1924 Krawinkler h. Pbee

19-20 July 2007 – Belgirate, Italy LESSLOSS Final Workshop Krawinkler

PerformancePerformance--based assessment and based assessment and design of buildingsdesign of buildings

(the PEER approach)(the PEER approach)

LESSLOSS Final WorkshopLESSLOSS Final WorkshopRisk Mitigation for Earthquakes and Risk Mitigation for Earthquakes and

LandslidesLandslides

Priority 1.1.6.3 - Global Change and Ecosystems / European Integrated Project GOCE-CT-2003-505488

19-20 July 2007Hotel Villa Carlotta, Belgirate (VB) - Italy

Helmut KrawinklerStanford University, California, USA


Measures of Measures of Performance Performance -- PBEEPBEE

Forces and deformation?Yes, but only for engineering calculationsIntermediate variables Not for communication with clients and community

Communication in terms of the three D’s:Dollars (direct economic loss)Downtime (loss of operation/occupancy)Death (injuries, fatalities, collapse)

QuantificationLosses for a given shaking intensityLosses for a specific scenario (M & R)Annualized lossesWith or without rigorous consideration of uncertainties


Vision of PBEEVision of PBEE

Joe’s

Beer!Beer!Food!Food!

1. Complete simulation

2. Defined performance objectives

• Quantifiable performance targets

• Annual probabilities of achieving them

3. Informed owners

Joe’sBeer!Beer!Food!Food!

Joe’sBeer!Beer!Food!Food!

Sources: G. Deierlein, R. Hamburger


Evolution of PBEEEvolution of PBEE

Base Shear

Deformation

Damage Threshold

CollapseOnset

OPEN

OPEN

OPEN

FEMA 356 Performance LevelsIO LS CPPBEE yesterday

$, % replacement0 25% 50% 100%

Downtime, days0

1 7 30 180

Casualty risk0.0 0.0001 0.001 0.01 0.25

PBEE today


The PEER framework The PEER framework equation equation -- 19991999

BlessingCurse?

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

Performance (Loss) Models and Simulation HazardImpact


PBEE PBEE –– Probability Probability Framework EquationFramework Equation

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

Performance (Loss) Models and Simulation HazardImpact

IM – Intensity MeasureEDP – Engineering Demand ParameterDM – Damage MeasureDV – Decision Variable

ν(DV) – Probabilistic Description of Decision Variable

(e.g., Mean Annual Probability $ Loss > 50% Replacement Cost)


Engineering Demand Parameter


Intensity MeasureIntensity Measure

Damage MeasureDamage Measure

PerformancePerformance--Based Based MethodologyMethodology

Decision VariableDecision Variable• Collapse & Casualties

• Direct Financial Loss

• Downtime

drift as an EDP

Source: G. Deierlein



Intensity MeasureIntensity Measure0.0001

0.001

0.01

0.1

1

10

0 0.2 0.4 0.6 0.8 1.0Spectral Acceleration Sa(g)M

ean

Ann

ual F

req.

of E

xcee

danc

e, λ

Sa MEAN SPECTRAL ACC. HAZARD CURVE -- T = 1.8 sec.Van Nuys, CA, Horizontal Component

0.0001

0.001

0.01

0.1

1

10


ean

Ann

ual F

req.

of E

xcee

danc

e, λ




Medina & Krawinkler


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

IM (e

.g.,

S a(T

1))

IM Hazard curve(annual freq. of exceedance)

Individual recordsMedian84%

[ ] |)x(d|xIM|yEDPP)y( IMEDP λ=≥=λ ∫

Incremental Dynamic Incremental Dynamic AnalysisAnalysis



Decision VariableDecision Variable



Intensity MeasureIntensity Measure0.0001

0.001

0.01

0.1

1

10


ean

Ann

ual F

req.

of E

xcee

danc

e, λ


0.0001

0.001

0.01

0.1

1

10


ean

Ann

ual F

req.

of E

xcee

danc

e, λ


Medina & Krawinkler

Damage MeasureDamage Measure

Drywall Partitions with Metal Frame

0.0

0.2

0.4

0.6

0.8

1.0

0.000 0.005 0.010 0.015 0.020EDP (IDR)

DM 1 DM 2 DM 3

P(DM>dm | EDP)

Damage Fragility Curves:Drywall partitions

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.4 0.8 1.2 1.6 2.0 2.4Cost of Repair / Cost New

Tape, Paste & RepaintReplacement of gypsum boardsPartition replacement

P($>x | DM)

Cost Functions:

+

Drywall Partitions with Metal Frame

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.000 0.005 0.010 0.015 0.020 0.025 0.030EDP (IDR)

E[Loss | EDP]

Mean Loss Curve:

Aslani & Miranda

Performance Assessment types (ATC-58 definitions):Intensity-based:Scenario-based:Time-based:

Prob. performance, given intensity of ground motionProb. performance, given a specific eq. scenarioProb. performance In a specific period of time


TestbedTestbed BuildingBuilding


DeDe--aggregation of aggregation of expected annual lossexpected annual loss

Example: Van Nuys Testbed Building

Structural12%

Non-structural88%

Collapse29%

Non-collapse71%

Source: E. Miranda


Design Decision SupportDesign Decision Support

Structural System Domain

Loss Domain

Hazard Domain

NSDSS NSASS

EDP = Max. Interstory Drift EDP = Max. Floor Acceleration

Mean Subsystem Loss Curves

EDP = Max. Interstory Drift EDP = Max. Floor Acceleration

Mean IM-EDP Curves

Mean Hazard Curve

10/50

Expe

cted

$Lo

ss

Zareian & Krawinkler (2005)


Assessment of Assessment of Collapse PotentialCollapse Potential

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

5

10

15

20

[Sa(

T1)

/g] /

γ

γ = Vy

W Non-degrading systemDegrading system

Collapse Capacity

00 5 10

µsi,max

15 20


Modeling of Modeling of DeteriorationDeterioration

UCI G12 OSBFy=8.2 kips, δy=0.45 in, αs=0.047, αc=-0.081, αu=1.94, δc/δy=5.44

-10-8-6-4-202468

10

-4 -2 0 2 4Displacement (in)

Load

(kip

s)

UCI G12 OSBPinching Model, κ=0.5, Fy=8.2 kips, δy=0.45 in

αs=0.047, αc=-0.081, αc=1.94, δc/δy=5.44, γs=270, γc=270, γk=∞, γa=270

-10-8-6-4-202468

10

-4 -2 0 2 4Displacement (in)

Load

(kip

s)


Collapse Capacity for a Set Collapse Capacity for a Set of Ground Motionsof Ground Motions

M AX. STORY DUCTILITY vs. NORM . STRENGTHN=9, T1=0.9, ξ=0.05, K 1, S1, BH, θ=0.015, Peak-Oriented M odel,

α s=0.05, δc/δy=4, α c=-0.10, γs=8 , γc=8 , γk=8 , γa=8 , λ=0, LM SR

0

2

4

6

8

10

0 10 20 30M aximum Story Ductility Over the Height, µs,max

[Sa(

T1)

/g]/ γ

Individual responses


Collapse Fragility Collapse Fragility CurveCurve

Obtaining the collapse fragility curve (MRF)N = 8, T1 = 1.2, γ = 0.17, Stiff & Str = Shear, SCB = 2.4-2.4, ξ = 0.05

θp = 0.03, θpc/θp = 5, λ = 20, Mc/My = 1.1

0

0.25

0.5

0.75

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5IM[Sa(T1)]

Prob

abili

ty o

f Col

laps

e

Data points

Collapse fragility curve

Zareian & Krawinkler (2004)


Implementation of Implementation of MethodologyMethodology

ATC-58 – Guidelines for Seismic Performance Assessment of BuildingsATC-63 – Recommended Methodology for Quantification of Building System PerformanceTBI – Tall Building Initiative


ATCATC--5858Seismic Performance Seismic Performance Assessment of Assessment of BldgsBldgs..

Present emphasis is on damage assessment (PACT program)Next stage will be collapse and casualty assessmentNext step will be downtimeFinal step will be putting the pieces together


Importance of Damage Importance of Damage State Fragility FunctionsState Fragility Functions

Smallcracksonly

0.0

0.2

0.4

0.6

0.8

1.0

0 0.005 0.01 0.015 0.02 0.025

EPD (IDR)

P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall Frame

Smallcracksonly

Wide cracks in gypsum boards

Severe damage togypsum board anddistorsion of metal frame

Source: E. Miranda


ATCATC--58 relies heavily 58 relies heavily on Fragility specs.on Fragility specs.


Damage State 0

Damage State 2

Damage State 4

0.0 1.0 2.0 3.0 4.0 5.0 6.000.10.20.30.40.50.60.70.80.91

Drift (%)

MOR 0MOR 1MOR 2MOR 3MOR 4

0.0 1.0 2.0 3.0 4.0 5.0 6.000.10.20.30.40.50.60.70.80.91

Drift (%)



MOR 0MOR 1MOR 2MOR 3MOR 4Pr

obab

ility

of R

equi

ring

a M

OR

Example of compilations for:

• RC Beam-Columns, Joints, Walls

• Interior Partitions

• Laboratory benches & equipment

• Ceiling & MEP Systems

P[DM:EDP]

Fragility Functions for Fragility Functions for BeamBeam--Column JointColumn Joint


Example ApplicationExample Application


Example ApplicationExample ApplicationPACT ResultsPACT Results


ATCATC--63 Project 63 Project ObjectivesObjectives

Primary – Create a methodology for determining Seismic Performance Factors (R-factor, Cd-factor, overstrength factor) for different lateral-force-resisting systems

Secondary – Evaluate a sufficient number of different lateral-force-resisting systems to provide a basis for Seismic Code committees to develop more rational Seismic Performance Factors that will more reliably achieve the inherent earthquake safety performance objectives of building codes


Example IDA Results and Example IDA Results and Collapse Margin RatioCollapse Margin Ratio

((44--story, SDC D, space frame with 30story, SDC D, space frame with 30--foot bays)foot bays)

0 0.05 0.1 0.150

2

4

6

8

Sa(T

=0.8

1s) [

g]

Maximum Interstory Drift Ratio

Median Collapse SCT = 2.77g

MCE SMT = 1.11g

MC = 2.5 (2.77/1.11)



Collapse Fragility with Collapse Fragility with Modeling UncertaintyModeling Uncertainty

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sag.m.(T=1.0s) [g]

Cum

mul

ativ

e P

roba

bilit

y of

Col

laps

e

Empirical CDFLognormal CDF (RTR Var.)Lognormal CDF (RTR + Modeling Var.)

MC



Exercised on Several Exercised on Several SeismicSeismic--ForceForce--Resisting Resisting

SystemsSystemsReinforced-Concrete Structures

4-Story SMF, IMF and OMF

12-Story IMF/OMF and Shear Wall (Core Wall)

Parametric Study of RC Frames1, 2, 4, 8, 12 and 20 stories

Space vs. perimeter configurationsWood Structures:

Townhouse – Superior, typical, poor quality

Apartment – Superior, typical and poor quality

Other (Japanese Home, Templeton Hospital)

Autoclaved Aerated Concrete (AAC) Test Structures

Steel Structures:

4-Story (RBS) SMF (IMF, OMF) Source: C. Kircher


Index Archetype Index Archetype Configuration (4Configuration (4--Story)Story)


Tall Building Tall Building InitiativeInitiative

Source: R. Klemencic

19-20 July 2007 – Belgirate, Italy LESSLOSS Final Workshop KrawinklerSource: J. Maffei


Source: R. Klemencic


WhatWhat’’s different about s different about these buildings?these buildings?

after MKA

High-performance materialsFraming systems not satisfying code prescriptive limitsNon-prescriptive designs are accepted in the code by demonstrating at least equivalent seismic performance.

UBC 1629.10.1, 1605.2, 104.2.8

Source: J. Moehle


Tall Building Tall Building InitiativeInitiative

Identify performance objectivesGround motion selection and scalingEffects of GM selection and scaling on responseGuidelines on modeling and acceptance criteriaInput ground motions for tall buildings with embedded foundationsDissemination and consensus building


Gaps in KnowledgeGaps in Knowledge

For damage assessment:Fragility curves for damage in structural and nonstructural componentsConsequence functions and loss curvesEffects of correlations

For downtime assessmentLength of downtimeScenario dependence of consequences


Gaps in KnowledgeGaps in Knowledge

For collapse prediction and life safetyBetter analytical modeling rules for incorporation of all deterioration and brittle failure modes at the component level

Modeling of propagation of local collapseIncorporation of intangible contributions to collapse capacityRelationship between collapse and casualty rate


Concluding remarks Concluding remarks --19991999

• Performance based engineering is here to stay

• It enforces a transparent design/assessment approach

• Much more emphasis must be placed on $ losses andloss of function (downtime)•

• Performance based design should be reliability based

• We have a long road ahead of us

1924 Krawinkler h. Pbee

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