David Mar Guidelines for Seismic Retrofit of Weak-Story Two-Frame Buildings ATC 71-1

Guidelines forSeismic Retrofit of Weak-Story

Wood-Frame Buildings ATC 71-1

FEDERAL EMERGENCY MANAGEMENT AGENCY

Michael Mahoney (Contracting Officer’s Technical Representative)

Cathleen Carlisle(Contracting Officer’s Technical Representative)

TASK ORDER CONTRACT MANAGEMENT

Christopher Rojahn(Project Executive Director)

Thomas R. McLane(Project Manager)

Jon A. Heintz(Project Quality Control Monitor)

William T. Holmes (Project Technical Monitor)

PROJECT

MANAGEMENT COMMITTEE

David Mar -

Project Technical DirectorDavid Bonowitz

Kelly CobeenDan Dolan

Andre FiliatraultJohn Price

Mike Korolyk

-

Analysis Consultant

PROJECT REVIEW PANEL

Chris Poland -

ChairBret Lizundia

Andrew MerovichLaurence KornfieldJoan MacQuarrieTony DeMascole

Tom Tobin

Daniel Shapiro (Subject Matter Expert)

Robert Hanson(Subject Matter Expert)

The Team

4,400 Dangerous Multi-unit Buildings: 8% of population

Create Seismic Retrofit Program for

Weak-Story Wood-framed Apartment Buildings

in Western US

Inexpensive to Construct(Work Only In Ground Story)

Inexpensive to Design(Unsophisticated Engineers)

Performs Well(Shelter-In-Place)

Inexpensive to Construct(Cheap)

Inexpensive to Design(Fast)

Performs Well(Good)

The Scope

Typically:

Non-Engineered

No Plans

Archaic Materials

Archaic Construction Practices

1989 Loma Prieta

earthquakeImage by Raymond B. Seed

National Information Service for Earthquake EngineeringUniversity of California, Berkeley.The Problem

San Francisco, CA, Loma Prieta

Earthquake 11/17/1989Beach and Divisadero

in the Marina District. U.S.G.S. by Nakata,

J.K.

FEMA News Photo FEMA News Photo

Northridge, CA: Northridge earthquake FEMA News Photo

Design for a Population of Buildings,

not an Individual Building

Pattern Recognition

Strong but Brittle Upper Structure

Weak and Brittle Lower Structure

Pattern Recognition

Limited Damage to Upper Structure

Damage Concentrated in Lower Structure

Pattern Recognition

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%

Interstory Drift Ratio

Stor

y Sh

ear,

kip

s

Ground story fixed

Ground story with uplift

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%


Stor

y Sh

ear,

kip

s

Second story fixed

Second story with uplift

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%


Stor

y Sh

ear,

kip

s

Third story fixed

Third story with uplift

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%


Stor

y Sh

ear,

kip

s

Fourth story fixed

Fourth story with uplift

Overturning Reductions

Overturning Reduction Factor Qot , for Upper Structure

Level Perpendicular to

Framing Parallel to Framing

Unknown or mixed

Two or more stories above

0.95 0.85 0.85

One story above 0.85 0.8 0.8

Top story 0.75 0.8 0.75

The Relative-Strength Method

0

50

100

150

200

250

300

350

400

0% 1% 2% 3% 4% 5% 6%

Drift Ratio

Elev

atio

n, in

.(E) Structure

Optimal-performance retrofit

Overly strong retrofit

Optimal-cost retrofit

Pattern Recognition

Can a Building’s Capacity be Determined from a Few

Parameters?

Epidemiology

Predict Risk of Heart Disease Based on a Few Indicators

Genetics

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Period, sec.

Spec

tral

Acc

eler

atio

n, g

Mean Median Geomean

Local Seismicity

Body Mass Index

Translational Weakness

Structural Use of Non-conforming Materials

Load-Drift Data for Wall Bracing Material

Standard Drift Ratio, aj

Material ID 0.5 % 0.7 % 1.0 % 1.5 % 2.0 % 2.5 % 3.0 % 4.0 %

Up to late 1940s

Stucco L01 333 320 262

Horizontal 1x wood sheathing

L02 85 96 110 132 145 157 171

Diagonal 1x wood sheathing

L03 429 540 686 913

Plaster on wood lath L04 440 538 414 200

After the 1950s

Stucco L01 333 320 262

Plywood panel siding, “T1-11”

L05 354 420 496 549 565

Gypsum wallboard L06 202 213 204 185 172 151 145 107

Plaster on gypsum lath L07 402 347 304

Wood structural panel 8d@6

L08 521 621 732 812 836 745 686


L09 513 684 826 943 1,018 1,080 1,112 798


L10 1,072 1,195 1,318 1,482 1,612 1,664 1,686 1,638


L11 1,607 1,792 1,976 2,222 2,418 2,496 2,529 2,457


L12 548 767 946 1,023 1,038 1,055 1,065 843


L13 707 990 1,275 1,420 1,466 1,496 1,496 1,185


L14 940 1,316 1,696 1,889 1,949 1,990 1,990 1,576


L15 1,414 1,979 2,551 2,841 2,931 2,993 2,993 2,370

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Unit

Forc

e, p

lf

Stucco

Horizontal wood sheathing

Diagonal wood sheathing

Brick veneer

Plaster on wood lath

Plywood panel siding

Gypsum wall board

Plaster on gypsum lath









Structural Use of Non-conforming Materials

V1,y

1,y

Ground Story translationalload-deflection curve in they-direction, F1,y

Wall: 1 32 4

1,y 1,y 1,y 1,y

1,yf 2,yf

shea

r for

ce

drift ratio

3,yf4,yf

Drift ratio at which translationalstrength occurs

Translational strengthof the Ground Story

Translational Weakness

Smoking

Torsional Weakness

Ground Floor Plans Upper Floor Plans

eq.

eq.

L

0.2L

L

0.0

Lateral strength proportionalto building length in eachdirection

Edge of floor above

0.000.00

AW

0.600.80

C

0.330.33

0.600.80

0.670.67

0.600.80

1.001.00

0.600.80

T

Torsional Imbalance

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Torsion Coefficient, C T

Cap

acity

Red

uctio

n Fa

ctor

Ductile, Aw = 0.60AB

Ductile, Aw = 0.60R

Ductile, Aw = 0.80AB

Ductile, Aw = 0.80R

Brittle, Aw = 0.60AB

Brittle, Aw = 0.60R

Brittle, Aw = 0.80AB

Brittle, Aw = 0.80R

Dire

ctio

n of

drif

t as

sess

men

t

Torsional Imbalance

Stress

Low Displacement Capacity

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Forc

e

Hysteresis of low displacement capacity material

High Activity Level

High Displacement Capacity

Hysteresis of high-displacement capacity material

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Forc

e

Strength Degradation Ratio

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Drift Ratio, %

Uni

t For

ce, p

lf

Load-Deflection CurvePeak Strength, V

Strength at 3% Drift, V3%

Strength Degradation Ratio,C D = V 3% /V

Ground-story Strength

Upper-story Strength

Upper to Ground Strength Ratio

Toughness

Torsional Imbalance

Characteristic Structural Coefficients

s

s

Ni

N

ijj

xixU

W

VC

2

,, min

sN

jj

xxs

W

VC

1

,1,

TCT

x

xxD V

FC

,1

,1,

%)3(

xU

xsxW C

CC

,

,,

Create a Controlled Experiment

Determine the Influence of Each Characteristic

Analytical Engine:Surrogate Structure Concept

Ductile

Upper-story strength ratios, Au:(4) per mat'l form

Material forms:(2) total

0.1 0.2 0.4

Weak-story ratios, Aw:0.6 to 1.1 by 0.1(6) per upper-story strength

Retrofit strengths:Aw to 1.6(51) per upper-story strength ratio

TOTAL NUMBER OFBUILDINGS:

612

Time-historyseed records:

(22) Bi-directional records = (44) individual

Scaled so that median Sa( T = 0.3 sec ) = 1.0g

0.6

Brittle

0.1 0.2 0.4 0.6

(35) intensities per seedrecord varying from 0.1to 3.5 by 0.1

Given drift criteria, fitlog-normal CDF

Recover peak interstorydrift ratios for eachanalysis

Earthquake Intensity0 1.0 (Sa = 1g) 3.5

0

1.0

0.5

Simplified Building Model

W 50 in.H 100 in.L 111.8q 1.107 rad,

63.4 deg.cos(q) 0.447Astrut 1 in2

Mg 1 kip (total weight of building)

Perform Tool –Post Processing Utility

612 surrogate structures x 44 EQs

x 35 intensities

1 million nonlinear response-history analyses

Analytical Engine:Surrogate-Structure Concept

Analysis Results

Aw=0.6Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

0.7

1.2

1.7

2.2

2.7

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Total Ground Floor Strength/Upper Floor Strength

Spec

tral

Cap

acity

, Sc

Au = 0.4

Au = 0.6

Au = 0.2

Au = 0.1

Analysis Results

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

Aw = 1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Upper-Story Strength Ratio, A U

20th

Per

cent

ile In

tens

ity S

pect

ral C

apac

ity, S

c,20 48.0

,,20, 47.134.0 xUxWc AAS

Curve fit for Incremental Dynamic Analysis

Excel –Visual Basic Applications

Structural Capacity

48.0,,,1 5.0124.2525.066.0 xUsTxWxc AQCAS

60.0,,,0 5.0159.1122.060.0 xUsTxWxc AQCAS

xcDxcDxc SCSCS ,03

,13

, 1

CD

= 1.0

CD

= 0.0

for intermediate values

MSxc SS , if true –

no retrofit required

Onset of Strength Loss drift criteria, OSL

20% Probability of Exceedance, POE

Modifier for POE

= 0.2 Mean spectral capacity, Sm

Retrofit Strength Requirements

xUxUxr VAV ,,max, 22.111.0 upper limit

lower limit

31

31

32

32

, 11

DD

DDMSxre CYCX

CYCXSV

TsU CQAX 5.0148.00 01 48.1 XX 02 35.0 XX

TsU CQAY 5.016.00 01 96.0 YY 02 07.0 YY

Strength of Retrofitted Ground-Story

Spec

tral

Cap

acity

, Sc

Au = 0.4, Aw = 0.6

Maximum Strength, V r max

(Best Performance)Minimum Strength, V r min

(Adequate Performance)

Acceptable Retrofit Range

S c = S MS

Range of Retrofit Strength

xUxUxr VAV ,,max, 22.111.0 3

13

1

32

32

, 11

DD

DDMSxre CYCX

CYCXSV

Strength of Retrofitted Ground-Story

Spec

tral

Cap

acity

, Sc

Acceptable Retrofit Range

Au = 0.1, Aw = 0.6 Maximum Strength, V r max

Minimum Strength,V r min = 0.9V r max

S MS

Estimated Minimum Strength, V re

S c

2/3 S MS

Range of Retrofit Strength

xUxUxr VAV ,,max, 22.111.0

= 0.5

0.55

0.30

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Site-Specific Spectral Acceleration, S S

Prob

abili

ty o

f Exc

eeda

nce

ofSe

lect

ed D

rift C

riter

ia

Site-specific seismic intensity, S S ( = 0.521 in this example).

Fragility curve after retrofit identified by mean spectral capacity S . (S = 0.55 in this example)

Fragility curve before retrofit identified by mean spectral capacity S . (S = 0.30 in this example)

Log-normal standard deviation, , determines relavent set of fragiltiy curves. ( = 0.5 in this example)

0.47

0.87

Probability of exceedance before retrofit (P = 0.87 in this example)

Probability of exceedance after retrofit (P = 0.47 in this example)

Given Spectral Demand, Find Probability of Exceedance

WST IDA –Data Base Graphic Utility

Purpose: The Weak-StoryTool IDA application exists as an interface to query the raw IDA data.

Weak-StoryTool

IDA Application

Predictive Understanding

David Mar Guidelines for Seismic Retrofit of Weak-Story Two-Frame Buildings ATC 71-1

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