PPEEEERR

2002 PEER Annual Meeting

PEER 2002 Annual Meeting

Practical Application of the PEER

Limit State Checking Methodolgy

Allin Cornell with F. Jalayer, M. Motahari,

D. Vamvatsikos, and P. Bazzurro Stanford University

Based on Results from a PEER Core Project and

PEER/PG&E Lifelines Project

PBEE Limit State OptionsPBEE Limit State Options

Current (FEMA 273):Current (FEMA 273): Several Performance Several Performance Levels and Tolerable Levels and Tolerable Ground MotionGround Motion Probabilities Probabilities

Several Performance Levels and Tolerable Several Performance Levels and Tolerable Performance StatePerformance State Probabilities in “LRFD-like” Form Probabilities in “LRFD-like” Form

CD CSS|D fPa

a⋅φ≤⋅γ

0

PEER PROPOSALPEER PROPOSAL

Components of Drift-Based Assessment

, max Sa(sa a > sa ]

= a Sa b

0

S 0

max

| sa PLS C

Maximum Interstory drift Angle) = Pr [S

P

aP

max

The Safety Checking Equation

CD CSS|D fPa

a⋅φ≤⋅γ

0

]b

kexp[

a

a

S|D

S|D

2

2β

=γ

]b

kexp[

C

C

2

2β

=φ

Median

CapacityMedian Demand

under records with

Sa at hazard level Pfo

Example: PG&E 3-Story Pre-Northridge SMRF

32’6’’32’6’’ 28’

14’

14’

W 24x76

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 =

0.0004 / year

1.7g

DS1DS2

Static Pushover: Capacity

Intact SPO and Damage States

0

200

400

600

800

1000

0.00 0.01 0.02 0.03 0.04 0.05

Roof Drift

Bas

e S

hea

r (

Kip

s )

DS3DS4

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

0.0

0.5

1.0

1.5

2.0

2.5

0.0 1.0 2.0 3.0 4.0 5.0

Sa

( g

) 1.7

Intact SPO

Median IDA 84% IDASa = 1.7 g

Limit State Safety Check

CD CSS|D fPa

a⋅φ≤⋅γ

0

)yearsin%(.P:Conclusion

..:OKCheck

%.%).)(.(C

%.%).)(.(D

.]).(exp[]b

kexp[

.]).(exp[]b

kexp[

b;k

%.C

%.D

fo

C

SD

Sa|DD

CC

S

Pfoa

Pfoa

502000404354

5484940

4372251

25139023

2

9402023

2

1384

72

22

22

<>

==φ

==γ

==β=γ

=−=β=φ

≈≈=

=

241241 241241 241241

157157

105105

105105

105105

106106

105105

105105

•Beam Column Model with Stiffness and Beam Column Model with Stiffness and Strength Degradation in Shear and Flexure Strength Degradation in Shear and Flexure (but no axial column failure modes!) (but no axial column failure modes!) using using DRAIN2D-UW by J. Pincheira et al.DRAIN2D-UW by J. Pincheira et al.

Seismic Design Assessment of RC Seismic Design Assessment of RC Structures.Structures.

( (Holiday Inn Hotel in Van NuysHoliday Inn Hotel in Van Nuys))

Tolerable Probability: 0.03 per year

0.4g

0.03 / year

Capacity: Onset of Story Mechanism

Onset of System Mechanism

0.75%

Van Nuys: Drift Demand (via NLD Analysis)

SSaa==00..4400 ggPP00

39.040.0|max==aSβ

0046.0ˆ 40.0|max==aS

O.4g

Median: 0.46%

Dispersion; 0.39

Limit State Safety Check

0fPa

a SS|DCDC ⋅γ≥⋅φ

annumper.)(P:Conclusion

..:OKNotCheck

%.%).)(.(C

%.%).)(.(D

.}]).().{(exp[]b

kexp[

.]).(exp[]b

kexp[

b;k

%.C

%.D

fo

C

SD

Sa|DD

CC

S

Pfoa

Pfoa

030670650

650750870

670460451

4513039023

2

8703023

2

13750

460

222

22

≈><==φ

==γ

=+=β=γ

=−=β=φ

≈≈=

=

Note addition of epistemic

uncertainty in demand

estimation

PPEEEERR

2002 PEER Annual Meeting

Probability-Based Assessment BasisProbability-Based Assessment Basis

∫∫ =y x

SS|DCcollapse |)x(d|)x|y(f)y(FPaa

∫∫ =y x

IMIM|EDPEDP|DVDV |)x(d||)x|y(dG|)y|z(G)z(v

0fcollapse PP ≤Safe if:Safe if: CD CSSD fPa

a

ˆˆ0| ⋅≤⋅ φγ

)](2

exp[)ˆ( 22|2

2

CSDScollapse aa b

kCHP ββ += ]

b

kexp[

a

a

S|D

S|D

2

2β

=γ

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