1. PEER 2002 PEER Annual Meeting PEER 2002 Annual Meeting uPractical Application of the PEER Limit State Checking Methodolgy uAllin Cornell uwith F. Jalayer, M. Motahari, uD. Vamvatsikos, and P. Bazzurro uStanford University uBased on Results from a PEER Core Project and PEER/PG&E Lifelines Project

2. PBEE Limit State Options Current (FEMA 273): Several Performance Levels and Tolerable Ground Motion Probabilities Current (FEMA 273): Several Performance Levels and Tolerable Ground Motion Probabilities Several Performance Levels and Tolerable Performance State Probabilities in “LRFD-like” Form PEER PROPOSAL

3. Components of Drift-Based Assessment,  max S a (s a a > s a ]  = aS a b 0 S 0  max   | s a P LS C Maximum Interstory drift Angle ) = Pr [S P a P max 

4. The Safety Checking Equation Median Capacity Median Demand under records with Sa at hazard level Pfo

5. Example: PG&E 3-Story Pre- Northridge SMRF 32’6’’ 28’ 14’ W 24x76 Box 18x18x 3/4 W 33x118 PG&E Substation Frame 15’6” W 24x162

6. Tolerable Probability Check: 2% in 50 Years 2% in 50 years = 0.0004 / year 1.7g

7. DS1 DS2 Static Pushover: Capacity Intact SPO and Damage States 0 200 400 600 800 1000 0.000.010.020.030.040.05 Roof Drift Base Shear ( Kips ) DS3 DS4 Focus here: Damage State 4: Local Collapse: First loss of shear tab It occurs at local rotation of 0.07 or Roof Drift of 0.048

8. Demand: Static (SPO) to Dynamic (IDA) “SPO2IDA” - an instantaneous web-site tool See Poster by D. Vamvatsikos

9. Roof Drift ( % ) Median 2.7% 84th %-tile 4.0% BetaD = ln (4/2.7)= 0.39 Dynamic Demand Results for This Structure 0.0 0.5 1.0 1.5 2.0 2.5 0.01.02.03.04.05.0 Sa ( g ) 1.7 Intact SPO Median IDA 84% IDA Sa = 1.7 g

10. Limit State Safety Check

11. 241 241 241 157 105 105 105 106 105 105 Beam Column Model with Stiffness and Strength Degradation in Shear and Flexure (but no axial column failure modes!) using DRAIN2D-UW by J. Pincheira et al.Beam Column Model with Stiffness and Strength Degradation in Shear and Flexure (but no axial column failure modes!) using DRAIN2D-UW by J. Pincheira et al. Seismic Design Assessment of RC Structures. (Holiday Inn Hotel in Van Nuys)

12. Tolerable Probability: 0.03 per year 0.4g 0.03 / year

13. Capacity: Onset of Story Mechanism 0.75%

14. Van Nuys: Drift Demand (via NLD Analysis) O.4g Median: 0.46% Dispersion; 0.39

15. Limit State Safety Check Note addition of epistemic uncertainty in demand estimation

16. PEER 2002 PEER Annual Meeting Probability-Based Assessment Basis Safe if:

17. Notes For Codified Versions Some of These Demand and Capacity Betas Might be Tabulated The Estimation of Epistemic Uncertainties Demands Good Judgement In the PEER/PG&E Buildings Fragility Project we are Taking a Slightly Different Tact Based on the Same Methods. The Objective is to Establish the Likelihoods of the Building Being Yellow or Red Tagged