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

PPEEEERR

2002 PEER Annual Meeting

PEER 2002 Annual Meeting

Helmut Krawinkler

Seismic Demand Analysis

Performance Assessment

( ) ∫∫∫= )(||| IMdIMEDPdGEDPDMdGDMDVGDVv λ

Performance (Loss) Models and Simulation HazardImpact

Please accept my apologies for showing the(in)famous framework equation

Engineering Demand Parameters

Collapse: Maximum Story Drift (and others)

Struct. Damage: Story Drifts (each story) andComponent Deformations

Nonstr. Damage: Story Drift (each story)

Content Damage: Floor Acceleration andVelocity (each story)

Probabilistic Seismic Demand Analysis (PSDA)

Given:•Structural system•Base shear strength, = Vy/W•Story shear strength distribution

•Ground motion hazard, (Sa(T1))•Set of representative ground motions

Asked:•EDP hazard, (EDP), max. drift, average drift, floor accel.

[ ] |)x(d|xIM|yEDPP)y( IMEDP λ=≥=λ ∫

Probabilistic Seismic Demand Analysis

EDP(y) = mean annual frequency of EDP exceeding

the value yP[EDP y | IM = x] = probability of EDP exceeding y given

that IM equals xIM(x) = mean annual frequency of IM exceeding

the value x (ground motion hazard)

EDP (e.g., max. interstory drift)

IM (

e.g.

, Sa(

T1)

)

IM Hazard curve(annual freq. of exceedance)

Individual recordsMedian84%

Incremental Dynamic Analysis (IDA)

Hazard Curve for Average of Max. Drifts

AVERAGE DRIFT HAZARD CURVE-T1=1.8 sec.N=9, =0.10, =0.05, Peak-oriented model, =0.060, BH, K1, S1, LMSR

0.0001

0.001

0.01

0.1

1

10

0 0.005 0.01 0.015 0.02 0.025Average of Maximum Story Drifts,

si

,ave(

)

Numerical Integration

Ground Motion Hazard:

[ ] koIM xkxIMP)x( −=≥=λ

Median EDP-IM relationship:

( )bIMaPD̂E =

EDP Hazard Curve:

[ ] ( )[ ]⎥⎥⎦

⎤

⎢⎢⎣

⎡σ=≥=

− 2IM|EDPln2

2kb/1oEDP

b

k

2

1expa/ykyEDPP)y(

Closed Form Expression for EDP Hazard

AVERAGE DRIFT HAZARD CURVE-T1=1.8 sec.N=9, =0.10, =0.05, Peak-oriented model, =0.060, BH, K1, S1, LMSR

0.0001

0.001

0.01

0.1

1

10

0 0.005 0.01 0.015 0.02 0.025Average 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

First modeparticipationfactor

Roofdrift/(Sd(T1)/H)

Maximumdrift/(Sd(T1)/H)

Averagedrift/(Sd(T1)/H)

FEMA 273/356 “Validation”

Median

84%

Design – Strong Column Concept

[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

Non-Deteriorating Hysteretic Systems

Displacement

Force

Displacement

Force

Displacement

Force

Basic Modes of Deterioration

Calibration - RC Component

Very Ductile – Slow Deterioration

Medium Ductile – Moderate Deterioration

Deterioration Effect, MDOF System

NORM. STRENGTH VS. MAX. STORY DUCT.N=9, T1=0.9, =0.05, =0.03, =0.015, H3, BH, K1, S1, NR94nya

0

5

10

15

20

0 5 10 15 20si,max

[Sa(

T1)

/g]

/

Non-degrading system

Degrading system

Median

Global Collapse Assessment

Collapse Fragility Curves – SDOF Systems

Collapse Fragility Curves – SDOF Systems

Median R-factors at Collapse - SDOF Systems

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)