Computer-Aided Design, Analysis and Load Rating of Precast-PrestressedSpliced Girder Bridges
Western Bridge Engineersβ SeminarReno, NV September 2015
Lynn PetersonSecretary of Transportation
Richard Brice, PESoftware Applications Engineer
Outline
β’ LRFD Requirements for Spliced Girder Bridgesβ’ Overview of Spliced Girder Analysisβ’ Computer Aided Design, Analysis, and Load Rating
Design, Analysis, and Rating of Spliced Girder Bridges
β’ Basic requirements of conventional precast-prestressed girder bridges β Service stress limitations, ultimate strength
requirements, etc.β’ LRFD 5.14.1.3 β Spliced Precast Girders
β Additional requirements for contract documents β Additional service stress limitationsβ Additional analysis requirements
LRFD Requirement for Time-Step Analysis
LRFD 5.9.5.4.1For segmental construction and post-tensioned spliced precast girders, other than during preliminary design, prestress losses shall be determined by the time-step method... including consideration of the time-dependent construction stages and schedule shown in the contract documents.
For components with combined pretensioning and post-tensioning, and where post-tensioning is applied in more that one stage, the effects of subsequent prestressing on the creep loss of previous prestressing shall be considered.
Introduction to Time-Step Analysis
β’ Models design life through discrete time intervalsβ’ Uses fundamental principles of engineering mechanicsβ’ Accounts for time-dependent material properties and
responses (ππππβ², ππ, πππ π π ππππππππππππππ, relaxation)
β’ Step-wise pseudo-linear solution to a nonlinear problem
β’ Structural response at the end of any interval is the summation of the responses of all the preceding intervals
Challenge of Time-Step Analysis
β’ Sheer quantity of computations that must be performedβ Deformations are computed at many locationsβ Deformations are computed in every piece of the spliced girderβ Deformations are computed for the design life of the structureβ Transformed section properties change with time and location
β’ Non-prismatic segments (haunches, varying tendon locations)β’ πΈπΈππ and thus the modular ratios vary with time
β Loading conditions change with timeβ’ Staged application of superimposed loadsβ’ Multi-staged post-tensioning
β Statical structural system changes with timeβ’ Composite closure jointsβ’ Composite deckβ’ Temporary support removal
Composition of Spliced Girders
β’ Precast concrete segments
β’ CIP concrete closure joints and deck
β’ Prestressing Strands and Tendons
β’ Non-prestressedreinforcement
Time Variation of Material Properties
β’ Three distinct materialsβ’ Concrete
β Strength (ππππβ²) and stiffness (πΈπΈππ) vary with timeβ Creep rate varies with time and time of loadingβ Shrinkage rate varies with time
β’ Prestressing steelβ Relaxation rate varies with time and loading
β’ Non-prestressed Reinforcementβ Constant with time. Obeys Hookeβs Law
Timeline Modeling
β’ Modeled as a sequence of discrete intervalsβ Begins when segments are constructedβ Ends at conclusion of design life
β’ Interval duration is based on changes in loading and the statical structural system
β’ Intervals are sub-divided to capture time-dependent material responses immediately following a change in forces
Typical Timeline
Construction Event Day of Occurrence
Construct Segments 0Erect Segments 28Cast Closure Joints and Deck 35Install tendons 42Install traffic barrier 60Open to traffic 70
Incremental Deformations
β’ Time-step analysis is simply computing incremental deformations during each interval
β’ Axial strain and curvatureβ Computed for every part of the girderβ Caused by
β’ externally applied loadsβ’ change in statical structural systemβ’ creep and shrinkage of concreteβ’ relaxation of prestressing strands and tendons
Computing Incremental Deformations
βππππ ππππ , ππππ =βππππ πππππ΄π΄πππΈπΈππ ππππ
1 + ππ ππππ , ππππ + οΏ½ππ=1
ππβ1βππππ πππππ΄π΄πππΈπΈππ ππππ
ππ ππππ , ππππ β ππ ππππ, ππππ + βπππ π π ππππ , ππππ
βππππ ππππ , ππππ =βππππ πππππΌπΌπππΈπΈππ ππππ
1 + ππ ππππ , ππππ + οΏ½ππ=1
ππβ1βππππ πππππΌπΌπππΈπΈππ ππππ
ππ ππππ , ππππ β ππ ππππ , ππππ
βπππππ π ππππ , ππππ = βππππππ πππππ΄π΄πππππΈπΈππππ
+ ββππππ ππππ,πππππΈπΈππππ
βπππππ π ππππ , ππππ = βππππππ(ππππ)π΄π΄πππππΈπΈππππ
βππππ = βπππ΄π΄π‘π‘πππΈπΈπ‘π‘ππ
+ βππ πππ‘π‘ππβπππππΌπΌπ‘π‘πππΈπΈπ‘π‘ππ
π΄π΄πππΈπΈππ, βππππ = βππ πΌπΌπππΈπΈπππΌπΌπ‘π‘πππΈπΈπ‘π‘ππ
οΏ½ππππ = βπΈπΈπππ΄π΄ππππππ, οΏ½ππππ = βπΈπΈπππΌπΌπππππποΏ½ππ = βππ=1ππ οΏ½ππππ, οΏ½ππ = βππ=1ππ οΏ½ππππ + οΏ½ππππ πππ‘π‘ππ β ππππΜ ππ =
οΏ½πππΈπΈπ‘π‘πππ΄π΄π‘π‘ππ
, οΏ½ππ =οΏ½ππ
πΈπΈπ‘π‘πππΌπΌπ‘π‘ππ
Time Variation of Material Properties
0
1
2
3
4
5
6
7
1 10 100 1000 10000
f'c (k
si)
Time (days)
Time Variation of Concrete Strength
0
1000
2000
3000
4000
5000
6000
1 10 100 1000 10000
Ec (k
si)
Time (days)
Time Variation of Concrete Modulus
0
1
2
3
4
5
1 10 100 1000 10000
Cre
ep C
oeffi
cien
t
Time (days)
Time Variation of Creep Coefficient
Day 1
Day 2
Day 3
0
0.2
0.4
0.6
0.8
1
1.2
1 10 100 1000 10000
Shrin
kage
Str
ain
X 10
00
Time (days)
Time Variation of Shrinkage Strain
Time Step 1 β Analyze Loading Condition
β’ Moment due to self-weight (external force)β’ Use transformed section analysis
β Neglect bending stiffness of reinforcement
οΏ½ππ = 0 = ππππ β ππππ οΏ½ππ = ππ = ππππ + ππππππππ β ππππππππ
Time Step 1 β Incremental Deformations
β’ Incremental forces on the various parts of the cross section are determined by a transformed section analysisβ βππππ1 = ππππ ,βππππ1 = ππππ ,βππππ1 = ππππ
β’ Incremental Deformationsβ Computed using modulus at time of loading and net
section properties
β βππππ1 = βππππππΈπΈππππ΄π΄ππππ
,βππππ1 = ΞππππππΈπΈππππΌπΌππππ
β Ξππππ1 = ΞππππππΈπΈπππ΄π΄ππ
Time Step 1 β End of Interval
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5
Nor
mal
ized
Axi
al S
trai
n
Time Step
Incremental Axial Deformation in Concrete
βΞ΅c1
Time Step 2 β Time-Dependent Effects
β’ Only Time Passesβ’ Time-dependent response of materials
β Unrestrained Creep of Concreteβ’ Ξππππππ = Ξπππππ
πΈπΈππ΄π΄ππππ(π‘π‘2, π‘π‘1)
β’ Ξππππππ = ΞππππππΈπΈππΌπΌππ
ππ(π‘π‘2, π‘π‘1)
β Unrestrained Shrinkageβ’ Ξπππ π π (π‘π‘2, π‘π‘1)
Time Step 2 β Initial Strain Analysis
β’ Reinforcing causing internal restraintβ’ Compute restrained deformations and
internal restraining forces, Ξππππ2,Ξππππ2,Ξππππ2, Ξππππ2,Ξππππ2,Ξππππ2
Time Step 2 β End of Interval
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5
Nor
mal
ized
Axi
al S
trai
n
Time Step
Incremental Axial Deformation in Concrete
βΞ΅c1
βΞ΅c2
Time Step 3 β Time-Dependent Effects
β’ Only Time Passesβ’ Time-dependent response of materials
β Unrestrained Creep of Concreteβ’ Ξππππππ = Ξπππππ
πΈπΈππ΄π΄ππππ π‘π‘3, π‘π‘1 β ππ π‘π‘2, π‘π‘1 + Ξπππππ
πΈπΈππ΄π΄ππππ π‘π‘3, π‘π‘2
β’ Ξππππππ = ΞππππππΈπΈππΌπΌππ
ππ π‘π‘3, π‘π‘1 β ππ π‘π‘2, π‘π‘1 + ΞππππππΈπΈππΌπΌππ
ππ π‘π‘3, π‘π‘2
β Unrestrained Shrinkageβ’ Ξπππ π π (π‘π‘3, π‘π‘2)
Time Step 3 β Incremental Unrestrained Deformations
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 2 3 4 5 6Time Step
Unrestrained Axial Creep Strain
ππ1 π‘π‘ =ππππ1
πΈπΈππ1π΄π΄ππππππ(π‘π‘, π‘π‘1)
ππ2 π‘π‘ =ππππ2
πΈπΈππ2π΄π΄ππππππ(π‘π‘, π‘π‘2)
Ξππ π‘π‘3, π‘π‘2 = ππ π‘π‘3 β ππ(π‘π‘2)
Time Step 3 β Initial Strain Analysis
β’ Reinforcing causing internal restraintβ’ Compute restrained deformations and
internal restraining forces, Ξππππ3,Ξππππ3,Ξππππ3, Ξππππ3,Ξππππ3,Ξππππ3 If reinforcement were
prestressed, this would be the change in prestress force (aka loss)
Time Step 3 β End of Interval
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
1 2 3 4 5
Nor
mal
ized
Axi
al S
trai
n
Incremental Axial Deformation in Concrete
βΞ΅c1
βΞ΅c2
βΞ΅c3
Time Step i β Repeat, Repeat, Repeat
β’ This procedure is repeated for every cross section and every time interval
β’ Analysis is more involved for spliced girdersβ Continuity externally restrains free deformationsβ Several concrete types cast at different timesβ Changes in statical structural systemβ Pretensioning and multi-stage post-tensioningβ Intrinsic and reduced relaxation of prestressed steel
β’ Computers are great at performing repetitive computations and keeping track of numbers!
Computer Aided Design of Spliced Girders
β’ NCHRP Report 517 β Extending Spansβ Suggests DOT produced software was a
significant contributing factor for wide-spread use of PT Box Girder technology
β Implies same will be true for adoption of spliced girder technology
β Notes the lack of a preferred industry standardβ Recommends owner agencies and industry
pursue development of high quality software tools for spliced girder bridges
PGSpliceβ’
β’ Part of the new WSDOT BridgeLinkβ’ suite of softwareβ’ Design, analyze, and load rate continuous precast-prestressed spliced
girder bridgesβ’ Modeling
β Cantilever pier segmentsβ Drop-in field segmentsβ Temporary erection towersβ Strong back hangersβ Multi-stage post-tensioning
β’ Analysisβ Non-linear time step analysisβ AASHTO, ACI 209 and CEB-FIP Model Code
β’ User interface, modeling, graphing and reporting features are very similar to PGSuperβ’
Bridge Configurations4 Span Variable Depth Girder with Cantilever Piers Segments and Drop In Field Segments
Bridge Configurations3 Span U-Beam with Segments Supported at Permanent Piers and Temporary Erection Towers
Case Study
β’ Two Span Continuous Spliced Girder Bridgeβ’ Presented in PCI State-of-the-Art of Spliced-
Girders report
Baseline Comparison
-2.5
-2
-1.5
-1
-0.5
01 10 100 1000 10000
Stre
ss (K
SI)
Time (Days)
Top of Girder Stress at 0.4L in Span 1 without Time Dependent Effects
Abdel-Karim
PGSplice
Comparison including Time-Dependent Effects
-2.5
-2
-1.5
-1
-0.5
01 10 100 1000 10000
Stre
ss (K
SI)
Time (Days)
Top of Girder Stress at 0.4L in Span 1 with Time Dependent Effects
Abdel-Karim
PGSplice
Software Availability
β’ Free download from WSDOTβ’ http://www.wsdot.wa.gov/eesc/bridge/software
β’ Open Sourceβ’ BridgeLinkβ’ v1.0
β PGSuperβ’ v3.0 (Beta)β PGSpliceβ’ v3.0 (Beta)β BEToolboxβ’ v3.0