On The Ultimate Strength of RC Shear Wall under Multi-Axes Seismic Loading Condition KITADA Yoshio JNES (Japan Nuclear Energy Safety Organization), Tokyo, Japan 0
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 multidirectional 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. 1
OUTLINE AND THE SCHEDULE OF THE PROJECT Execution items FY(Japan) 94 95 96 97 98 99 00 01 02 03 Planning and Check & Review of The Test Results Comprehensive Evaluation of The Test Results Tests Item to be studied Outline of Test Shear transfer Element mechanism of cracked test RC plate under multiaxis loads Plate (12 test specimens) Static test test Dynamic Diagonal loading test Multidirectional Simultaneous loading test Shaking Table test Restoring force characteristics of RC seismic shear wall under diagonal load Restoring force characteristics of RC seismic shear wall under multi-axis loads Verification of restoring force and FEM analytical model under multi-axis dynamic loads Box (9 test specimens) Box Cylinder (8 test specimens) Box Cylinder (3 test specimens) (simultaneous horizont al and vertical loadi ng) (simultaneous horizont al two-axis loading) 2
1. Element Test RC Plates Proposed the constitutive equation for shear transfer on crack surface of RC plate. Setting up of the Test Gcr = γcr 85 G0 2 2 + 0.06 εcr G0 Gcr γcr εcr : Shear stiffness of non-cracking reinforced concrete : Shear stiffness along crack surface : Shear strain parallel to crack surface : Strain normal to crack surface Where, Gcr< 1.0 G0 Reduction factor of shear stiffness = (Gi / G0) = Gi / G0= 85 2 2 γi + 0.06 εi A Specimen after the Testing γi εi Proposed constitutive equation 3
2. Diagonal Loading Test (Box-type RC Shear Walls A larger deformation capacity is confirmed. (? =90 deg. )? yf (? =63.4 deg. ) (? =45 deg. )? yf yf? Loading direction xf Test Result Example 4.0 x 10-3? xf? = 4.0 x 10-3 0.0? (? =0 deg. ) 40x10-3? xf (Plus) (Minus) (? =26.6 deg. ) M/(Qd)=0.6 M/(Qd)=0.8 M/(Qd)=1.0 Concept of evaluation model Test Setup Example 4
3. Horizontal & Vertical Loading Test 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. Q(kN) (H+V) i Horizontal loading Horizontal and vertical loading δ Stiffness reduction rate 1.0 0.8 0.6 0.4 0.2 Axial stiffness reduction rate Horizontal stiffness reduction rate 0.0 0.0 2.0 4.0 6.0-3 Experienced strain (x10 ) 5
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. 1.6 0.8 (mm) 0-0.8 X 1.6 0.8 (mm) 0-0.8 Y 1.6 0.8 X (mm) 0-0.8 Y X -1.6-2 -1 0 1 2-1.6 (mm) -2-1 0 1 2 Y -1.6 (mm) -2-1 0 1 2 (mm) 6
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. 7
INPUT MOTION OF THE SHAKING TABLE TEST NS EW UD 8
Maximum Horizontal Acceleration : 1400 Gal. 9
Orbital Expression of Acc. and Displ. in the Hor. Two Directions 10
Relationship b/w Response Acc. & Displ. in the Hor. Two Directions 11
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. 12
Concluding Remarks Through 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 the behavior of the RC structures up to collapse under the multiaxes 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. 13