on the ultimate strength of rc shear wall under multi-axes
TRANSCRIPT
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On The Ultimate Strength of RC Shear Wall under Multi-Axes Seismic Loading Condition
KITADA YoshioJNES (Japan Nuclear Energy Safety Organization), Tokyo, Japan
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BACKGROUND AND PURPOSES OF THE STUDY�There are opinions that recent quake damage and observation
data indicate that 3D effect of quake motion cannot be ignored�The findings on vertical quake motion characteristics are getting
piled up, the time is coming to define design ground motion both in horizontal and vertical direction
�Conventional RC data are mainly obtained by one directional loading tests. The data are difficult to apply the study for multi-directional loading case
The test is planning to confirm whether or not the current seismic design methodology is reliable for the input motions of 3-D.
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OUTLINE AND THE SCHEDULE OF THE PROJECTSt
atic
test Restoring force
characteristics of RC seismic shear wall under diagonal load
Verification of restoring force and FEM analytical model under multi-axis dynamic loads
FY(Japan)
Tests Item to be studied Outline of Test
94 95 96 97 98 99 00 01Planning and Check & Review of The Test ResultsComprehensive Evaluation of The Test Results
Dyna
mic
Elementtest
Diagonalloadingtest
Multi-directionalSimultane-ous loading test
ShakingTable test
Execution items 02 03
(simultaneous horizontal and vertical loading)
(12 test specimens)
Plate
Box
Cylinder
(9 test specimens)
(8 test specimens)
(3 test specimens)
test
Restoring force characteristics of RC seismic shear wall under multi-axis loads
Box
Shear transfer mechanism of cracked RC plate under multi-axis loads
Box Cylinder
(simultaneous horizontaltwo-axis loading)
Stat
ic te
st Restoring force characteristics of RC seismic shear wall under diagonal load
Verification of restoring force and FEM analytical model under multi-axis dynamic loads
FY(Japan)
Tests Item to be studied Outline of Test
94 95 96 97 98 99 00 01Planning and Check & Review of The Test ResultsComprehensive Evaluation of The Test Results
Dyna
mic
Elementtest
Diagonalloadingtest
Multi-directionalSimultane-ous loading test
ShakingTable test
Execution items 02 03
(simultaneous horizontal and vertical loading)
(12 test specimens)
Plate
Box
Cylinder
(9 test specimens)
(8 test specimens)
(3 test specimens)
test
Restoring force characteristics of RC seismic shear wall under multi-axis loads
Box
Shear transfer mechanism of cracked RC plate under multi-axis loads
Box Cylinder
(simultaneous horizontaltwo-axis loading)
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1. Element Test RC Plates Setting up of the TestProposed the constitutive equation for shear transfer on crack surface of RC plate.
: Shear strain parallel to crack surface
G0
Gcr
γcr
εcr
Gcr =85 G0
γcr + 0.06 εcr2 2
: Shear stiffness of non-cracking reinforced concrete
: Shear stiffness along crack surface
: Strain normal to crack surface
Where, Gcr < 1.0 G0=
: Shear strain parallel to crack surface
G0
Gcr
γcr
εcr
Gcr =85 G0
γcr + 0.06 εcr2 2
Gcr =85 G0
γcr + 0.06 εcr2 2γcr + 0.06 εcr2 2
: Shear stiffness of non-cracking reinforced concrete
: Shear stiffness along crack surface
: Strain normal to crack surface
Where, Gcr < 1.0 G0=Where, Gcr < 1.0 G0= (Gi / G0)
εi
Reduction factor of shear stiffness
Proposed constitutive equation
γi
Gi / G0= 85γi + 0.06 εi
2 2
(Gi / G0)
εi
Reduction factor of shear stiffness
Proposed constitutive equation
γi
Gi / G0= 85γi + 0.06 εi
2 2Gi / G0= 85
γi + 0.06 εi2 2γi + 0.06 εi2 2
A Specimen after
the Testing
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2. Diagonal Loading Test(Box-type RC Shear Walls�A larger deformation capacity is confirmed.
Test Setup Example
Test Result Example
(? =63.4 deg. )
(? =45 deg. )
(? =90 deg. )
(? =26.6 deg. )
(? =0 deg. )?
? = 4.0 x 10 -3
4.0 x 10-3
4 0 x 10-3
? y�f
? x�f
? y�f
? x�f
y�f
x�f?
0.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
Concept of evaluation model
Loading direction
(? =63.4 deg. )
(? =45 deg. )
(? =90 deg. )
(? =26.6 deg. )
(? =0 deg. )?
? = 4.0 x 10 -3? = 4.0 x 10 -3
4.0 x 10-3
4.0 x 10-3
4 0 x 10-3
4 0 x 10-3
? y�f
? x�f
? y�f
? x�f
y�f
x�f?? y�f
? x�f
y�f
x�f?
0.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
Loading direction
(? =63.4 deg. )
(? =45 deg. )
(? =90 deg. )
(? =26.6 deg. )
(? =0 deg. )?
? = 4.0 x 10 -3? = 4.0 x 10 -3
4.0 x 10-3
4.0 x 10-3
4 0 x 10-3
4 0 x 10-3
? y�f
? x�f
? y�f
? x�f
y�f
x�f?? y�f
? x�f
y�f
x�f?
0.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
Concept of evaluation model
Loading direction
(? =63.4 deg. )
(? =45 deg. )
(? =90 deg. )
(? =26.6 deg. )
(? =0 deg. )?
? = 4.0 x 10 -3? = 4.0 x 10 -3
4.0 x 10-3
4.0 x 10-3
4 0 x 10-3
4 0 x 10-3
? y�f
? x�f
? y�f
? x�f
y�f
x�f?? y�f
? x�f
y�f
x�f?
0.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
M/(Qd)=0.6(Plus) (Minus)
M/(Qd)=0.8
M/(Qd)=1.0
Loading direction
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3. Horizontal & Vertical Loading Test
0.0
0.2
0.4
0.6
0.8
1.0
0.0 2.0 4.0 6.0
Experienced strain (x10 )-3
Stiff
ness
redu
ctio
n ra
te
Axial stiffness reduction rate
Horizontal stiffness reduction rate0.0
0.2
0.4
0.6
0.8
1.0
0.0 2.0 4.0 6.0
Experienced strain (x10 )-3Experienced strain (x10 )-3
Stiff
ness
redu
ctio
n ra
te
Axial stiffness reduction rate
Horizontal stiffness reduction rate
Horizontal loading
Horizontal and vertical loading
δi
Q(kN)
(H+V) Horizontal loading
Horizontal and vertical loading
δi
Q(kN)
(H+V) Horizontal loading
Horizontal and vertical loading
δi
Q(kN)
(H+V)
Within the axial load fluctuation is ±1.0g,Reduction of RC shear wall stiffness is
mainly caused by horizontal plastic deformation rather than vertical stress fluctuation.
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4. Simultaneous Horizontal Two Directional Loading Test
(Box and Cylindrical RC Shear Walls)
Shear Force-Deformation Angle:The relationshipis similar to
�that for conventional 1D loading in the range of the deformation angle smaller than 2.0X10-3.
Analytical Model:The four way multi-directional
crack models is confirmed to be a powerful tool for the analysis under multi-axes loading conditions.
Y0 1 2-1-2
0
0.8
1.6
-0.8
-1.6
Y
X
�
�
�
�
�
�
�
�
�
�
(mm)
(mm)0 1 2-1-2
0
0.8
1.6
-0.8
-1.6
(mm)
�
�
Y
X
�
�
�
��
�
��
��
� �
� �
(mm)
0 1 2-1-2
0
0.8
1.6
-0.8
-1.6
�X
�
� �
� �
� �� �
� �
(mm)
(mm)
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5. Dynamic Loading Test(Box and Cylindrical RC Shear Walls)
� Damage at Final Stage�� All three specimen are
collapsed with shear slip failure
�Maximum Capacity�� All three specimen reached
the deformation angle of 6/1000 before collapse.
�Hysteretic Loop�� Nearly the same hysteretic
loop are obtained analytically.
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INPUT MOTION OF THE SHAKING TABLE TESTNS EW UD
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Maximum Horizontal Acceleration : 1400 Gal.
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Orbital Expression of Acc. and Displ. in the Hor. Two Directions
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Relationship b/w Response Acc. & Displ. in the Hor. Two Directions
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Major Results(1) Shear deformation angle:
smaller than 2×10-3:The effect of multi-axes loading is negligibly small. Then the methodology applying lumped mass model recommended in JEAG-4601, for one directional loading , can be applied continuously.
exceeding 2×10-3;The seismic capacity of the specimen decreased explicitly due to an effect
of simultaneous multi-axes loading. Then in the analysis, the effect of multi-axes loading should be considered.
(2) Non-linear response of an RC structure and its hysteretic curve for the restoring force to the multi-axes loading can be evaluated satisfactory if we apply FEM analysis with the four-way crack model.
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Concluding RemarksThrough the test project we have had a series of test data with many findings relating to the behaviors of RC shear walls up to collapse under the multi-axes loading conditions. Based on these data and findings, we have confirmed the validity of the analytical methodology using FEM to evaluate thebehavior of the RC structures up to collapse under the multi-axes loading condition. If the soil structure interaction phenomena for NPP structures could keep in linear response up to the collapse of the building, we could have established the analytical methodology to evaluate earthquake response behaviors of NPP RC structures by applying the 3-D earthquake ground motions simultaneously.