Performance-Based Earthquake EngineeringAn assessment, design, and implementation system in which resulting performance is compatible with the degree of loading.

Degree of damage

Intensity of earthquake shaking

Collapse of Buildings in Past Earthquakes

Column failures

Collapse of Buildings in Past Earthquakes

Beam-column joint failures

Collapse of Buildings in Past Earthquakes

Slab-column connections

Collapse of Buildings in Past Earthquakes

Operational Heavy Collapse

Mexico City, 1985

Erzincan, 1992

0

20

40

60

80

100

Percentage

Kobe, 1995

Luzon, 1990

Otani, 1999

Traditional Approach –still used today

Joe’s

Beer!Beer!Food!Food!

WR

ZICSV =

• Linear analysis model

• Simplified design base shear

• Uncertain outcomes

• Owners informed of code conformance, but not building performance

• Prescriptive details

Joe’s Bar and Grill, a fictitious college campus hangout, courtesy of Ron Hamburger

Implicit Performance Objectives

According to SEAOC commentary since 1960s, the intended performance is as follows:

Event

Minor

Moderate

Major

Performance

No Damage

Some Nonstructural Damage

Some Structural Damage

StructurallyStable

Explaining PBEE to Stakeholders (owners, lenders, insurers, ….)

Life Safe

Joe’s

Beer!Beer!Food!Food!

Rare events(10%/50yrs)

Very rare events(2%/50yrs)

Operational

Frequent events(50%/50yrs)

Lateral Deformation

Base Shear

DemandJoe’s

Beer!Beer!Food!Food!

Occasional events(20%/50yrs)

USGS Hazard Maps

Peak acceleration in percent of gravity acceleration with 2% probability of exceedance in 50 years

Assessing Structural Performance –two different methods are used for different purposes

Component-Based Approach (FEMA 273, 1996 – existing buildings)

Global model

Global displacement, δ

EQ effect

Force

DeformationA

B

D E

C

Life Safety limit

δj

δi

θi

θj

System-Based Approach (SEAOC, 1999 – new buildings)

Relating Earthquake Demand and System Performance – Secant stiffness approximation

Displacement

Acceleration

5% damping

Teffective

increaseddamping consistent with performance level

∆T = Target Displacement

Tinitial = Teffective /õ

Case Study:University of California, Berkeley

USGS projections:80% chance in 30 years of M6.5 or greater in Bay Area30% chance in 30 years of M6.5 or greater on Hayward

UC Berkeley

pushover curve

•CA Building Code for minimum strength

•EQIII - Collapse Prevention

•EQII – Life Safety

•Cost efficient performance enhancements

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Period ( sec)

Spec

tral

Acc

eler

atio

n (g

)

EQ-III(10%/100yr)

(10%/50yr)

EQ-II(10%/50yr with cap)

'97 UBC, Soil Type Sb

EQ-I((50%/50yr)

Seismic Performance Objectives

Example 1: Hildebrand Hall

• 1966 construction• 3 stories tall• Vertical system

• flat plate• interior columns• bearing walls

• Lateral system• light shear walls

• Foundation• spread footings

• Deficiencies• flexure/shear critical walls• deficient columns• punching at slab-column connection

Hildebrand Tower Plan

Steel braced frame, typ.

Concrete wall, typ.

Hildebrand Longitudinal Retrofit

Foundation details not shown

Hildebrand Retrofit

Vertical reinforcement

continuous through floor.

Horizontal reinforcement

epoxy-anchored to columns

Concrete placed from one side by

shotcrete method.

Hildebrand Transverse Retrofit

Hildebrand Retrofit

Installation of unbonded braces

Slab punchinglimit

Stanford University

Stanford University

Life Safety DamageControl

Functional

EQ-IEQ-IIAAEQ-IEQ-IIBBEQ-IEQ-IICC

Applications

New and existingfacilities critical todisaster response

New facilities andexisting facilities criticalto academic program

All otherexisting facilities

CollapsePrevention

Stanford seismic performance objectives

Example 2: Escondido Village Midrises

• 1961-64 construction• 8 stories tall• Vertical system

• columns• bearing walls

• Lateral system• walls controlled by flexure

• Foundation• spread footings

• Deficiencies• shear-critical columns• inadequate boundary steel in walls• punching at slab-column connection

Typical Floor PlanD

12' 12' 12'-7" 12' 12' 12' 12'-7" 12' 12'

6'-3"

6'-3"

10'-7"

10'-7"

6'-3"

6'-3"

18'-4"

1 2 3 4 5 6 7 8 9 10

H

G

F

E

D

C

B

A

Concrete shear walls

Concrete columns

Escondido Village(before retrofit)

Baseshear(k)

Roof displacement (in.)

500

1000

1500

2000

5 10 15

Capacity curve before retrofitShear wall

boundary splice failure

Floor beam shear failures

Column shear failures

Reinforce basement walls at some locations

Retrofit Measures

1st

2nd

3rd

Basement

Strengthen shear wall boundary reinforcement splices

Steel collars all interior columns, all floors

Jacket first-floor columns

Escondido Villageafter retrofit

Baseshear(k)

Roof displacement (in.)

500

1000

1500

2000

5 10 15

Column shear failures

Capacity curve before retrofitShear wall

boundary splice failure

Floor beam shear failures

Equal displacement approx.

Time history (ave.)

Time history (max.)

Displacementcoefficient

Capacityspectrum

Capacity curve after retrofit

Boundary Steel

Column Collars and Fiber Wrap

Example 3: Wurster Hall• 1960’s construction• 10 – 12 story tall towers• Vertical system

• interior slab on columns• precast perimeter frame

• Lateral system• miscellaneous walls

• Foundation• piers

• Deficiencies• shear-critical interior columns• eccentric beam-column connections at perimeter

5A7.1

(E) GRADE

2A6.1

3A6.1

3A6.1

24A6.1

24A6.1

13A6.5

14A6.5

13A6.5

10A6.5

12A6.2

1A4.3

S O U T H E L E V A T I O N / S E C T I O N

∆ Large

Foundation Rocking

Largedisplacementscause framedamage

Existing RC column

Pipe column to catch floor if existing columnfails

Typical frame details

symm.

#3U @ x in. #3U @ d/2

Column Beam

20 bardia.

h typ.

h

newelements

vulnerableelement

BaseShear

Roof Displacement

original target displacement

target displacementof rehabilitated

structure

existing structure

rehabilitatedstructure

Global modification of the structural system

BaseShear

Roof Displacement

original and rehab target displacement

existing structure

rehabilitatedstructure

vulnerableelement

Local modification of structural components

Infill wall

Epoxy dowels

Shear transfer

unstrengthened

additional internal ties

fully grouted external ties

welded splices withadditional tie

actual yield strength of bars

angles and straps

retrofit column lap splices

Wing-wall retrofit.

Precast wall retrofit. Note PT for boundary reinforcement.

Steel bracing retrofits.

Drift at Collapse of Columns

Drift at shear failure

Axial Load Failure

Axial Load Capacity versus Shear Damage

Tasai, 2000

Shear-Friction Model for Axial Failure

Drift Ratio

Shear

Drift Ratio

FrictionCoefficient

Shear-Friction Model for Axial FailureP

s

Aswfy

AswfyN Vsf

θ

Elwood, 2002

Model for Column Failure

Dy Ds

Column Lateral Displacement

ColumnShear

Shear failureenvelope

Flexurestrength

Axial failurepoint

Dp

Column Lateral Displacement

ColumnAxialLoad

Axial failureenvelope

see web site of Ken Elwood

Failure of Beam-Column Joints

σyτcr

τcr

'

'

5.015.0

c

yccr

ff

στ −= , MPa

Priestley and Hart, 1994

Deformation Capacity of Beam-Column Joints Without Hoops

Drift at “tensile failure”

Drift at axial failure

Late

ral L

oad

Lateral Deflection, mm

0

0.02

0.04

0.06

0.08

0.1

0 0.05 0.1 0.15 0.2 0.25 0.3

Axial load ratio

Drif

t rat

io }Interior

Exterior, hooks bent in

Exterior, hooks bent out

0.03

-0.

06

0.12

-0.

18

0.20

-0.

22

Range of γ values

Corner

Deformation Capacity of Beam-Column Joints Without Hoops

One test with axial load failure

BaseShear

Roof Displacement

original and rehab target displacement

existing structure

rehabilitatedstructure

vulnerableelement

Local modification of structural components

Steel jacket retrofit of column laps

Steel jacket retrofit for shear

Basic

Welded

Partial Jacket

Basic

Welded

PartialJacket

Collars

Bolted

composite fiber retrofits

Column jackets

Column jackets

Concrete encasement of columns

Retrofit to add column flexural strength

Jacketed beam-column joints

Late

ral D

rift R

atio

at F

ailu

re

Gravity Shear / Nominal Punching Shear

0.00

0.02

0.04

0.06

0 0.2 0.4 0.6 0.8 1.0

Measured

PT Slabs

Deformation capacity of flat-plate construction

Retrofit of slab-column connections

Column retrofit by carbon FRPC