Wall Modeling & Behavior

John WallaceUniversity of California, Los Angeles

with contributions fromMr. Leonardo Massone & Dr. Kutay OrakcalUniversity of California, Los Angeles

2

Presentation Overview

Flexure

Shear

P-M-V Interaction & Modeling

Preliminary Test Results

3

Modified Beam - Column ModelRectangular walls (hw/lw ≤ 2.5)& Flanged walls (hw/lw ≤ 3.5):

Use of modified beam-column elementwith added shear spring

Nonlinear flexure/shearare uncoupled using thisapproach

Beams

Wall

Shear spring

Column at wall centroid

Hinges

4

Modified Beam - Column ModelShear force – deformation properties

A

B

C

D

E

∆/h

V Vn

1.0

0.2

CPLSIO

Deformation-controlled componenta b - a

c

( )

0.4

1 and 0.21 2

yy

c c

c c

Vh

G E A

G E νν

⎛ ⎞∆ = ⎜ ⎟⎜ ⎟=⎝ ⎠

⎛ ⎞= ≈⎜ ⎟+⎝ ⎠

∆y/h

5

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 hinge length (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 hinge model, is needed to impose a “reality” check on the element size and integration points used.

Actual cross section

Concrete Fibers

Steel Fibers

6

Response Correlation StudiesTen Story Building in San Jose, CaliforniaInstrumented: Base, 6th Floor, and RoofModerate 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)

7

Response Correlation StudiesTen Story Building in San Jose, CaliforniaInstrumented: Base, 6th Floor, and RoofModerate Intensity Ground Motions – Loma Prieta

0 10 20 30Time (sec)

-1.5

0

1.5

Dis

plac

emen

t (in

.)

Analysis - 0.5Ig

Measured

8

Strength RequirementsACI 318 Provisions

Pn- MnFor extreme fiber compression strain of εc =0.003.

VnACI 318-99,02,05 Equation 21-7

'

3.0 for / 1.52.0 for / 2.0

n cv c c t y

c w w

c w w

V A f f

h lh l

α ρ

αα

⎡ ⎤= +⎣ ⎦= ≤

= ≥

Linear interpolationallowed for intermediatevalues

9

Definition of Wall Cross Section

Flexural strengthConsider all vertical reinforcement within web and within the effective flange width

Consider the influence of openings on the 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 A A

+

+

10

MVLE (Fiber) Model

h

(1-c)h

ch

12

3

45

6 Rigid Beam

Rigid Beam

k 1 k 2 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.

11

Strain, ε

O

TensionNot to scale

Compression

( εc ' , f c

' )

(ε0, 0)

(ε0+ εt , ft)

Material (Uni-axial) Models

Strain, ε

εy

E0

E1= bE0σy

OR

Concrete:• Chang and Mander (1994)

Generalized (can be updated)Allows refined calibrationGap and tension stiffening

Reinforcing Steel :• Menegotto and Pinto (1973)• Filippou et al. (1984)

Simple but effectiveDegradation of cyclic curvature

r

Stre

ss, σ

12

Model AssessmentApproximately 1/4 scaleAspect ratio = 3Displacement – based evaluation for detailing provided at the wall boundaries12 ft tall, 4 ft long, 4 inches thick#3 vertical steel, 3/16” hoops/ties#2 deformed web steelConstant axial loadCyclic lateral displacements applied at the top of the walls

13

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 measure wall response at various locations

Massone & Wallace; ACI SJ, Jan-Feb 2004.

14

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

k 1 k2 knkH . . . . . . .

15

Concrete Model - Unconfined

0 0.001 0.002 0.003 0.004

Strain

0

10

20

30

40

50

Stre

ss (M

Pa)

Test Results1st Story2nd Story3rd Story4th Story

Analytical (Unconfined)

16

Concrete Model - Confined

0 0.005 0.01 0.015 0.02 0.025

Strain

0

10

20

30

40

50

60

70

Stre

ss (M

Pa)

Unconfined ModelMander et al. (1988)Saatcioglu and Razvi (1992)

RW2

TW2 Flange

TW2 Web

17

Concrete Model - Tension

0 0.0005 0.001 0.0015 0.002 0.0025

Strain

0

0.5

1

1.5

2

2.5

Stre

ss (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(εt ,ft )

r

18

Reinforcement Material Model

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

Strain

-600-500-400-300-200-100

0100200300400500600

Stre

ss (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

0100200300400500600700

#3 rebar#2 rebar4.76 mm wire

Tension

Compression Test Results

19

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

Late

ral L

oad,

Pla

t (k

N)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Lateral Flexural Drift (%)

TestAnalysis

≈Pax 0.07Ag f c'

Plat , ∆top

0100200300400500

P ax

(kN

)

RW2

20

Model Assessment – RW2

-80 -60 -40 -20 0 20 40 60 80

Lateral Flexural Displacement (mm)

0

1

2

3

4

5

Stor

y N

umbe

r

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Lateral Flexural Drift (%)

TestAnalysis

1.5%2.0%2.5%

0.75%1.0 %

RW2

Applied LateralDrift Levels:

Top

21

Model Assessment – RW2

-0.01

0

0.01

0.02

Rot

atio

n

( r

ad)

0 100 200 300 400 500 600 700-15-10

-505

1015

Dis

plac

emen

t

(

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

22

Model Assessment - Stability

Rebar Buckling at Wall Boundary Rebar Fracture Following Buckling 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

23

Backbone Curve – RW2

( )( )3/3

n w wy

c cr

M h hE I

δ =

P = 0.07Agf'cvu,max = 2.32√f'c psi

-4.0 -2.0 0.0 2.0 4.0Top Displacement (in.)

-40

-20

0

20

40

Late

ral L

oad

(kip

s)

-2.8 -1.4 0.0 1.4 2.8Lateral Drift (%)

Plat@Mn(εc=0.003)=29.4k-100

0

100

Late

ral L

oad

(kN

)

- - - Analytical prediction , First yield

FEMA 356

24

Cantilever Wall TestsPaulay, 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 ) 4.63 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 kmmE I ksi psit l f

mm m

δ

δ

= =

= = = = =

≈ = 0.015(3300 ) 50bm mm mmδ ≈ =

(59”)

ConformingP=10%, V=3

ConformingP=10%, V=6

25

Cantilever Wall TestsPaulay, 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 ) 4.63 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 kmmE I ksi psit l f

mm mm

δ

δ

= =

= = = = =

≈ = 0.015(3300 ) 50b mm mmδ ≈ =

ConformingP=10%, V=3

ConformingP=10%, V=6

26

SummaryFEMA 356 Backbone Curves

In general, quite conservativeThis appears to be especially true for cases where moderate detailing is provided around boundary barsPossible reformat

Compute neutral axis depthIf s <12db over c/2, then modest ductility If s < 8db and transverse steel ratio is ~1/2 of ACI 318-05, then moderate ductility If s < 8db and transverse steel ratio is > 3/4 of ACI 318-05, then high ductility Do not reduce deformation capacity for shear stress below 5 roots f’c

27

Presentation Overview

Flexure

Shear

P-M-V Interaction & Modeling

Preliminary Test Results

28

Shear DesignWall shear studies

Aktan & Bertero, ASCE, JSE, Aug. 1985Paulay, EERI 1996; Wallace, ASCE, JSE, 1994.Eberhard & Sozen, ASCE JSE, Feb. 1993

Design RecommendationsBased on Mpr at hinge regionUniform lateral force distribution

( )( )( )lim

0.9 /10

0.3

prwall v u v

u

wall it m e

MV V n

M

V V D W weight A EPA

ω ω⎛ ⎞

= = +⎜ ⎟⎝ ⎠

= + = = =

Paulay, 1986

Eberhard, 1993

29

Modified Beam - Column ModelUse of modified beam-column element with added shear spring for both horizontal and vertical wall segments

Fiber model or general wall model with nonlinear shear backbone curve (uncoupled flexure/shear)

If plastic hinge model –EIeffective might be less than 0.5EIg lightly-reinforced wall segments

Spandrels

Pier

Joint

30

P-M (flexural) Strength ProvisionsPn- Mn for εc =0.003Fiber model or general wall model

Typically use a more refined mesh where yielding is anticipated However, in this case, where nonlinear shear behavior is anticipated, use enough elements to capture moment gradient. Nonlinear “backbone” relations (force – displacement) relations are commonly used to capture the shear behavior.

Actual cross section

Concrete Fibers

Steel Fibers

31

FEMA Modeling ParametersFEMA 356 Tables 6-19: Wall segments

Modeling Parameters, Drift % Acceptable Drift %

Performance Level

d e c Immediate Occupancy

Life Safety

Collapse Prevention

0.75 2.0 0.40 0.40 0.60 0.75

∆/h

CPLSIO

d e - d

c

∆y/h

nV

rV

32

Shear Strength ProvisionsVn per ACI 318-99,02,05 Equation 21-7

'

3.0 for / 1.52.0 for / 2.0

n cv c c t y

c w w

c w w

V A f f

h lh l

α ρ

αα

⎡ ⎤= +⎣ ⎦= ≤

= ≥

Linear interpolationallowed for intermediatevalues

If axial load exceeds 0.15Agf’c ; then force controlled

ρ need not be taken less than 0.15% (Wood, ACI SJ, 1990)

33

Shear Strength Database# of Curtains

Researcher Protocol 2 1Sugano (1973) Monotonic 7 1Barda Cyclic 6 0Cardenas Monotonic 0 2Hidalgo (2002) Cyclic 0 7Hirosawa (1975) Cyclic 1 0Aoya Cyclic* 5 0* One full cycle, then monotonic to failure

'

' ' 'g g g

= 3.15 to 6.3 inches 0.25% 0.67%

3.3 ksi, = 1 ksi 64 ksi, = 14 ksi

(7) < 0.12A , (1)=0.15A , (1)=0.22A

w

c y

c c c

t

f f

f f f

ρ

σ σ

≤ ≤

= =

34

Shear Strength – Expanded Databaseρ need not be taken less than 0.15% (Wood, 1990)Shear strength is relatively insensitive to the web reinforcementFor relatively thin walls, use of one or two curtains of web reinforcement, strength is similarResults similar for monotonic and cyclic tests

0 1 2 3 4(ρ fy)min

0

1

2

3

V tes

t / V

n (A

CI)

One CurtainTwo Curtains

35

Shear Strength – Restricted Databaseρ need not be taken less than 0.15% (Wood, 1990)Shear strength is relatively insensitive to the web reinforcementFor relatively thin walls, use of one or two curtains of web reinforcement, strength is similarResults similar for monotonic and cyclic tests

0 1 2 3 4(ρ fy)min

0

1

2

3

V tes

t / V

n (A

CI)

One CurtainTwo Curtains

Tests with at least minimum reinforcement

36

FEMA Modeling ParametersFEMA 356 Tables 6-19: Wall segments

Modeling Parameters, Drift % Acceptable Drift %

Performance Level

d e c Immediate Occupancy

Life Safety

Collapse Prevention

0.75 2.0 0.40 0.40 0.60 0.75

∆/h

CPLSIO

d e - d

c

∆y/h

nV

rV

37

Shear Force-Deformation BehaviorShear backbone curve

( )

( )

c

'

0.4

= (i.e., no hardening)

1 = 0.4E1 2

/1 0.6

4 to 6

yy

c c

y n

c c

gcr t n

t

t c

Vh

G E A

V V

G E

P AV f V

f

f f

ν

⎛ ⎞∆ = ⎜ ⎟⎜ ⎟=⎝ ⎠

⎛ ⎞= ⎜ ⎟+⎝ ⎠⎡ ⎤

= + ≈⎢ ⎥⎣ ⎦

= Sozen & Moehle, 1993 EPRI Report

Strength of materials

=EGτ γ σ ε=

38

Revised Backbone RelationBased on prior tests (limited database):

5WCEE, Rome, 1973, pp. 1157-11669WCEE, Tokyo, 1988, pp. IV 517-522Hidalgo et al, 2002, EERI SpectraHirosawa, 1975, Japanese Report

d e - d

c

0.6n

cr n

r

VV V

V≈

∆/h = 0.004 to 0.005

0.4Ec

39

ObservationsLimited test data

Stiffness and Deformation capacity –specimens tend to be stiff and strong, test control is challenging and reported stiffness and deformation values may be suspectResidual strength – most tests not continued beyond modest strength degradation (~20%)One row in FEMA table 6-19

Nominal StrengthTest results indicated nominal strength in the range of 100 to 200% of the ACI value

40

New Data Since ~1995Salonikios, Thomas N.; et al. (1999)

11 tests on cantilever walls with axial load of 0.0 and 0.07Agf’cAspect ratios of 1.0 (1.2m tall) and 1.5 (1.8m tall)Cross section: 1.2m x 100mm (4 ft x 4”)4 tests with diagonal web bars for sliding – Eurocode 8 requires 50% Reasonably-well detailed (Eurocode 8)

Hidalgo, Pedro A.; Ledezma, Christian A.; Jordan, Rodrigo M., (2002)26 tests for reverse bending (zero moment at mid-height), no axial loadM/Vl ratios: 1.0(3), 0.69(9), 0.5(7), 0.35(7): 1m x 2m tall; 1.5m x 1.05m tallCross section: 80 to 120 mm (3.15” to 4.72”) by 1.0m to 1.7m (40” to 67”) Light web reinforcement: 0%, 0.125%, 0.25%, 0.375% (only one)

Greifenhagen, H.; Lestuzzi, P, (2005) 4 tests on cantilever walls with axial load (0.027, 0.027, 0.043, 0.094Agf’c)M/Vl ratio: 0.69Cross section: 1 m x 100 mm (40” x 4”)Light web reinforcement: 0.3%, 0% (one case with no horizontal web bars)

Massone, Orakcal, Wallace (2005, 2006)

41

Hidalgo et al. 2002M/Vlw = 1.0 Specimen #2

d

e

0.004 .004(78.74") 0.31" (8 mm)

0.0075(2000 ) 15 mm0.02(2000 ) 40 mm

y wh

mmmm

δ

δδ

= = =

= == =

'

y 2

5.74 =57 kips (253 kN) 0.5 30 kips (133 kN)

(56.86 kips)(78.74") 0.02" (0.5 mm)0.4(3040 ksi)(186 in )

n c w w

crack n

n w

V f t lV V

V hGA

δ

=

= =

= = =

40mm

Displacement (mm)

Load

(kN

)

42

Hidalgo et al. 2002M/Vlw = 1.0 Specimen #1

d

e

0.004 .004(78.74") 0.31" (8 mm)

0.0075(2000 ) 15 mm0.02(2000 ) 40 mm

y wh

mmmm

δ

δδ

= = =

= == =

' '

y 2

4.4 =43 kips (193 kN) = 2.81 ksi0.5 22 kips (98 kN)

(43 kips)(78.74") 0.015" (0.4 mm)0.4(3020 ksi)(186 in )

n c w w c

crack n

n w

V f t l fV V

V hGA

δ

=

= =

= = =

30 40

Displacement (mm)

Load

(kN

)

43

Hidalgo et al. 2002M/Vlw = 0.69 Specimen #8

d

e

0.004 .004(70.9") 0.284" (7.2 mm)

0.0075(1800 mm) 13.5 mm0.02(1800 mm) 36 mm

y whδ

δδ

= = =

= =

= =

'

y 2

6.6 =76 kips (337 kN) 0.5 38 kips (169 kN)

(76 kips)(70.9") 0.0205" (0.52 mm)0.4(2720 ksi)(242 in )

n c w w

crack n

n w

V f t lV V

V hGA

δ

=

= =

= = =

Displacement (mm)30 35

Load

(kN

)

44

Presentation Overview

Flexure

Shear

P-M-V Interaction & Modeling

Preliminary Test Results

45

Slender Wall Tests - ResultsExternal Instrumentation

Lateral displacement at different floor levels

Internal InstrumentationShear deformation at different floor levelsFlexural deformation at different floor levels

Uncouple deformationsShear/FlexureAssess data reliability

Wall base instrumentation

Internal External

46

Tests Results: Observations

-0.8 -0.4 0 0.4 0.8

Displ. 1st floor (lateral) [in]

-0.8

-0.4

0

0.4

0.8

Dis

pl. 1

st f

loor

(she

ar +

flex

ural

) [in

]

Utot XcorrectedUtot XoriginalU flex (α=0.67)

Y = 1.02 * X

Y = 1.20 * X

Flexural displ.Shear Xcorrected

Shear Xoriginal

Y = 0.71 * X

Consistent and repeatable resultsTop displacement

Small shear contribution, about 5%

1st Story Displacement

4-story walls30% shear contribution

47

Uf

αh θ

Uf

h

Us

Test Results - Observations

0 0.1 0.2

Shear displacement [in]

0

20

40

1st Floor2nd Floor

P(@Vn) = 62 [kips]

P(@Mn) = 29.4 [kips]

0 2 4 6 8 10

Flexural displacement [in/in]

0

20

40

1st Floor2nd Floor

P(@Vn) = 62 [kips]

P(@Mn) = 29.4 [kips]

∆flexure/∆y ∆shear

Late

ral L

oad

(kip

s)

P(@Vn) =62 kips P(@Vn) =62 kips

P(@Mn) =30 kips P(@Mn) =30 kips

Interaction between nonlinear flexure and shear deformations is evident even for relatively slender walls where Vmax ~ ½Vn

48

Modeling P-M-V Interaction1. Modified MVLE model to

incorporate shear – flexure interaction

2. Parallel pairs of “flexure” and “shear” fibers are used

3. Behavior of each set of springs described by a constitutive RC rotating-angle panel model (e.g., MCFT or RA-STM), that incorporates axial-shear interaction

4. Requires additional model iterations to establish equilibrium condition

Strip (i)

chh

N, ∆uy

V, ∆ux

M, ∆θ

εx - unknown

γxy - trial

εy - trial

49

AssigningIteration Variable

ConstitutiveMaterial Models

Horizontal (Transverse) Equilibrium

ε2ε1

α

εy- trial

εx - unknown

γxy- trialguess α

σc2σc1

α

ε2ε1

α

εy

εx

σsy

σsx

σy = σcy+ ρy σsy

σx = σcx + ρx σsx

τyx

Local Iteration Scheme

σ - ε

concrete

σ - ε

steel

σx = 0iterations α

εx

50

Constitutive Panel Element Behavior

0.00 0.01 0.02 0.03Shear Strain

0

4

8

12

Shea

r Str

ess

(MPa

)

A2A3A4B1B2

TestAnalysis

0.00 0.01 0.02 0.03Shear Strain

0

1

2

3

4

5

Shea

r Str

ess

(MPa

)

PV6PV11PV16PV19

TestAnalysis

Pang and Hsu (1995) Vecchio and Collins (1982)

• RC Panel Specimens tested under pure shear

51

Model Assessment – RW2

-100 -80 -60 -40 -20 0 20 40 60 80 100Top Displacement, ∆top (mm)

-200

-150

-100

-50

0

50

100

150

200

Late

ral L

oad,

Pla

t (k

N)

TestAnalysis

≈Pax 0.07Ag f c'

Plat , ∆top

RW2

Thomsen & Wallace, ASCE JSE, April 2004; Massone et al, 13WCEE & 8NCEE

Monotonic versusCyclic comparison

52

-6 -4 -2 0 2 4 6Lateral Shear Displacement (mm)

-200

-150

-100

-50

0

50

100

150

200

()

TestAnalysis

-20 -15 -10 -5 0 5 10 15 20Lateral Flexural Displacement (mm)

-200

-150

-100

-50

0

50

100

150

200

Late

ral L

oad

(kN

)

TestAnalysis

Uf

P P Us

• flexural and shear displacements at first story level of RW2• coupled nonlinear flexural and shear deformations

Model Assessment – RW2Flexural Deformations Shear Deformations

53

Model Assessment

0 0.4 0.8 1.2 1.6 2Lateral Displacement (cm)

0

400

800

1200

Lat

eral

Lo

ad (

kN)

Flexural AnalysisTestAnalysis

Hirosawa (1975)Specimen 74: M/Vlw = 1.0

0 0.4 0.8 1.2 1.6Lateral Displacement (cm)

0

50

100

150

200

Lat

eral

Lo

ad (

kN)

TestAnalysis

Hidalgo (2002)Specimen 10: M/Vlw = 0.7

54

Presentation Overview

Flexure

Shear

P-M-V Interaction & Modeling

Preliminary Test Results

55

Research Motivation & Sponsors

St John’s, Santa Monica

Example pushover

Sponsors:St. Joseph Health SystemKPFF Consulting Engineers

In collaboration with:California Office of Statewide Health Planning & Development (OSHPD)

56

Test Specimens - Piers

hp = 62.5”

lp = 72”

tp = 8”

ρv = ~0.25%ρh = ~0.35%

Prototype (Actual Building)

hp = 48”

lp = 54”

tp = 6”

ρv = ~0.25%ρh = 0.35%

¾ Scale Test Specimen

57

Test Specimens – Piers

Specimen Geometry (inches) Reinforcement3 P/Agf 'c4 SpecimensID Height Length Thickness Edge1 Vert. Web2 Horiz. Web2 (kips) (#)(1) (2) (3) (4) (5) (6) (7) (8) (9)

WP1-1-10 48 54 6 2 - #4 0.26% 0.35% 0.10 2WP2-1-05 48 54 6 2 - #4 0.26% 0.35% 0.05 2WP3-1-00 48 54 6 2 - #4 0.26% 0.35% 0.00 2WH1-1-0 60 60 6 1-#4 1-#5 0.35% 0.26% 0.0 2WH2-1-0 60 60 6 4 - #5 0.35% 0.26% 0.0 2

Hooks removed

58

Test Program - Construction

Cast upright, no joints

59

Test Program - Setup

Axial Load = P = P1 + P2 (controlled)Lateral Load = F (controlled for the first two levels)Lateral Displacement = (δtop − δbottom) (controlled after first two levels)Top Rotation θ = (δ1 – δ2)/a =0 (controlled)

Strong Floor

Reaction block

Reaction block

Reaction blockSpecimen

Foundation

Floor anchor rods

Steel reaction frame

FActuator

P1 P2

CL

δtopTop beam

δ1 δ2

a

δbottom

60

Test Program - Setup

Horizontal LoadVertical Load

Vertical Load

Reaction FrameOut-of-plane support

Specimen

61

Test Program – Load History

-60

-40

-20

0

20

40

60

0 1 2 3 4 5 6

cycle

Load

[kip

s]

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.5

3

6 11 16 21 26 31

cycle

Dis

p

Load Control

Displacement Control

62

Test Program - Instrumentation~ 100 Sensors (load, strain, displacement)

West Face Instrumentation (flexural deformations)

East Face Instrumentation(shear and anchorage deformations)

Pedestal sliding and uplift measuredVariation of measurements used on repeated tests

63

Test Program - Objectives

Backbone RelationsFailure modeInfluence of details

– Jamb bars– No hooks– No Hoops/Ties Axial load failure

64

FEMA 356 – Backbone Curves2.8.3(1.2): Smooth “backbone” curve shall be drawn through the intersection of the first cycle curve for the (i)th deformation step with the second cycle curve of the (i-1)the deformation step, for all i steps.

Force

Deformation

Backbone curve

FEMA 356 Figure 2-4

65

FEMA 356 2.8.3(1.2) Approach

0

50

100

0.0 0.5 1.0 1.5

Resulting backbone curve applying 2.8.3(1.2) was suspect

66

Test-Derived Backbone Curves

0

50

100

0.0 0.5 1.0 1.5

Yield Strength degradation

Residual

Crack

Load

Displacement

67

Test Photos ~5% Axial Load

Axial collapse

Yield level 3 x Yield

68

Axial Failure

69

Deformations – Flexure/ShearSame Scale

0

0

0

flex-expshear-expshear-envelope

Late

ral L

oad

Lateral Displacement

Flexural deformations are essentially elastic, nonlinear shear

70

Test Derived Backbone Relations (Pier)

top disp.-expshear-envelope shear-backbone

shear- backbone (+) shear- backbone (-) shear- backbone (avg)

~150%VnFEMA

Late

ral L

oad

Lateral Displacement 1%

2%

FEMA 356 Default

Not as stiff in the post-cracked range as FEMA relationPost-cracked stiffness ~1/10 to 1/20 of the initial stiffnessPeak strength (85 to 175%) of Vn – Consistent with prior testsLess pronounced strength degradation, less residual strengthDeformation capacity > FEMA at initiation of strength degradation

Axial loadcollapse

71

Additional ReferencesGreifenhagen, H.; Lestuzzi, P, “Static cyclic tests on lightly reinforced concrete shear walls”, Engineering Structures, vol. 27, pp. 1703-1712, Sept. 2005Palermo, D.; Vecchio, F.J. , ”Compression field modeling of reinforced concrete subjected to reversed loading: verification,” ACI Structural Journal. Vol. 101, no. 2, pp. 155-164. Mar.-Apr. 2004.Hidalgo, Pedro A.; Ledezma, Christian A.; Jordan, Rodrigo M., “Seismic behavior of squat reinforced concrete shear walls ,” Earthquake Spectra. Vol. 18, no. 2, pp. 287-308. May 2002.Hwang, Shyh-Jiann; et al., “Analytical model for predicting shear strength of squat walls,” Journal of Structural Engineering. Vol. 127, no. 1, pp. 43-50. Jan. 2001.Petrangeli, Marco, “Fiber element for cyclic bending and shear of RC structures, II: Verification,” Journal of Engineering Mechanics. Vol. 125, no. 9, pp. 1002-1009., Sept. 1999.Salonikios, Thomas N.; et al., “Cyclic load behavior of low-slenderness reinforced concrete walls: Design basis and test results,” ACI Structural Journal. Vol. 96, no. 4, pp. 649-660. July-Aug. 1999.Salonikios, Thomas N.; et al., “Cyclic load behavior of low-slenderness reinforced concrete walls: Failure Modes, Strength and Deformation Analysis, and design Implications,” ACI Structural Journal. Vol. 97, no. 1 , pp. 132-142. Jan.-Feb. 2000.Kappos, A. J.; Salonikios, T. N., “Premature sliding shear failure in squat shear walls: fact or myth?” Proceedings of the Second Japan-UK Workshop on Implications of Recent, Earthquakes on Seismic Risk; pp. 169-180. 1998.Saatcioglu, M.; Wiradinata, S., “The effect of aspect ratio on seismic resistance of squat shear walls,” Proceedings of the 8th European Conference on Earthquake Engineering; pp. 7.3/17-23. 1986.Wiradinata, Sanusi, “Behaviour of squat walls subjected to load reversals,” Dept. of Civil Engineering, University of Toronto, 1985. 171 pp.Paulay, T.; Priestley, M. J. N.; Synge, A. J., “Ductility in earthquake resisting squat shearwalls,” Journal of the American Concrete Institute. Vol. 79, no. 4, pp. 257-269. July-Aug. 1982Lefas, et al., “Behavior of RC Structural Walls: Strength, Deformation Characteristics, and Failure Mechanism, ACI Structural Journal, 87(1), pp. 23 – 31, Jan – Feb 1990. Saatcioglu, M., “Hysteretic Shear Response of Low-Rise Walls,” Concrete Shear in Earthquake, Elsevier Applied Science, New York, New York, pp. 105-114.

Bold, underlined: Test results presented