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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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
The Scope
Inexpensive to Construct(Work Only In Ground Story)
Inexpensive to Design(Unsophisticated Engineers)
Performs Well(Shelter-In-Place)
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
Pattern Recognition
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
Strong but Brittle Upper Structure
Weak and Brittle Lower Structure
Pattern Recognition
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
Limited Damage to Upper Structure
Damage Concentrated in Lower Structure
Pattern Recognition
RELATIVE
STRENGTH
METHOD
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
•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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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?
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
Translational Weakness
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
%
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
Torsional Weakness
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
,
,,
Ground-story Strength
Upper-story Strength
Upper to Ground Strength Ratio
Toughness
Torsional Imbalance TCT
x
xxD V
FC
,1
,1,
%)3(
Ground-story Strength
Upper-story Strength
Upper to Ground Strength Ratio
Toughness
Torsional Imbalance TCT
xU
xsxW C
CC
,
,,
x
xxD V
FC
,1
,1,
%)3(
Ground-story Strength
Upper-story Strength
Upper to Ground Strength Ratio
Toughness
Torsional Imbalance TCT
s
s
Ni
N
ijj
xixU
W
VC
2
,, min
xU
xsxW C
CC
,
,,
x
xxD V
FC
,1
,1,
%)3(
Ground-story Strength
Upper-story Strength
Upper to Ground Strength Ratio
Toughness
Torsional Imbalance TCT
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
Wood structural panel 8d@4
Wood structural panel 8d@3
Wood structural panel 8d@2
Wood structural panel 10d@6
Wood structural panel 10d@4
Wood structural panel 10d@3
Wood structural panel 10d@2
Structural Use of Non-conforming Materials
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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%
Interstory Drift Ratio
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%
Interstory Drift Ratio
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%
Interstory Drift Ratio
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
Retrofit
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
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
FEMA P-807: Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings with Weak First Stories
WST IDA –Data Base Graphic Utility