Seismic Perfomance Assessment

Performance based Earthquake Engineering

Slide: 2/55

• Conjunction of the design, constructionand maintenance procedures necessary toreach, through engineering means,predictable performances for multipledesign objectives.

• Its purpose is to minimize the economiclosses after a seismic event during theuseful life of the structures.

Performance Based Seismic Design

• Limit permissible drifts under

specified forces

• Require buildings have complete

structural systems

Code Procedures

• Require systems have sufficient

strength to resist specified forces

• Require members and connections

be “detailed” prescriptively

2003

Building Codes Imply Performance

> Ability to resist frequent, minor earthquakes without damage

> Ability to resist infrequent, moderate earthquakes with limited structural and nonstructural damage

> Ability to resist worst earthquakes ever likely to occur without collapse or major life safety endangerment

100 yrs

500 yrs

2,500 yrs

Performance is not guaranteed

2003

Slide: 5/53

Building Codes & Peformance Warranties

> If a building is affected by an extreme event and performs poorly:

• There is an expectation of how the building

should have performed but no implied

warranty> The only warranty is that the engineer complied with

the standard of care

• For most buildings, demonstration that a

design was performed in accordance with

the building code will provide adequate

proof of conformance to the standard of

care

Slide: 6/55

To transform earthquake engineering assessment and design ...

Perform.-Based Approach

• Scientifically-defined seismic hazard

• Direct design

approaches

• Defined outcomes with probabilities of achieving them

Traditional Approach

•Non-scientifically defined seismic hazard

•Indirect design approaches

•Undefined and uncertain outcomes

Performance-Based Earthquake Engineering

Slide: 7/53

Performance Based Seismic

Design

Seismic performance level.

Seismic design level.

Seismic design objectives.

Expression the maximum acceptable damage in a structure subjected to earthquake action.

Seismic demand representing the hazard of a site where the structure would be located.

Union of a performance level and a level of seismic design.

Slide: 8/53

Performance Based Seismic Design

•ATC-33

• FEMA – 273, ATC 40

• SEAOC- Vision 2000

• Euro Code 8

• Japanese code

Slide: 9/53

EC8: Conventional Criterion

• Explicitly satisfy the level of performance “Life

safety” under a design level “rare”

• Limit the economic losses through a check of

the damage limits for a “frequent” demand

• Prevent the collapse under any imaginable

demand through a “Capacity Design ”

Slide: 10/55

Selecting PerformancePresent Generation

Joe’s

Beer!Beer!

Food!Food!

Operational

Operational – negligible impact on building

Beer!Beer!

Food!Food!

Joe’s

Beer!Beer!

Food!Food!

Beer!Beer!

Food!Food!

Joe’sJoe’s

Immediate

Occupancy

Immediate Occupancy – building is safe to occupy but

possibly not useful until cleanup and repair has occurred

Beer!Beer!

Food!Food!

Beer!Beer!

Food!Food!

Beer!Beer!

Food!Food!

Life

Safety

Life Safety – building is safe during event but possibly not

afterward

Collapse

Prevention

Collapse Prevention – building is on verge of

collapse, probable total loss

Slide: 11/53

Performance LevelS

eism

ic D

esig

n L

evel

Frequent (43 years)

50% in 30 years

Ocassional (72 years)

50% in 50 years

Rare (475 years)

10% in 50 years

Very Rare (970 years)

10% en 100 years

Fully

operationalLife safety

Operational

Collapse

prevention

Slide: 12/55

Code-equivalent Performance

Beer!Beer!

Food!Food!

Joe’s

Beer!Beer!

Food!Food!

Beer!Beer!

Food!Food!

Joe’sJoe’s

Immediate

Occupancy

Frequent event (varying between

50- and 100- year return periods)

Beer!Beer!

Food!Food!

Beer!Beer!

Food!Food!

Beer!Beer!

Food!Food!

Life

Safety

DBE

Collapse

Prevention

MCE

Slide: 13/55

Structurally

Stable

Assessment by Static Pushover Analysis (FEMA 273/356 and ASCE 41)

Life Safe

Beer!

Food!

Rare events

(10%/50yrs)

Very rare events

(2%/50yrs)

Operational

Frequent events

(50%/50yrs)

Lateral Deformation

Base

Shear

DemandJoe’s

Beer!

Food!

Occasional events

(20%/50yrs)

Ref: R.O. Hamburger

Slide: 14/55

Deformatio

n

Damage

Threshold

Collaps

e

Onset

OPEN

OPEN

OPEN

FEMA 356 Performance

Levels

IO LS CP

Performance-Based Earthquake Engineering

PBEE today

$, % replacement0 25% 50% 100%

Downtime, days0

1 7 30 180

Casualty rate0.0

0.0001 0.001 0.01 0.25

PBEE tomorrow

Slide: 15/53

Damage Assessment: Nonstructural Fragilities

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

Small cracks

only

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

Small cracks

only

Wide cracks in gypsum

boards

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

Small cracks

only

Wide cracks in gypsum boards

Severe damage to gypsum board and distorsion of metal frame(Replace partition)

(Replace gypsum boards)

(Patch, Retape & Paint)

Ref: E. Miranda

Interstory Drift Ratio

Pro

bab

ilit

y o

f

Dam

ag

e S

tate

Slide: 16/55

Engineering Demand

Parameter

Intensity Measure

Damage Measure

Performance-Based Methodology

Decision Variable• Collapse &

Casualties

• Direct Financial

Loss

• Downtime

drift as an EDP

Slide: 17/55

0 0.05 0.1 0.150

0.5

1

1.5

2

2.5

3

3.5

4

Sa

g.m

.(T=

1.0

s)[

g]

Maximum Interstory Drift Ratio

Incremental Dynamic Analysis –Collapse

STRUCTURAL RESPONSE (DRIFT)

GR

OU

ND

MO

TIO

N IN

TE

NS

ITY

44 Ground Motion Records

EQ: 11111, Sa: 2.06g EQ: 11112, Sa: 2.19g

EQ: 11121, Sa: 2.86g EQ: 11122, Sa: 2.32g

Slide: 19/53

Nonstructural Damage and Losses (Caltech)

Slide: 20/53

PBEE Methodology: IM-EDP-DM-DV

> Ground Motion Hazard Characterization

• IM Definition (Sa, …)

• Selection and Scaling of Ground Motions

> Simulation: IM – EDP

• Choice of EDPs (Drift, Floor Accel., other …)

• Fidelity of simulations to model collapse

> Damage Modeling: EDP – DM

• Taxonomy of components

• Definition of conditional EDP-DM “damage function”

> Loss Modeling: DM – DV

• Definition of conditional DM-DV loss functions

• Downtime and injuries/fatalities are a challenge

Slide: 21/53

Performance Assessment Components

Decision

Variable

Intensity

Measure

Damage

Measure

Engineering

Demand

Parameter

Relating Performance to Risk Decision Making

Quantifying Damage Measures

Simulation of System Response

Earthquake Hazard Characterization

Slide: 22/53

Performance Assessment Components

Decision

Variable

Intensity

Measure

Damage

Measure

Engineering

Demand

Parameter

DV: $ loss, functionality, downtime, casualties

DM: physical condition & consequences/ramifications

EDP: Drift Ratio (peak, residual), Floor Acceleration, Local Indices (Qp, strain, …)

IM: Sa(T1), multiple Sa’s, epsilon, Sdinelastic, duration

Slide: 23/53

• Linear static analysis • Equivalent static analysis

• Linear dynamic analysis • Modal analysis

• Direct time-history analysis

• Nonlinear static analysis - Nonlinear static procedures (NSPs)

• Capacity spectrum analysis (ATC-40, FEMA-440)

• Displacement coefficients method (FEMA-273-274,356,440)

- Improved NSPs• Modal pushover analysis (MPA) (Chopra & Goel, 2002)

• Adaptive Modal Combination (AMC) (Kalkan & Kunnath, 2006)

• Nonlinear dynamic analysis

Seismic Analysis Methods of Structures

Most common in

routine applications

Slide: 24/53

Nonlinear Static Analysis

Conceptual Theory&

Current Practice

Slide: 25/55

Multi-degree-of-freedom (MDF) system seismic behavior can be approximated

with certain accuracy by

equivalent SDF systems.

Equivalent SDF (ESDF) system properties are computed by conducting pushover analyses…

Slide: 26/53

Conventional Nonlinear Static (Pushover) Analysis

Choose height-wise distribution of lateral forces

Monotonically increase lateral forces till the “control node” reaches a

“target displacement” i.e., increasing load factor while fixing load

pattern.

Develop pushover (capacity) curve: Plot of base shear vs. roof

displacement

ur

Vb

Slide: 27/55

Summary of Nonlinear Static Analysis

V

D

D

V

Inelastic

SDF System

Target Displacement

of MDF System ut

ut

uj

dj

Capacity estimation at

target displacement

Pushover Analysis

Participation

Factor, Gn

Dn

Fsn/Ln

ESD System

Force-Deformation Relation

Slide: 28/53

Fundamental Assumptions:

• The response of the multi-degree-of-freedom (MDF) structure can be related to the response of an equivalent SDF system, implying that the response is controlled by a single mode and this mode shape remains unchanged even after yielding occurs.

• The invariant lateral force distribution can represent and bound the distribution of inertia forces during an earthquake.

Slide: 29/55

Two Important Components of Nonlinear Static Analysis

• Construct loading vector shape

• Determine target roof displacement

Slide: 30/55

*

*1

*

*

Uniform:

First Mode :

ELF : 1 2

SRSS : from story shears

j j

j j j

kj j j

j

s m

s m

s m h k to

s

ELF and SRSS distributions

intended to consider higher mode

responses

Height-wise Distribution of Lateral Forces: FEMA Recommendations

Slide: 31/53

FEMA Recommended Force Distributions

Each force distribution pushes all floors in same direction

Slide: 32/53

Higher Mode Response

Initial Yielding Initial Yielding

Initial Yielding Initial Yielding

Slide: 33/55

Two Important Components of Nonlinear Static Analysis

• Construct loading vector shape

• Determine target roof displacement

Slide: 34/53

Target Displacement Estimation(Displacement Coefficient Method)

2

0 24e

t inel A

Tu C C S u

f

Elastic SDF System

u

f

Inelastic SDF System

u

f

Inelastic MDF System

C0 = Constant to relate elastic deformation of SDF and MDF system

Slide: 35/55

Displacement Coefficient Method

FEMA-356: Cinel =C1C2C3

• C1 = Ratio of inelastic and

elastic SDF systems

• C2 = Constant to account for

effects of pinching, stiffness

degradation, and strength

deterioration

• C3 = Constant to account for P-

Delta effects

ASCE-41: Cinel = C1C2

• C1 = Ratio of inelastic and

elastic SDF systems

• C2 = Constant to account for

cyclic degradation of stiffness

and strength

• Upper limit on R to avoid

dynamic instability

Slide: 36/53

Capacity Spectrum Method

0 ( , )t D eq equ C S T

u

f

Inelastic MDF System

u

f

Equivalent Linear Elastic SDF System

Teq, zeq

u

f

Inelastic SDF System

Slide: 37/55

Capacity Spectrum Method –Equivalent Damping Concept

z

1

1 110.05

1

eq o

eq

T T

For bilinear systems

Requires iterations to compute Teq and zeq

because of unknown ductility (uinel / uelas)

10.05

4D

eq

So

E

E

Teq= Tsec

Sd

Sa

ESo

ED

Slide: 38/55

FEMA-440 Capacity Spectrum Method

z z

z

z

2 3

2

2

1 1 ; 4.0

1 ; 4.0 6.5

1 1; 6.5

1

eq o

o

eq

o

o

A B

C D

F TE

TF

A to K = Constants that depend on hysteretic behavior and post-

yield stiffness ratio

2 31 1 1 ; 4.0

1 1 ; 4.0 6.5

-1K 1 1 ; 6.5

1+L 2

eq o

o

o

T G H T

I J T

T

Slide: 39/53

Limitations of Conventional (FEMA & ATC) Nonlinear Static Analysis Procedures

> Restricted to single mode response, can be reliably apply to 2D response of low-rise structures in regular plan.

> Gives erroneous results in case of:

Higher Mode Effects

Plan Irregularities (i.e., Torsion, Vertical Irregularities)

> No established procedure for 3D pushover analysis yet.

Slide: 40/53

Energy-based ESDF system representation of nth-mode MDF system capacity curve

Roof Displacement, u r,n

Base S

hear,

V b

,n

F 1(i)

F 2(i)

F 3(i)

Dd 3(i)

Dd 2(i)

Dd 1(i)

Forces

(sn(i))

( ) ( ) ( ) ( )

, , , ,

1,3 1,3

( ) / ( )i i i i

d n n n j n j n j

j j

S D F d F

D D

Dd 3(i)

Capacity

curve

(i-1)

(i)

(i)(i-1)

ur,n(i)ur,n

(i-1)

Spectral Displacement, S d,n

Sp

ectr

al

Accele

rati

on

, S

a,n

DD n(i)

wn(i)

zn(i)

,

,

b n

a n

n

VS

W

DD n(i)

Tn(elastic)

wn(i)) 2

Capacity

spectrum

MDF

Level

SDF

Level

Slide: 41/53

Performance point evaluation using system ductility through a set of inelastic spectra

Spectral Displacement, S d,n

Sp

ectr

al A

ccele

rati

on

, S

a,n

wn(i)

zn(i)

wn(ip)) 2

Global

Yield

( )

,

yield

d nS ( )

,

ip

d nS

With computed system ductility, ( )ip

n

Tn(elastic)

Tn(ip)

( )

,( )

( )

,

ip

d nip

n yield

d n

S

S

Spectral Displacement, S d,n

Sp

ectr

al A

ccele

rati

on

, S

a,n

( )ip

n

Dynamic Target

Point

Inelastic phase,

period elongation

Tn(elastic)

Tn(ip)

Inelastic Demand Spectra

plotted at different

ductility levels

M odal Capacity

Curve

Capacity

Side

Demand

Side

Slide: 42/55

Thank You