guidelines for seismic retrofit of weak-story wood … · guidelines for . seismic retrofit of...

FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories

Guidelines for Seismic Retrofit of Weak-Story Wood-Frame Buildings

Learning Objectives1.

Understand the vulnerabilities and failure modes of weak-story buildings under EQ demands.

2.

Recognize the influence of “non-structural”

finishes on the capacity of wood buildings.

3.

Learn how to determine the capacity at “near” collapse.

4.

Learn how to determine the optimal retrofit.

5.

Understand the use of the Weak Story Tool.

Background and Theory

Nuts and Bolts

Making it Simple

BACKGROUND

&

THEORY

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

Create Seismic Retrofit Program for

Weak-Story Wood-framed Apartment Buildings

in Western US


The Scope

Inexpensive to Construct(Work Only In Ground Story)

Inexpensive to Design(Unsophisticated Engineers)

Performs Well(Shelter-In-Place)


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

RELATIVE

STRENGTH

METHOD


•Optimize

benefits of ground story retrofits

•Retrofit to add both strength and displacement capacity, and reduce torsion

•Strength limit

established by the upper structure

•Create a damage and deformation absorption level

•The tough ground story protects the upper stories

•If too strong, no damage absorption –

forces are transmitted to upper structure

The Relative Strength Method


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

Can a Building’s Capacity be Determined from a Few

Parameters?


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


Translational Weakness


Analysis Methodology -

Material Forms

Interstory Drift

Shea

r For

ce

Sheathing material with C D = 0.0

L =

1.2

5%

Sheathing material with C D = 1.0

L =

4.0

%


Damping and Hysteretic Models

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Forc

e

Hysteresis of idealized high displacement capacity material

“ductile“

form

Hysteresis of idealized low displacement capacity material

“brittle“

form

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Forc

e


Torsional Weakness


Characteristic Structural Coefficients

sN

jj

xxs

W

VC

1

,1,

s

s

Ni

N

ijj

xixU

W

VC

2

,, min

xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(

T

CT

Ground-story Strength

Upper-story Strength

Upper to Ground Strength Ratio

Strength Degradation

Torsional Imbalance

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)

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


Structural Capacity

48.0,,,1 5.0124.2525.066.0 xUsTxWxc AQCAS

60.0,,,0 5.0159.1122.060.0 xUsTxWxc AQCAS

CD

= 1.0

CD

= 0.0

NUTS

&

BOLTS


Limitations on the Guidelines

•Up to four stories

•Strong basement and strong sloped base can be accommodated

•Wood-framed stud walls and existing steel moment frames

•No concrete or masonry walls or steel braced frames

•8’

–

12’

floor heights for upper structure

•8’

–

15’

floor heights for ground floor

•Sloped sites can be accommodated

•Torsionally regular upper structure

•No vertical irregularities in upper structure





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

,

,,




Toughness

Torsional Imbalance TCT

x

xxD V

FC

,1

,1,

%)3(




Toughness


xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(




Toughness


s

s

Ni

N

ijj

xixU

W

VC

2

,, min

xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(




Toughness


TCT

x

xxD V

FC

,1

,1,

%)3(

TCT

xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(

TCT

s

s

Ni

N

ijj

xixU

W

VC

2

,, min

xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(

TCT

sN

jj

xxs

W

VC

1

,1,

s

s

Ni

N

ijj

xixU

W

VC

2

,, min

xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(

TCT

sN

jj

xxs

W

VC

1

,1,

s

s

Ni

N

ijj

xixU

W

VC

2

,, min

xU

xsxW C

CC

,

,,

x

xxD V

FC

,1

,1,

%)3(

TCT

STORY

STRENGTH


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

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

Wood structural panel 8d@6








Structural Use of Non-conforming Materials


Deflection Criteria

High Displacement Capacity (Hd)

Low Displacement Capacity (Ld)

Name Ground Story

Upper Stories

Ground Story

Upper Stories

Onset of Strength Loss, Original Condition

4.0 4.0 1.25 1.25

Onset of Strength Loss, Retrofitted

4.0 4.0 4.0 1.25

Brittle Backbone Curves

0

100

200

300

400

500

600

700

800

900

1,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Uni

t For

ce, p

lf

L01 L03 L04 L05 L06 L08

Ductile Backbone Curves

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, %

Uni

t For

ce, p

lf

L02 L07 L09 L10 L11 L12 L13 L14 L15 L16


Perforated Shearwalls

L

HFl

oor t

o C

eilin

g

w

L L L1 2 3

Openings

A = A + Ai 1 2 L = L + L + Li 1 2 3

Full-height wallsegments

A1

A2

32 80.072.092.0 perfQ

i

i

LHA

1

1


Story Height Adjustment Factor

Perform Model

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 50 100 150 200 250

Height of Bottom Story, in.

Nor

mal

ized

Mea

n Sp

ectr

al C

apac

ity

Linear fit for Story-Height Adjustment Factor, Q s :

Q s = 0.55 + 0.0045 H

where H is the mean ground-story height in inches.

Wall Height Adjustment Factor

H

HTa

llest

wal

l in

grou

nd s

tory

2

H2

Drift ratio, = / H1

Drift ratio, = / H2 2

Normalized Drift Ratio

1 2

Actual Drift Ratio

2

1

1 2 = / H

2

1

Assembly unitload-deflection curve

Unit load-deflection curveadjusted for height of Wall 1

Wall 2

Wall 1

Unit load-deflection curveadjusted for height of Wall 2

Unadjusted assembly unitload-deflection curve

H

Talle

st w

all i

n gr

ound

sto

ry

Wall 2

Wall 1

HH

D wallh

Dh < 1.0

Dh > 1.0)

Dh = 1.0

0

200

400

600

800

1,000

1,200

0 1 2 3 4 5 6 7 8

Drift Ratio, %

Uni

t For

ce, p

lf

Adjusted load-deflection curve

Taller wallsShorter walls

Pushover Curve to Find Peak Strength

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

otperfwjwjw QQLvf )()(

SIMPLIFIED

OVERTURNING

ADJUSTMENT


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 Reduction Factor

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

STRENGTH

DEGRADATION

RATIO


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

TORSIONAL

IMBALANCE


Weak-Story Wood-Frame Buildings

Torsion Demand

Center of strengthat Story 2 (above),COS

ex

ey

Center of strength atGround Story, COS

32 4

1,yV

1,xV

1,xV

1,yV

Ground Storytorsion demand, = V e + V e1,y x 1,x y

Wall: 1

1

2

xyyx VeVe ,1,1

xxx COSCOSe ,1,2

yyy COSCOSe ,1,2

Torsion Capacity

Center of strengthat Ground Story

j

Torsional moment thatcauses a twist of for theGround Story, t ( )

Wall: 1 32 4

A

B

C

D

E1,

x

d j

A,y dj

1,x

j d1,x

jf

at

d1,

x1,

y

j d2,x j d3,x j d4,x

jf

at

d2,

x2,

y

jf

at

d3,

x3,

y

jf

at

d4,

x4,

y

1 j

j

d

d

2,x d

d

3,x

4,x

d

d

d

d

d

B,y

C,y

D,y

A,y

E,y

jf at dA,yA,x

jf at dB,yB,x

jf at dC,yC,x

jf at dD,yD,x

jf at dE,yE,x

t ( )1

j 1

Maximum twist angle toconsider for the Ground Story

j

Torsional moment thatcauses a twist of for

the Ground Storyj

T1

Torsional strength ofthe Ground Story

Twist Level 2 bythe twist angle, j

Ground Story torsionalload-deflection curve, t1

Torsion Backbone Curve

wallsN

w

jywywxw

jywxwywj H

dfd

Hd

fdt1 1

,,,

1

,,, ))(

)(max jtT


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

Accounting for Torsion

TCT

CALCULATE

SPECTRAL CAPACITY


Spectral Capacity, Sc

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

CALCULATE

OPTIMAL RETROFIT


Range of Retrofit Strength

xUxUxr VAV ,,max, 22.111.0

3

13

1

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

For buildings with strong upper structures (Vrmax

> Vre

)

upper limit

lower limit

For buildings with weak upper structures (Vrmax

< Vre

)

xUxUxr VAV ,,max, 22.111.0 use 90% –

110% of upper limit

If the upper structure is extremely weak, such that MSxcr SS32

,

the Guidelines are not applicable –

use alternative methodology

this corresponds to a 50% POE at the MCE

Estimate of the minimum ground-story strength that gets POE

below 0.2


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


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


xUxUxr VAV ,,max, 22.111.0

Retrofit


Depending on the width, this portionmay be considered a separatesub-diaphragm, D

D D

W

WW

LCantileveredDiaphragm

Chord capacity must bechecked if L > 10 feet.

> 0.

25y

y

x

> 0.25xNorth-South Analysis

D

D

This wall must supportlateral loads from bothdiaphragms D and D

y : x < 2 : 1

y : x < 2 : 1

x x

E

S

W

N

DD

x

y

x : y > 2 : 1

xx

x : y < 2 : 1 x : y < 2 : 1

This frame must supportlateral loads from bothdiaphragms D and D

Direction of motionconsidered

Regularizing Diaphragms

Aspect ratios Cantilevers

Re-entrant corners

Openings


ex

1,yV

COS

1,yVr,yV

e

L

e

Center of strength atStory 2 (above), COS

Existing Center of strengthat Ground Story, COS1

2

Center of strength at GroundStory after retrofit, COS r

r,x V,x

x

2,x

Retrofit element

Retrofit element

Force resultant of strengthsof retrofit elements in they-direction

Retrofit Placement to Minimize Torsion

xxrx VVV ,1,,1

xxy

yxxV COSL

VVe

e ,2,1

,1,

xVxyr

yxx ee

VV

ee ,,

,1min,

xxx Lee 05.0min,max,

Added retrofit strength -

Place to eliminate torsion, limited by building dimension

Range of acceptable eccentricity -

MAKING

IT

SIMPLE


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guidelines for seismic retrofit of weak-story wood … · guidelines for . seismic retrofit of...

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