1. PEER 2002 PEER Annual Meeting PEER 2002 Annual Meeting uHelmut Krawinkler Seismic Demand Analysis

2. Performance Assessment Performance (Loss) Models and Simulation Hazard Impact Please accept my apologies for showing the (in)famous framework equation

3. Engineering Demand Parameters Collapse:Maximum Story Drift (and others) Struct. Damage:Story Drifts (each story) and Component Deformations Nonstr. Damage:Story Drift (each story) Content Damage:Floor Acceleration and Velocity (each story)

4. Probabilistic Seismic Demand Analysis (PSDA) Given: Structural system Base shear strength,  = V y /W Story shear strength distribution Ground motion hazard, (S a (T 1 )) Set of representative ground motions Asked: EDP hazard, (EDP), max. drift, average drift, floor accel.

5. Probabilistic Seismic Demand Analysis EDP (y)= mean annual frequency of EDP exceeding the value y P[EDP  y | IM = x]= probability of EDP exceeding y given that IM equals x IM (x)= mean annual frequency of IM exceeding the value x (ground motion hazard)

6. EDP (e.g., max. interstory drift) IM (e.g., S a (T 1 )) IM Hazard curve (annual freq. of exceedance) Incremental Dynamic Analysis (IDA)

7. Hazard Curve for Average of Max. Drifts AVERAGE DRIFT HAZARD CURVE-T 1 =1.8 sec. N=9,  =0.10,  =0.05, Peak-oriented model,  =0.060, BH, K 1, S 1, LMSR 0.0001 0.001 0.01 0.1 1 10 00.0050.010.0150.020.025 Average of Maximum Story Drifts,   si,ave (  ) Numerical Integration

8. Ground Motion Hazard: Median EDP-IM relationship: EDP Hazard Curve: Closed Form Expression for EDP Hazard

9. AVERAGE DRIFT HAZARD CURVE-T 1 =1.8 sec. N=9,  =0.10,  =0.05, Peak-oriented model,  =0.060, BH, K 1, S 1, LMSR 0.0001 0.001 0.01 0.1 1 10 00.0050.010.0150.020.025 Average of Maximum Story Drifts,   si,ave (  ) Analytical Sol.-Variable Std. Dev.of Log. Drfit/Given Sa Analytical Sol.-Constant Std. Dev. of Log. Drift/Given Sa Numerical Integration Hazard Curve for Average of Max. Drifts

10. First mode participation factor Roof drift/(Sd(T1)/H) Maximum drift/(Sd(T1)/H) Average drift/(Sd(T1)/H) FEMA 273/356 “Validation”

11. Median 84% Design – Strong Column Concept

12. [Sa(T1)/g]/ = 1.0 [Sa(T1)/g]/ = 2.0 [Sa(T1)/g]/ = 4.0 [Sa(T1)/g]/ = 6.0 [Sa(T1)/g]/ = 8.0 OTM-simplifed proc.      Design – Overturning Moment

13. Non-Deteriorating Hysteretic Systems Displacement Force Displacement Force Displacement Force

14. Basic Modes of Deterioration

15. Calibration - RC Component

16. Very Ductile – Slow Deterioration

17. Medium Ductile – Moderate Deterioration

18. Deterioration Effect, MDOF System NORM. STRENGTH VS. MAX. STORY DUCT. N=9, T 1 =0.9,  =0.05,  =0.03,  =0.015, H 3, BH, K 1, S 1, NR94nya 0 5 10 15 20 05101520  si,max [S a (T 1 )/g] /  Non-degrading system Degrading system

19. Median Global Collapse Assessment

20. Collapse Fragility Curves – SDOF Systems

22. Median R-factors at Collapse - SDOF Systems

23. Summary Assessment PSDA, leading to EDP hazard curves, is feasible for 2-D and 3-D systems We need refinements/improvements in IMs and ground motion selection procedures Site effect and SFSI quantification Quantification of uncertainties Modeling of deterioration Collapse prediction necessitates Modeling of deterioration Modeling of propagation of local collapses Consideration of ground motions associated with long return period hazards (near-fault)