peer 2002 peer annual meeting seismic performance modeling of reinforced concrete bridges stephen...
TRANSCRIPT
2002 PEER Annual Meeting
PPEEEERR Seismic Performance Modeling
of Reinforced Concrete Bridges
Stephen MahinByron and Elvira Nishkian Professor of Structural Engineering
Mahmoud Hachem, Brian Buckman and Colin Cook Graduate Student Reseachers
University of California at Berkeley
2002 PEER Annual Meeting
PEER Bridge Program
Focus on:• Monolithic reinforced
concrete bridge construction
• New rather than older construction detailing
• Representative of:– Viaducts
– Overcrossings
– Major interchanges
2002 PEER Annual Meeting
Many Elements Involved
• Approaches• Abutments• Foundations• Movement Joints• Columns/Piers• Superstructure• Nonstructural Features
Thrust Area 5
Structural Performance
2002 PEER Annual Meeting
Spirally Reinforced Column Tests
Test Matrix • Loading history
– Traditional cyclic– Pulse initiated cyclic– Variable axial load– Shaking table testing
• Loading rates: Fast and quasi-static
• Aspect ratios: Moderate and low
• Cross-sectionCircular and interlocking spirals
2002 PEER Annual Meeting
Discuss: Shaking Table Tests
Objectives:• Data to validate analytical models• Compare performance for near-fault
and long-duration excitations• Assess effects of multiple components
of ground motion• Assess cumulative damage models• Effect of cross-sectional geometry
•Circular sections with spirals•Noncircular with interlocking spirals
2002 PEER Annual Meeting
Column Performance
After Design Level Event (R=4) After First Maximum Level Event (=6)
2002 PEER Annual Meeting
Condition at end of tests
Fractured Spiral Fractured Bar
Buckled Bars
After sixth repetition of Maximum Run - Olive View
2002 PEER Annual Meeting
Long Duration Excitations
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
1985 Llolleo, Chile Record
2002 PEER Annual Meeting
Peak Displacement Response
Maximum Bottom and Top Disp. in Long and Lat directions, Test A2
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
A2-Run1Yield
A2-Run2Design 1
A2-Run3Max 1
A2-Run4Design 2
A2-Run5Max 2
A2-Run6Max 3
A2-Run7Design 3
A2-Run8Max 4
A2-Run9Max 5
A2-Run10Max6
Displacement [in]
Long. Column Disp Lat. Column Disp Long. Peak Ground Disp Lat. Peak Ground Disp
First Bar
Buckling
Bar
Fracture
Bi-directional input has limited effect and in the cases considered extends life of column
2002 PEER Annual Meeting
Bi-directional Response
- 8 - 6 - 4 - 2 0 2
- 8
- 7
- 6
- 5
- 4
- 3
- 2
- 1
0
1
2
Δl a t
( i n )
Δ
l
o
n
g
(
i
n
)
Dis
pla
cem
ent
, in
.
Displacement, in.
Ground motion characteristics have a large effect on:
• Nature of bi-directional response• Sensitivity of maximum
displacements to intensity• Residual displacements
Currently design criteria, for ideal conditions and without significant P-Δ effects or eccentric gravity loads, result in well-performing columns with significant reserve capacity
2002 PEER Annual Meeting
Verification of Analytical Models
Global: Displacements, Residual
Displacements, Forces, Moments
Local: 1. Curvatures, 2. Strains, 3. Slip Rotations, …4. Cumulative Damage
Response quantities: Analytical Models:• Elastic Analysis with
equivalent sectional Stiffness (EI e)
• Concentrated hinge models with equivalent plastic hinge properties
• Fiber models with distributed section properties with equivalent material properties
2002 PEER Annual Meeting
Elastic Models
Various assumptions for approximating “effective” section stiffness EI EIe as defined by Caltrans
gives reasonable results for maximum displacement
EIeTest
Maximum Credible
2002 PEER Annual Meeting
Elastic Models
EIeTest
Maximum Credible
Maximum Credible
Lateral Direction
Various assumptions for approximating “effective” section stiffness EI EIe as defined by Caltrans
gives reasonable results for maximum displacement
Not always
2002 PEER Annual Meeting
Elastic Models
Various assumptions for approximating “effective” section stiffness EI EIe as defined by Caltrans
gives reasonable results for maximum displacement
Not always
EIeTest
Maximum Credible
Design Level
2002 PEER Annual Meeting
Elastic Models
Various assumptions for approximating “effective” section stiffness EI EIe as defined by Caltrans
gives reasonable results for maximum displacement
Not always No information on residual
displacements Other engineering demand
parameters inferred from pushover analyses
EIeTest
Residual Displacement
Maximum Credible
Design Level
2002 PEER Annual Meeting
Concentrated Plastic Hinge Models
• Various methods for estimating equivalent properties for concentrated plastic hinge (Lp, M-, etc.)
• Various idealized hysteretic models– Bilinear vs. Stiffness
Degrading
– Coupled and uncoupled
BilinearStiffness Degrading
Maximum Credible
2002 PEER Annual Meeting
Concentrated Plastic Hinge Models
BilinearStiffness Degrading
Maximum Credible
• Most models provide adequate estimate of maximum displacement
BilinearStiffness Degrading
Design Level
2002 PEER Annual Meeting
Concentrated Plastic Hinge Models
• Most models provide adequate estimate of maximum displacement
• Nonlinear models provide indication of yielding and degradation on wave form and residual displacement– Estimates are often poor
– Stiffness degrading models generally better
BilinearStiffness Degrading
Maximum Credible
Stiffness Degrading Bilinear
Lateral Direction
2002 PEER Annual Meeting
Concentrated Plastic Hinge Models
BilinearStiffness Degrading
Maximum Credible
Stiffness Degrading Bilinear
Lateral Direction
2002 PEER Annual Meeting
Concentrated Plastic Hinge Models
• Local information on strains, bar buckling, fatigue, etc. must be inferred from detailed analysis of member– Problem under cyclic
loads?
2002 PEER Annual Meeting
Fiber Models
• Useful for well confined members controlled by ductile yielding
• Approximations at material level, number of fibers used to model section, manner in which member is discretized longitudinally
BilinearStiffness Degrading
Maximum CredibleFiber Model
Concentrated Hinge Models
2002 PEER Annual Meeting
Fiber Models
• Generally, much better fidelity• Results, especially for residual displacement and local deformations
(strain) sensitive to modeling of section• Fixed end rotations due to bar pullout not yet accounted for in OpenSees
Maximum Credible
Fiber Model
2002 PEER Annual Meeting
Model Performance vs. Test
2002 PEER Annual Meeting
where 2Nf is the number of half cycles to failure at a plastic strain
Performance Evaluation
Park & Ang:
• Damage Indices:
Bar Fatigue Damage Index:
bfp Na −= )2(ε
D =1
2Nf∑
D =dmax
dult+β
dE∫
Fydult
Section Fatigue, spalling, bar buckling, residual displacement, etc.
2002 PEER Annual Meeting
Damage Idecies at First Bar Fracture
2002 PEER Annual Meeting
Parametric Study
• Design multiple columns with varying:
Dcol
P
HAspect Ratio (ar)
Axial Load (Pr)
Diameter (Dcol)
2002 PEER Annual Meeting
Design Procedure Used
• Given Dcol, ar, Pr
– Determine sp from BDS
– Solve iteratively for l that would result in the
required strength: Fy =mass×Sa
Z For each l value:
Perform M- analysis, determine My, EIeff, Mu and u (failure reached when εc>εcu or εs>εsu)
2002 PEER Annual Meeting
Column Design according to ARS
ZMass
StrengthSa =
2002 PEER Annual Meeting
Moment-Curvature Analysis
Also determine c (Neutral Axis Depth)
2002 PEER Annual Meeting
Idealized Force-displacement Model
Deformation
Force Exact BehaviorIdealized
Fy
K
Kh
dult
Fu
Also determine Lp and T
2002 PEER Annual Meeting
Ground Motions Used 20 LMSR motions and 50 LMLR motions
LMSR motions
2002 PEER Annual Meeting
Mean Results
2002 PEER Annual Meeting
Mean+1 SD Results
2002 PEER Annual Meeting
Fragility Curves
Compute Fragility curves for: Park & Ang Index (Minor and Significant
damage) Fatigue Index Spalling (|εcu| > 0.009)
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.5 1 1.5 2
Transverse Reinforcement Ratio (%)
Calculated Compressive Strain
Onset of Spalling
Onset of Bar Buckling
Assumes analysis model and preformance criteria are correct
2002 PEER Annual Meeting
Fragility Curves for Events with Large Magnitude at Small Distance
Spalling
Fatigue Failure
SignificantDamage
(Park&Ang)
MinorDamage
(Park&Ang)
2002 PEER Annual Meeting
Fragility Curves for Events with Large Magnitude at Large Distance
MinorDamage
(Park&Ang) Spalling
Fatigue Failure
SignificantDamage
(Park&Ang)
2002 PEER Annual Meeting
Summary
• New design and detailing criteria for circular columns generally result in performance consistent on average with performance objectives
• Ground motion characteristics effect: – Maximum response– Bi-directional response characteristics– Residual displacements
2002 PEER Annual Meeting
Summary
• Analytical models involve significant levels of judgement to get adequate prediction of performance
• Nearly all models with reasonable stiffness estimates can predict max. displacements– Small diameter, low aspect ratio (low periods), high loads, P-Δ
effects and gravity load eccentricities potential problems – Fiber models provide best fidelity, but need further assessment
and refinement
• Residual displacements and local deformations (spalling, bar buckling, steel fracture, etc.) sensitive to modeling
2002 PEER Annual Meeting
Summary
• Parametric and fragility analyses provide useful basis for understanding behavior, but integration into overall PEER assessment methodology essential
• Additional shaking table tests will be carried out along with analytical studies to:– get data on more complex bridge systems requiring
significant redistribution of load once yielding occurs
– Identify damping and strain rate effects