Level (m-1)

Level m

h

(1-c)h

ch

12

3

45

6Rigid Beam

Rigid Beamx1 x

k1 k2 knkH. . . . . . .

RC AND SRC SHEAR WALLMACRO-MODELING

Multiple Vertical Line Element Model [MVLEM]

RC Wall Model

Modeling Criteria

(1-c)h

h

ch

12

3

45

6

x1 x

k1 k2 knkH. . . . . . .

k1 k6k2 k3 k4 k5

k1 & k6 Stiffness of boundary columnsk2 - k5 Stiffness of tributary web areas kH Shear stiffness (Horizontal spring simulates shear deformations)

Relative Rotation around a point on central

axis at height “ch”

Flexural and Shear Deformations of the

MVLEM are uncoupled

c depends on expected curvature distribution

Modes of Deformation

(1-c)h

ch

h

Experimental Calibration

-40

-30

-20

-10

0

10

20

30

40

-4 -2 0 2 4Top Displacement (in.)

La

tera

l Lo

ad

(ki

ps)

RW2P=0.07Agf`c

RC Wall TestsThompsen and Wallace (1995)

• Cyclic Tests performed on RC and Steel RC hybrid shear walls with rectangular and T-Shaped cross sections.

Stiffness of vertical bars

h)(A)(E

h)(A)(Ek ististicic

i00

E0 : initial tangent modulus

Stiffness of horizontal spring

hAG

kH'0

G0 : initial shear modulus

A’ : effective shear area

(1-c)h

ch

k1 k2 knkH. . . . . . .h

k1 k6k2 k3 k4 k5

Linear Analysis: Pre-Cracking

-12

-8

-4

0

4

8

12

-0.12 -0.08 -0.04 0 0.04 0.08 0.12

La

tera

l Lo

ad

(ki

ps)

Top Displacement (in.)

RW2P=0.07Agf`c

(Klat)experimental

P+

Pre-cracking range : (Klat)experimental 100 kip/in. (Klat)analytical 140 kip/in. } 40% deviation

Pre-cracking Lateral Stiffness

P

7 LVDT’s

Embedded ConcreteStrain Gages

d1 d2

Concrete Strain Gages :

csg

Mcsg = (P)(d1)

(csg)1

(csg)2

LVDT’s :

Data Assessment/Reliability

LVDT

MLVDT = (P)(d2) (LVDT)7

(LVDT)1 (LVDT)2

Analysis Results: (EI)uncr = 160*106 kip-in2

(Klat)uncr= 140 kip/in

-2000

-1500

-1000

-500

0

500

1000

1500

2000

-0.00002 -0.00001 0 0.00001 0.00002 0.00003

Mo

men

t (k

ip-i

n)

Curvature

Concrete Strain GagesLVDT’s

EIuncr

EIuncr

Concrete Strain Gages :(EI)uncr 100*106 kip-in2

(Klat)uncr 95 kip/in

LVDT’s :(EI)uncr 65*106 kip-in2

(Klat)uncr 65 kip/in

Lat. Load - Top Defl. :(Klat)uncr 100 kip/in

Experimental Results:

Data Assessment/Reliability

Iterative displacement-controlled nonlinear analysis scheme is applied.

Hysteretic constitutive material relations are globalized into non-linear hysteretic structural response level; to satisfy both equilibrium conditions and force-deformation relationships throughout iterative nonlinear analysis approach.

Nonlinear Analysis

Hysteretic Constitutive Relations

Concrete

SteelF

d

Shear Spring

• Shear Model to be improved• Coupling shear deformations with flexural deformations

Nonlinear Analysis Results

•Pushover Analysis•Pseudo – Static Analysis•Nonlinear Dynamic Analysis

P+

-4 -3 -2 -1 0 1 2 3 4-40

-30

-20

-10

0

10

20

30

40

Top Displacement (in)

Lat

eral

Lo

ad

(kip

s)

Quasi-StaticPushover

Correlation with Experiments

- 4 - 2 0 2 4T o p D i s p l a c e m e n t ( i n . )

- 4 0

- 2 0

0

2 0

4 0

Lat

eral

Loa

d (

kip

s)

T estA n a ly sis

-2 .8 -1 .4 0 .0 1 .4 2 .8

L a tera l D rif t (% )

Conclusions• MVLEM is an effective means to model shear wall

response; wall flexural capacity and cyclic response were captured by the model with reasonable accuracy

• Comparison with theoretical solution indicates micro-cracking has a significant impact of lateral stiffness

• Consistent lateral-load stiffness was obtained using local and global experimental data for pre-cracked behavior

• The model provides a flexible basis to implement various constitutive relations and calibration with test results

• Nonlinear shear response is to be improved by coupling flexural deformations and shear deformations

• The model is to be implemented into a nonlinear building analysis platform.