1. Assessing Effectiveness of Building Code Provisions Greg Deierlein & Abbie Liel Stanford University Curt Haselton Chico State University … other contributors (PEER TA I & ATC 63) PEER 2007 Annual Meeting

2. 2 PBEE: Collapse (SAFETY) Assessment Decision Variable Intensity Measure Damage Measure Engineering Demand Parameter DV: COLLAPSE DM: Loss of Vertical Carrying Capacity (LVCC) EDP: Interstory Drift Ratio IM: Sa(T 1 ) + Ground Motions EDPs: Deformations & Forces

3. 3 Illustration – 4 Story SMF Building Office occupancy Los Angeles Basin Design Code: 2003 IBC / 2002 ACI / ASCE7-02 Perimeter Frame System Maximum considered EQ demands: S s = 1.5g; S 1 = 0.9g S a(2% in 50 yr) = 0.82g Design V/W of 0.094g Maximum inelastic design drift of 1.9% (2% limit) Typical Perimeter Frame Members Beams: 32” to 40” deep Columns: 24”x28” to 30”x40” Governing Design Parameters - Beams: minimum strength - Column size: joint strength - Column strength: SCWB - Drift: just meets limit 8 inch PT slab

4. 4 Nonlinear Analysis & Calibration

5. 5 0.82g is 2% in 50 year motion Capacity Stats.: Median = 2.2g σ LN = 0.36 Incremental Dynamic Analysis – Collapse 2% in 50 year = 0.82g IDR col = 7-12% Median col = 2.2g σ LN, col = 0.36g

6. Simulation Results: Collapse Modes 40% of collapses 27% of collapses 17% of collapses **Predicted by Static Pushover 12% of collapses 5% of collapses 2% of collapses Incremental Dynamic Analysis

7. Collapse Fragility Curve Median = 2.2g  LN, Total = 0.36 Incremental Dynamic Analysis

8. 8 Uncertainty – Plastic Rotation Capacity Mean (  ) Plastic Rotation Capacity Reduced (  Plastic Rot. Cap.

9. 9 Correlation of Model Uncertainties Type A: Parameters within one element Type B: Between parameters of different elements

10. Collapse Capacity – with Modeling Uncert. Median = 2.2g  LN, RTR = 0.36 σ LN, Total = 0.64 w/mod. 0.82g 2% in 50 yrs P[collapse |Sa = 0.82g] = 5% 5% Margin 2.7x

11. Mean Annual Frequency of Collapse Collapse CDF Hazard Curve Margin: S a,collapse = 2.7 MCE 5% Probability of collapse under design MCE = 5% MAF col = 1.0 x 10 -4 (0.5% in 50 years) 2.7 Collapse Performance 5% 2/50

12. The 2% in 50 year ground motion Illustration:  Site dominated by single event (M 6.9, R 14 km) -- return period of 200 years (MAF 25% in 50 yr)  Boore-Joyner (BJ) attenuation function  Sa (25/50) -- median of BJ. At T=1 sec., Sa = 0.28g  Sa (2/50) -- +1.5  of BJ. At T=1 sec., Sa = 0.56g. Mean Annual Freq. = (Probability of Sa > Sa*, given EQ) x (MAF of EQ)

13. Ground motion selection (+  effect  Consider the Loma Prieta (11022 record): Close match to characteristic event [M 6.9, R 14, Sa(T=1) = 0.65g] Epsilon: +1.7 at T=1 sec; -0.3 at T = 0.45 sec General trend for +epsilon records to peak at the +e periods and drop off elsewhere

14. 14 Effect of Spectral Shape (  ) on collapse capacity ++ ++

15. 1967 and 2003 Design Comparisons Space Frame 1967 UBC, Zone 4 Design V/W: 0.068 g Member sizes Col. 20x20 to 24x24 Beam depth 20 to 26 No SCWB, no joint check, non-conforming ties 1967 Design 2003 Design Perimeter Frame 2003 UBC/2002 ACI Design V/W: 0.094 g Member sizes Col. 24x28 to 30x40 Beam depth 32 to 42 Fully conforming design

16. Comparison of 1967 vs. 2003 Designs Column Hinge Backbone Parameters  p,cap : 1967 = 0.02 rad (COV 50%) 2003 = 0.06 rad K c /K e : 1967 = -0.22 (COV 60%) 2003 = -0.08 Static Pushover Response  u : 1967 = 2.4 2003 = 2.7  u : 1967 = 1.5% roof drift ratio 2003 = 5.0% FEMA 356  p limits: 1967 = 0.006 rad 2003 = 0.015 rad

17. Incremental Dynamic Analysis – Sidesway Collapse IDR col = 7-12% col = 0g Median Sa = 2.2g Median Sa = 1.0 g IDR col = 3-6% 1967 Design Strength: Median Sa = 1.0g, COV = 30% Deformation: IDR max = 3 to 6% 2003 Design Strength: Median Sa = 2.2g, COV = 36% Deformation: IDR max = 7 to 12%

18. Simulated (sidesway) collapse fragility: 4-story building FACTORS CONSIDERED Beams & Cols: flexure-shear B-C Joints: shear/bond Modeling Uncertainty Spectral Shape (  ) Margins (  collapse /MCE) 2003: 2.7 1967: 1.0 P[C/MCE] 2003: 4% 1967: 50% 2.7 1.0 50% 4%

19. 1967 Sidesway and Vertical Collapse (4-story) Total Collapse Probability Sidesway Collapse Probability at IM i Probability of LVCC (given drift ratio) =+ X Probability of No SS Collapse at IM i Per Elwood/Moehle & Aslani/Miranda: Column Shear Failure: Column IDR = 0.024 (mean) Column Axial Failure: Column IDR = 0.056 (mean) Recall – Sidesway collapse occurs at peak drift ratios of 0.03 to 0.06. Shear failure reduces median capacity by about 15%

20. RC Building Archetype Study Archetype Design Space & Parameters heights & configurations seismic design shears capacity design/detailing Archetype Analysis Model 3-Bay Multistory Interior/Exterior Joints Deterioration, P-  Archetype Index Buildings Heights: 1, 4, 8, 12, 20 Space & Perimeter Perimeter Frame (A trib /A total = 0.16) Space Frame (A trib /A total = 1.0)

21. Effects of Codes (’67 vs ’03) and Building Heights Normalized Sidesway Collapse Fragilities 1967: 8 – 12 – 4 stories 2003: 12 – 8 – 4 stories

22. 1967 Sidesway and Vertical Collapse: 8-story Total Collapse Probability Sidesway Collapse Probability at IM i Probability of LVCC (given drift ratio) =+ X Probability of No SS Collapse at IM i From Elwood/Moehle & Aslani/Miranda: Column Shear Failure: Column IDR = 0.022 (avg.) = 0.014 (1 st -story) Column Axial Failure: Column IDR = 0.050 (avg) = 0.025 (1 st -story) Sidesway collapse occurs at peak (median) drift ratio of 0.038. AXIAL collapse reduces median by ~ 40%

23. SUMMARY – Key Collapse Results Simulated Sidesway Collapse Statistics Including Shear-to-Axial Column Failure for 1967 Designs: 4-story building: little change 8-story building: significant change (column IDR = 0.025) MAF,collapse = 190 x 10 -4 c/yr (35x rate of 2003 design) 5 to 12x 10 to 30x

24. Comments on Collapse Assessment Accuracy of Assessment Procedure stiffness/strength degrading models characterization of ground hazard (spectral shape effect) modeling uncertainties.. Comparison of 1960-70’s versus modern frames “regular” frames have 10 to 30x collapse risk what about irregular frames? validation & corroboration of results appropriate level of safety? Interpretations and Implications communicating risks in consistent & meaningful ways providing tools and engineering solutions (new buildings & retrofit) action/implementation strategies