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.
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