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PEER 2002 PEER Annual Meeting Seismic Performance Modeling of Reinforced Concrete Bridges Stephen Mahin Byron and Elvira Nishkian Professor of Structural.

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Presentation on theme: "PEER 2002 PEER Annual Meeting Seismic Performance Modeling of Reinforced Concrete Bridges Stephen Mahin Byron and Elvira Nishkian Professor of Structural."— Presentation transcript:

1 PEER 2002 PEER Annual Meeting Seismic Performance Modeling of Reinforced Concrete Bridges Stephen Mahin Byron and Elvira Nishkian Professor of Structural Engineering Mahmoud Hachem, Brian Buckman and Colin Cook Graduate Student Reseachers University of California at Berkeley

2 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

3 2002 PEER Annual Meeting Many Elements Involved Approaches Abutments Foundations Movement Joints Columns/Piers Superstructure Nonstructural Features Thrust Area 5 Structural Performance

4 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-section Circular and interlocking spirals

5 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

6 2002 PEER Annual Meeting Column Performance After Design Level Event (R=4) After First Maximum Level Event ( =6)

7 2002 PEER Annual Meeting Condition at end of tests Fractured Spiral Fractured Bar Buckled Bars After sixth repetition of Maximum Run - Olive View

8 2002 PEER Annual Meeting Long Duration Excitations 1985 Llolleo, Chile Record

9 2002 PEER Annual Meeting Peak Displacement Response Bi-directional input has limited effect and in the cases considered extends life of column

10 2002 PEER Annual Meeting Bi-directional Response 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- effects or eccentric gravity loads, result in well-performing columns with significant reserve capacity

11 2002 PEER Annual Meeting Verification of Analytical Models Ü Global: 4Displacements, 4Residual Displacements, 4Forces, Moments Ü 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

12 2002 PEER Annual Meeting Elastic Models Various assumptions for approximating effective section stiffness EI EI e as defined by Caltrans gives reasonable results for maximum displacement EI e Test Maximum Credible

13 2002 PEER Annual Meeting Elastic Models EI e Test Maximum Credible Lateral Direction Various assumptions for approximating effective section stiffness EI EI e as defined by Caltrans gives reasonable results for maximum displacement 4 Not always

14 2002 PEER Annual Meeting Elastic Models Various assumptions for approximating effective section stiffness EI EI e as defined by Caltrans gives reasonable results for maximum displacement 4 Not always EI e Test Maximum Credible Design Level

15 2002 PEER Annual Meeting Elastic Models Various assumptions for approximating effective section stiffness EI EI e as defined by Caltrans gives reasonable results for maximum displacement 4 Not always 4 No information on residual displacements 4 Other engineering demand parameters inferred from pushover analyses EI e Test Residual Displacement Maximum Credible Design Level

16 2002 PEER Annual Meeting Concentrated Plastic Hinge Models Various methods for estimating equivalent properties for concentrated plastic hinge (L p, M-, etc.) Various idealized hysteretic models –Bilinear vs. Stiffness Degrading –Coupled and uncoupled Bilinear Stiffness Degrading Maximum Credible

17 2002 PEER Annual Meeting Concentrated Plastic Hinge Models Bilinear Stiffness Degrading Maximum Credible Most models provide adequate estimate of maximum displacement Bilinear Stiffness Degrading Design Level

18 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 Bilinear Stiffness Degrading Maximum Credible Stiffness Degrading Bilinear Lateral Direction

19 2002 PEER Annual Meeting Concentrated Plastic Hinge Models Bilinear Stiffness Degrading Maximum Credible Stiffness Degrading Bilinear Lateral Direction

20 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?

21 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 Bilinear Stiffness Degrading Maximum Credible Fiber Model Concentrated Hinge Models

22 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

23 2002 PEER Annual Meeting Model Performance vs. Test

24 2002 PEER Annual Meeting where 2N f is the number of half cycles to failure at a plastic strain Performance Evaluation Park & Ang: Damage Indices: Bar Fatigue Damage Index: Section Fatigue, spalling, bar buckling, residual displacement, etc.

25 2002 PEER Annual Meeting Damage Idecies at First Bar Fracture

26 2002 PEER Annual Meeting Parametric Study Design multiple columns with varying: D col P H Aspect Ratio (a r ) Axial Load (P r ) Diameter (D col )

27 2002 PEER Annual Meeting Design Procedure Used Given D col, a r, P r –Determine sp from BDS –Solve iteratively for l that would result in the required strength: For each l value: Perform M- analysis, determine M y, EI eff, M u and u (failure reached when c > cu or s > su )

28 2002 PEER Annual Meeting Column Design according to ARS

29 2002 PEER Annual Meeting Moment-Curvature Analysis Also determine c (Neutral Axis Depth)

30 2002 PEER Annual Meeting Idealized Force-displacement Model Deformation Force Exact Behavior Idealized FyFy K KhKh d ult FuFu Also determine L p and T

31 2002 PEER Annual Meeting Ground Motions Used 20 LMSR motions and 50 LMLR motions LMSR motions

32 2002 PEER Annual Meeting Mean Results

33 2002 PEER Annual Meeting Mean+1 SD Results

34 2002 PEER Annual Meeting Fragility Curves Compute Fragility curves for: Park & Ang Index (Minor and Significant damage) Fatigue Index Spalling (| cu | > 0.009) Assumes analysis model and preformance criteria are correct

35 2002 PEER Annual Meeting Fragility Curves for Events with Large Magnitude at Small Distance Spalling Fatigue Failure Significant Damage (Park&Ang) Minor Damage (Park&Ang)

36 2002 PEER Annual Meeting Fragility Curves for Events with Large Magnitude at Large Distance Minor Damage (Park&Ang) Spalling Fatigue Failure Significant Damage (Park&Ang)

37 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

38 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- 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

39 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


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