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Slender Wall Behavior & Modeling
John Wallace
University of California, Los Angeles
with contributions fromDr. Kutay OrakcalUniversity of California, Los Angeles
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Presentation Overview
FEMA 356 Requirements! General requirements
! Modeling approaches
" Beam-column, fiber, general! Stiffness, strength
Experimental Results
! Model Assessment" Rectangular, T-shaped cross sections
! FEMA backbone relations
" Flexure dominant walls
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FEMA 356 Nonlinear Modeling for Buildings withSlender RC Walls
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FEMA 356 RC Walls
General Considerations 6.8.2.1! Represent stiffness, strength, and
deformation capacity
! Model all potential failure modes anywherealong the wall (member) height
! Interaction with other structural andnonstructural elements shall be considered
! So, we must consider any and everything
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Wall Modeling Approaches
Equivalent beam-column model!hw/lw! 3
Modified equivalent beam-column
! Rectangular walls (hw/lw" 2.5)
! Flanged walls (hw/lw" 3.5)
Multiple-line-element and Fiber models
! Concrete and rebar material models
General wall model
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Modified Beam - Column Model
Rectangular walls (hw/lw" 2.5)& Flanged walls (hw/lw" 3.5):
Use of modifiedbeam-column element
with added shear spring
Nonlinear flexure/shear
are uncoupled using this
approach
Beams
Wall
Shear
spring
Column at
wall
centroid
Hinges
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Modified Beam - Column Model
Shear force deformation properties
A
B
C
D
E
/h
V
Vn
1.0
0.2
CPLSIO
Deformation-controlled component
a b - a
c
, -
0.4
1and 0.2
1 2
y
y
c c
c c
Vh
G E A
G E .
.
/ 0+ $1 21 2$3 4
/ 0$ 51 2
63 4
y/h
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Fiber Section Model
! Typically use a more refined mesh where yielding is anticipated;however,! Nonlinear strains tend to concentrate in a single element, thus, typically
use an element length that is approximately equal to the plastic hingelength (e.g., 0.5lw). Might need to calibrate them first (this is essential).
! Calibration of fiber model with test results, or at least a plastic hingemodel, is needed to impose a reality check on the element size and
integration points used.
Actual cross section
Concrete Fibers
Steel Fibers
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Materials
Unconfined Concrete
Maximum permissiblecompressive strain forunconfined concrete
(FEMA 356 S6.4.3.1)
7 = 0.002 or 0.005
Limit state
associatedwith crackwidth
Stress
(ksi)
Strain
, - , -
2
' '
0 0
' '
0 85
2
Linear descending branch defined by:
0.002; and 0.0038; 0.85
c cc c c
c c c
f f f
f f
7 7
7 7
7 7
% &/ 0' ($ 8 91 2' (3 4) *
$ $
In the absence of cylinder stress-strain tests, Saatcioglu & Razvi (ASCE, JSE,1992) recommend relation based on work by Hognestad.
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Materials
Confined Concrete (FEMA 356 6.4.3.1)! Use appropriate model, e.g.:
" Saatcioglu & Razvi (ASCE JSE, 1992, 1995)
"Mander (ASCE JSE, 1988)"Modified Kent & Park (ASCE JSE, 1982)
! For reference
! FEMA 356 Qualifications:
"Maximum usable compression strain based onexperimental evidence and consider limitationsposed by hoop fracture and longitudinal barbuckling.
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Materials
Steel Material:
Stre
ss
(ksi)
Strain
Maximum usable strain limits per
FEMA 356 S6.4.3.1
7 = 0.02 7 = 0.05
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General Wall Models/FE Models
e.g., RAM-PERFORM:! Flexure - fiber model (2-directions)
! Shear - Trilinear backbone relation
! Flexibility to model complex wall
geometry! Mesh refinement issues
Flexure/Axial Shear
Concentration of nonlinear
Deformations in one element
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Stiffness Modeling
FEMA 356 Section 6.8.2.2 Use Table 6.5! Uncracked: EIeffective = 0.8EIg
! Cracked: EIeffective = 0.5EIg
30 x 2 ft Wall Section16 - #14 Boundary#6@12" Web
CURVATURE
MOMENT
P=0.30Agf'c
P=0.20Agf'c
P=0.10Agf'c1.0, 0.75, 0.5, 0.4EcIg
0.75EcIg 0.5EcIg
Wallace, et al., 4NCEE, Vol. 2, pp 359-368, 1990.
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Response Correlation Studies
! Ten Story Building in San Jose, California! Instrumented: Base, 6th Floor, and Roof
! Moderate Intensity Ground Motions Loma Prieta
4.53 m (14.88 ft)
1.68 m(5.5 ft)
PLAN VIEW: CSMIP BUILDING 57356
8.84 m (29 ft)
8.84 m (29 ft)
5 @ 10.97 m (36 ft)
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Response Correlation Studies
! Ten Story Building in San Jose, California! Instrumented: Base, 6th Floor, and Roof
! Moderate Intensity Ground Motions Loma Prieta
0 10 20 30Time (sec)
-1.5
0
1.5
Displa
cement(in.) Analysis - 0.5Ig
Measured
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Strength Requirements
ACI 318 Provisions! Pn- Mn
" For extreme fiber compression strain of 7c =0.003.
!Vn"ACI 318-99,02,05 Equation 21-7
'
3.0 for / 1.5
2.0 for / 2.0
n cv c c t y
c w w
c w w
V A f f
h l
h l
# :
#
#
% &$ 6) *
$ "
$ !
Linear interpolationallowed for intermediatevalues
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Definition of Wall Cross Section
Flexural strength
! Consider all vertical reinforcement within weband within the effective flange width
Consider the influence of openings onthe strength and detailing requirements
! ACI 318-02, 05 Appendix A Strut & Tie Approach
Cross-Section Definition
beff
0.25hw
' ', ,
'
, ,
s bound s flange s
s bound s flange s
A A
A A
6
6
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Behavior of Flanged Walls
Flange Compression versus Tension
7t7c
s
beff
Flange Compression
Low compressive strain
Large curvature capacity
Mn & Vu similar rectangle
beff
Flange Tension
Large compressive strain
Less curvature capacity
Mn; Vu;
7t7c
, ,s bound s flangeA A6
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Experimental Results
RW2 & TW1: ~ !scale tests
Thomsen & Wallace, ASCE JSE, April 2004.
Uncoupled designDisplacement-based design
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Experimental Results
P = 0.09Agf'c
vu,max= 4.85
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Experimental Results
RW2 & TW2: ~ !scale tests
Thomsen & Wallace, ASCE JSE, April 2004.
Displacement-based design of T-shape
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Experimental Results
P = 0.075Agf'c
vu,max= 5.5
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Model Assessment Comparison of Analytical andExperimental results
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MVLE (Fiber) Model
h
(1-c)h
ch
12
3
4
5
6Rigid Beam
Rigid Beam
k1 k2 knkH. . . . . . .
m
RC WALL WALL MODEL
1
2
.
.
.
.
.
Basic assumptions:
Plane sections (rigid rotation of top/bottom beams Uniaxial material relations (vertical spring elements)
MVLE Model versus Fiber Model:
Similar to a fiber model except with constant curvature
over the element height (vs linear for fiber model)
Orakcal, Wallace, Conte; ACI SJ, Sept-Oct 2004.
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Strain, 7
O
TensionNot to scale
Compression
( 7c' , fc' )
(70,0)
(70+7t ,ft)
Material (Uni-axial) Models
Strain, 7
7y
E0
E1=bE0>y
OR
Concrete:
Chang and Mander (1994)# Generalized (can be updated)
# Allows refined calibration
# Gap and tension stiffening
Reinforcing Steel:
Menegotto and Pinto (1973) Filippou et al. (1984)
# Simple but effective
# Degradation ofcyclic curvature
r
Stress,
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Model Assessment$
Approximately 1/4 scale$ Aspect ratio = 3$ Displacement based
evaluation for detailingprovided at the wall
boundaries$ 12 ft tall, 4 ft long, 4inches thick
$ #3 vertical steel, 3/16hoops/ties
$ #2 deformed web steel$ Constant axial load$ Cyclic lateral
displacements applied atthe top of the walls
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Instrumentation
Wire Potentiometers
(horizontal displacement)
Wire Potentiometers
(X configuration)
Steel Strain Gage Levels
Wire Potentiometers
(vertical displacement)
LVDT's
Concrete Strain Gages
Linear Potentiometers
(Pedestal Movement)
Rigid
Reference
Frame
RW2
Extensive instrumentation provided to measurewall response at various locations
Massone & Wallace; ACI SJ, Jan-Feb 2004.
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Applied Lateral Displacement
-80
-40
0
40
80
-2
-1
0
1
2RW2
0 100 200 300 400 500 600 700 800
Data Point Number
-80
-40
0
40
80
TopDisplacem
ent(mm)
-2
-1
0
1
2
DriftRatio
(%)
Applied displacementPedestal movement excluded
Pedestal movement andshear deformations excluded
TW2
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Model Details RW2
1219 mm
19 mm 19 mm3 @ 51 mm 153 mm 3 @ 191 mm 153 mm 3 @ 51 mm
64 mm
19 mm
19 mm
102 mm
#2 bars (db=6.35 mm) Hoops (db=4.76 mm)8 - #3 bars
1 2 3 4 5 6 7 8uniaxial element # :
(db=9.53 mm) @ 191 mm @ 76 mm
m=16
1
2
..
.
.
.h
(1-c)h
ch
k1 k2 knkH. . . . . . .
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Model Details TW2
19 mm 19 mm3 @ 51 mm153 mm 3 @ 191 mm 153 mm3 @ 51 mm
64 mm
19 mm
19 mm
1219 mm
3 @ 140 mm
102 mm
4 @ 102 mm
19 mm
102 mm
19 mm
3 @ 51 mm
102 mm
1219 mm
uniaxial element # : 1
2
345
6
7
8
9
10
12-19
118 - #3 bars(db=9.53 mm)
#2 bars (db=6.35 mm)@ 191 mm
Hoops (db=4.76 mm)@ 76 mm
#2 bars (db=6.35 mm)@ 140 mm
2 - #2 bars (db=6.35 mm)
Hoops and cross-ties (db=4.76 mm)@ 38 mm
8 - #3 bars(db=9.53 mm)
Hoops (db=4.76 mm)@ 32 mm
+
-
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Concrete Model - Unconfined
0 0.001 0.002 0.003 0.004
Strain
0
10
20
30
40
50
Stress(M
Pa)
Test Results
1stStory
2ndStory
3rdStory
4thStory
Analytical (Unconfined)
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Concrete Model - Confined
0 0.005 0.01 0.015 0.02 0.025
Strain
0
10
20
30
40
50
60
70
Stress(M
Pa)
Unconfined Model
Mander et al. (1988)
Saatcioglu and Razvi (1992)
RW2
TW2 Flange
TW2 Web
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Concrete Model - Tension
0 0.0005 0.001 0.0015 0.002 0.0025
Strain
0
0.5
1
1.5
2
2.5
Stress(M
Pa)
Chang and Mander (1994)Belarbi and Hsu (1994)
0 0.005 0.01 0.015 0.02 0.025 0.03
0
0.5
1
1.5
2
2.5
(7t,ft)
r
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Reinforcement Material Model
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
Strain
-600
-500-400
-300
-200
-100
0
100
200
300
400
500
600
Stress(M
Pa)
#3 (RW2 & TW2 Flange)
#3 (TW2 Web)
#2 (TW2 Web)
#2(RW2 & TW2 Flange)
#3
#2
0 0.02 0.04 0.06 0.08 0.1
0
100
200
300
400
500
600
700
#3 rebar
#2 rebar
4.76 mm wire
Tension
CompressionTest Results
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Model Assessment RW2
-80 -60 -40 -20 0 20 40 60 80
Top Flexural Displacement, +top (mm)
-200
-150
-100
-50
0
50
100
150
200
LateralLoad,Plat(kN)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Lateral Flexural Drift (%)
Test
Analysis5Pax 0.07Agfc
'
Plat,+top
0
100
200300
400
500
Pax
(k
N)
RW2
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Model Assessment RW2
-80 -60 -40 -20 0 20 40 60 80
Lateral Flexural Displacement (mm)
0
1
2
3
4
5
StoryNumber
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Lateral Flexural Drift (%)
Test
Analysis
1.5%
2.0%
2.5%
0.75%
1.0 %
RW2
Applied LateralDrift Levels:
Top
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Model Assessment RW2
-0.01
0
0.01
0.02
Rotation
(rad)
0 100 200 300 400 500 600 700-15
-10
-5
0
5
10
15
Dis
placement
(mm)
TestAnalysis
RW2 (First Story)
Results based on recommended values for material parameters; however,results could vary, maybe significantly, for different element lengths and
material parameters (particularly if no strain hardening)
1.5%2.0%
Data Point
0.008 FEMA 356 CP limit
d l 2
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Model Assessment RW2
RW2Boundary Zone
100 150 200 250 300 350 400 450 500 550 600
Data Point
-0.01
-0.005
0
0.005
0.010.015
0.02
0.025
0.03
0.035
Concrete
Strain
Concrete Strain Gage
LVDT
Analysis
0.25%0.5%
0.75%
1.0%
1.5%
1.0%
2.0%
1.5%
Orakcal & Wallace; ACI SJ, in-press for publication in 2006 (see 13WCEE).
M d l A RW2
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Model Assessment RW2
RW2Boundary Zone
100 150 200 250 300 350 400 450 500 550 600
Data Point
-0.01
-0.005
0
0.005
0.010.015
0.02
0.025
0.03
0.035
Concrete
Strain
Concrete Strain Gage
LVDT
Analysis
0.25%0.5%
0.75%
1.0%
1.5%
1.0%
2.0%
1.5%
Orakcal & Wallace; ACI SJ, in-press for publication in 2006 (see 13WCEE).
M d l A t TW2
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Model Assessment TW2
-80 -60 -40 -20 0 20 40 60 80
Top Flexural Displacement, +top (mm)
-400
-300
-200
-100
0
100
200
300
400
La
teralLoad,Plat(kN)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Lateral Flexural Drift (%)
Test
Analysis
5Pax 0.075Agfc'
Plat,+top
0
250500
750
Pax
(kN)
TW2
C
T
T
C
M d l A t TW2
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Model Assessment TW2
-80 -60 -40 -20 0 20 40 60 80
Lateral Flexural Displacement (mm)
0
1
2
3
4
5
StoryNumber
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Lateral Flexural Drift (%)
Test
Analysis
1.5%
2.0%
2.5%
0.75%
1.0 %
TW2
Applied LateralDrift Levels:
Top
C
T
T
C
M d l A t TW2
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Model Assessment TW2
-600 -400 -200 0 200 400 600
Distance along Flange from Web (mm)
-0.005
0
0.005
0.01
0.015
0.02
0.025
FlangeConcreteS
train
(LVDT
s)
Test
Analysis
0.5%1.0%
2.0%
2.5%
TW2
C
T
T
C
y7
2.0%
2.5%
2.5%
2.0%
M d l A t St bilit
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Model Assessment Stability
P = 0.09Agf'c
vu,max= 4.85
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Model Assessment - Stability
Rebar Buckling at Wall Boundary Rebar Fracture FollowingBuckling at Wall Boundary
Instabilities, such as rebar buckling and lateral web buckling, and rebar fractureare typically not considered in models; therefore, engineering judgment is required.
Loss of lateral-load capacity does not necessarily mean loss of axial load capacity
FEMA 356 T bl 6 18
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FEMA 356 Table 6-18
FEMA 356 Table 6 18
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FEMA 356 Table 6-18
FEMA 356 M d li P t
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FEMA 356 Modeling Parameters
' '
2
'
s
& 0.07 & Hoops @ 2" o.c.
2(0.027 in ) 0.09( )( 6" 3 /8" 3 /16")(5 ksi / 63 ksi)
1.2" Non-confo
WALL RW2:
WALL TW2: Flange Compre
rming
8 - #3
ssio
A 10 - #
n
s s g c
c
s
A A P A f
s h
s
A
$ $
$ $ 6 6
9
$ $
, - , -' 2
'
'
3 and 4 - #2 63 ksi & Hoops/Ties @ s=4"
No special detailing required: Conforming
0.42 in 63 ksi 0.075(2) 0.1274"(48")( 6 ksi)
40 kips2.7
4"(48") 6000 /1000
y
s s y
w w c
u
w w c
f
A A f Pt l f
V
t l f
5
% &8 6 8) *$ 6 $
$ $
!
FEMA 356 M d li P t
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FEMA 356 Modeling Parameters
'
s
2
8 - #3 & 2 - #2 A 24 - #3 and 8 - #2 & 63 ksi
Hoops/Ties @ s=1.25" (5 legs and 2 legs)
5(0.027 in ) 0.09( )( 16" 3/
WALL TW2: Flange
8" 3/16")(6 ksi / 63 ksi) 1.
Tension
"
(
0
2 0
s y
c
A f
s h s
$ $ 5
$ $ 6 6 9
, - ? @, -
2
'
'
'
.027 in ) 0.09( )( 2.5" 3 /8" 3 /16")(6 ksi / 63 ksi) 2.1"
Conforming
16(0.11) 6(0.049) 63 ksi
0.075(2) 0.264"(48")( 6 ksi)
80 kips5.4
4"(48") 6000 /1000
c
s s y
w w c
u
w w c
s h s
A A f P
t l f
V
t l f
$ $ 6 6 9
8 6 6
$ 6 $
$ $
!
!
FEMA 356 Modeling Parameters
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FEMA 356 Modeling Parameters
Tables 6-18 (partial):
Model Parameters, RadiansWalls Controlled by Flexure
'
')(
cww
yss
flt
PfAA Conf.Bound.
'
cww flt
V PlasticHinge
a
PlasticHinge
b
ResidualStrength
c
0.1 Yes 3 0.015 0.02 0.75
0.1 No 3 0.008 0.015 0.60
0.25 Yes 6 0.005 0.010 0.30
0.25 No 6 0.002 0.004 0.20
RW2
TW2Flange Tension
TW2Flange Comp
FEMA Backbone Relation RW2
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FEMA Backbone Relation RW2
, -
, -
4
3
y
3
29.4 kips
3 0.5
29.4 (150")0.41"
3(4000 )(18,432 )
0.008(144") 1.15"
0.015(144") 2.16"
0.6(29.4 ) 17.6 kips
nlateral
w
lateral load
c g
k
ksi in
a
b
k
residual
MPh
P h
E I
P
A
A
A
$ $
% &' ($
' () *
$ $
$ $$ $
$ $
FEMA Backbone Relations TW2
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FEMA Backbone Relations TW2
, -
, -
, -
4
3
y
3
4 48
40.2 kips
3 0.5
40.2 (150")
3(4400 )(40, 700 )
0.25"
2.2 =34.5"
0.015(144") 2.16"
0.020(144") 2.88"
0.75(40.2 ) 30.2 kips
nlateral
w
lateral load
c g
k
ksi in
g g x
a
b
k
residual
MP
h
P h
E I
I I y
P
A
A
A
$ $
% &' ($
' () *
$
$
$$ $
$ $
$ $
, -
, -
, -
4
3
y
3
4 48
77.0 kips
3 0.577.0 (150")
3(4400 )(40,700 )
0.48"
2.2 =34.5"
0.005(144") 0.72"
0.010(144") 1.44"
0.30(77.0 ) 23.1 kips
nlateral
w
lateral load
c g
k
ksi in
g g x
a
b
k
residual
MP
h
P h
E I
I I y
P
A
A
A
$ $
% &' ($' () *
$
$
$$ $
$ $
$ $
Flange Compression Flange Tension
Backbone Curve RW2
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Backbone Curve RW2
, -, -3
/
3
n w w
y
c cr
h h
E IA $
P = 0.07Agf'c
vu,max= 2.2
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Backbone Curve TW2
, -, -3
/
3
n w w
y
c cr
h h
E IA $
P = 0.075Agf'c
-4.0 -2.0 0.0 2.0 4.0
Top Displacement (in.)
-120
-80
-40
0
40
80
La
teralLoad
(
ips)
-2.8 -1.4 0.0 1.4 2.8
Lateral Drift (%)
Plat@Mn(7c=0.003)=77.0k
Plat@Mn(7c=0.003)=40.2k
-400
-200
0
200
LateralLoad
(
N)
FEMA 356 Conforming
vu,max= 5.4
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Paulay, EERI, 2(4), 1986 [Goodsir, PhD 1985 NZ]
h = 3.3 m= 10.83 ft
(3.94)
' '
g
3 3
y 3 '
& 0.163 A & Assume conforming
(70 )(130") 700.4" (10.0 ) 4.6
3 0.5 3(~
WALL Goodsir
3750 )(0.5)(4")(59") /12 (4")(59") 3750
0.01(33
, 1985:
00 ) 33
s s c
u
c g w w c
a
A A P f
VPL k kmm
E I ksi psit l f
mm m
A
A
$ $
$ $ $ $ $
5 $ 0.015(3300 ) 50bm mm mmA 5 $
(59)
ConformingP=10%, V=3
Conforming
P=10%, V=6
Cantilever Wall TestsP l EERI 2(4) 1986 [G d i PhD 1985 NZ]
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Paulay, EERI, 2(4), 1986 [Goodsir, PhD 1985 NZ]
h = 3.3 m= 10.83 ft
' '
g
3 3
y 3 '
& 0.12 A & Assume conforming
(70 )(130") 700.4" (10.0 ) 4.6
3 0.5 3(~ 3
WALL Goodsir,
750 )(0.5)(4")(59") /12 (4")(59") 3750
0.01(330
1
0
8
)
5
3
:
3
9
s s c
u
c g w w c
a
A A P f
VPL k kmm
E I ksi psit l f
mm mm
A
A
$ $
$ $ $ $ $
5 $ 0.015(3300 ) 50b mm mmA 5 $
ConformingP=10%, V=3
Conforming
P=10%, V=6
Summary
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Summary
FEMA 356 Backbone Curves! In general, quite conservative
! This appears to be especially true for cases wheremoderate detailing is provided around boundary bars
! Possible reformat" Compute neutral axis depth
" If s 3/4 of ACI 318-05,then high ductility
" Do not reduce deformation capacity for shear stress below 5roots fc
Shear Design
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Shear Design
Wall shear studies!Aktan & Bertero, ASCE, JSE, Aug. 1985
! Paulay, EERI 1996; Wallace, ASCE, JSE, 1994.
!
Eberhard & Sozen, ASCE JSE, Feb. 1993Design Recommendations
! Based on Mpr at hinge region
!
Uniform lateral force distribution
, -, -, -lim
0.9 /10
0.3
pr
wall v u v
u
wall it m e
MV V n
M
V V D W weight A EPA
B B/ 0
$ $ 61 23 4
$ 6 $ $ $
Paulay, 1986
Eberhard, 1993
Sl d W ll B h i & M d li
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Slender Wall Behavior & Modeling
John WallaceUniversity of California, Los Angeles
With contributions fromDr. Kutay OrakcalUniversity of California, Los Angeles