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

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

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 

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

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

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

DS1 DS2 Static Pushover: Capacity Intact SPO and Damage States 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

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

Roof Drift ( % ) Median 2.7% 84th %-tile 4.0% BetaD = ln (4/2.7)= 0.39 Dynamic Demand Results for This Structure Sa ( g ) 1.7 Intact SPO Median IDA 84% IDA Sa = 1.7 g

Limit State Safety Check

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)

Tolerable Probability: 0.03 per year 0.4g 0.03 / year

Capacity: Onset of Story Mechanism 0.75%

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

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

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

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