Wallace-Slender Walls FINAL V5 Present Handout

8/13/2019 Wallace-Slender Walls FINAL V5 Present Handout

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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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2

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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3

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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12

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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14

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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RW2 & TW1: ~ !scale tests

Thomsen & Wallace, ASCE JSE, April 2004.

Uncoupled designDisplacement-based design


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P = 0.09Agf'c

vu,max= 4.85


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RW2 & TW2: ~ !scale tests

Thomsen & Wallace, ASCE JSE, April 2004.

Displacement-based design of T-shape


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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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-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


Test

Analysis

1.5%

2.0%

2.5%

0.75%

1.0 %

RW2

Applied LateralDrift Levels:

Top


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-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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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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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


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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-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


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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-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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'

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 $

$ $

!

!



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50


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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54

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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55

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

Documents

Wallace-Slender Walls FINAL V5 Present Handout