1 + 2 (ηk – 0.1)2
Where;ηk = NED / (Ac fck)
Within the length of members that develop plastic hinge(s), thecapacity design bending moment Mc at the vicinity of the hinge shallnot be assumed to be greater than the relevant design flexuralresistance MRD of the nearest hinge
Dr. Naveed Anwar161
Capacity Design Approach
Capacity design moments Mc within the length of member containing plastic hinges
Dr. Naveed Anwar162
Flexural Resistance Criteria
Structures of Limited Ductile Behaviour
For flexural resistance of sections the following condition shall be satisfied
Ed < Rd
Ed is the design action effect in the seismic design
Rd is the design flexural resistance of the section
Dr. Naveed Anwar163
Flexural Resistance Criteria
Structures of Ductile Behaviour
For flexural resistance of sections of plastic hinges the following condition shall be satisfied
Med < MRd
MEd is the design value of the momentMRd is the design flexural resistance of the section
For flexural resistance of sections outside regions of plastic hingesthe following condition shall be satisfied
Mc < MRd
Dr. Naveed Anwar164
Vertical Shear Resistance
Verification of joints adjacent to plastic hinges
Any joint between a vertical ductile pier and the deck or a foundationadjacent to a plastic hinge in the pier, shall be designed in shear to resistthe capacity design effects of the plastic hinge in the relevant direction.
The design vertical shear of the joint, Vjz, shall be assumed as:
Vjz = γo TRC – VB1C
TRC = Resultant force of the tensile reinforcement of the pierVB1C = shear force of beam adjacent to tensile face of column
Dr. Naveed Anwar165
Horizontal Design Shear
The design horizontal shear of the joint Vjx may be calculated as
Dr. Naveed Anwar166
Shear Verification
The shear verification should be carried out at the centre of thejoint, and the influence of following axial forces may be takeninto account in addition to vertical and horizontal shear.
Vertical axial joint force Njz =
Dr. Naveed Anwar167
Joint Verification
For the joint verification the following average nominal stressesare used:
Shear stresses =
Axial Forces =
Dr. Naveed Anwar168
Reinforcement Arrangement
Vertical stirrups should enclose the longitudinal "beam"reinforcement at the face opposite to the pier. Horizontal stirrupsshould enclose the pier vertical reinforcement, as well as "beam"horizontal bars anchored into the joint. Continuation of pierstirrups/hoops into the joint is recommended
Up to 50% of the total amount of vertical stirrups required in thejoint may be U bars, enclosing the longitudinal "beam" reinforcementat the face opposite to the column
50 % of the bars of the top and bottom longitudinal reinforcement ofthe "beams", when continuous through the joint body and adequatelyanchored beyond it, may be taken into account for covering therequired horizontal joint reinforcement area Asx.
Dr. Naveed Anwar169
Reinforcement Arrangement
Dr. Naveed Anwar170
Reinforcement Arrangement
The longitudinal (vertical) pier reinforcement should reach as far aspossible into the "beam", ending just before the reinforcement layersof the "beam" at the face opposite to the pier-"beam" interface. In thedirection of flexure of the plastic hinge, the bars of both tensileregions of the pier should be anchored by a rectangular hookdirected towards the centre of the pier.
Vertical stirrups of amount ρiz > ρmin, acceptable from theconstructability point of view, may be placed within the joint body.
The horizontal reinforcement within the joint body may be reducedby ΔAsz < ΔAsx, provided that the ratio of the horizontalreinforcement remaining within the joint body satisfies expression
Dr. Naveed Anwar171
Deck Verification
It shall be verified that no significant yielding occurs in the deck. Thisverification shall be carried out
for bridges of limited ductile behaviour, under the most adversedesign action effect
for bridges of ductile behaviour, under the capacity designeffects
When the horizontal component of the seismic action in thetransverse direction of the bridge is considered, yielding of the deckfor flexure within a horizontal plane is considered to be significant ifthe reinforcement of the top slab of the deck yields up to a distancefrom its edge equal to 10 % of the top slab width, or up to thejunction of the top slab with a web, whichever is closer to the edge ofthe top slab
