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RC AND SRC SHEAR WALL MACRO-MODELING

5. Rigid Beam. 6. 4. Level m. (1-c)h. k 1. k 2. k n. k H. h. ch. Level (m-1 ). 2. Rigid Beam. 3. 1. x 1. x. RC AND SRC SHEAR WALL MACRO-MODELING. Multiple Vertical Line Element Model [MVLEM]. RC Wall Model. 5. 4. 6. (1-c)h. k H. k 1. k 2. k n. h. ch. 2. k 1.

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RC AND SRC SHEAR WALL MACRO-MODELING

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  1. 5 Rigid Beam 6 4 Level m (1-c)h k1 k2 . . . . . . . kn kH h ch Level (m-1) 2 Rigid Beam 3 1 x1 x RC AND SRC SHEAR WALLMACRO-MODELING • Multiple Vertical Line Element Model [MVLEM] RC Wall Model

  2. 5 4 6 (1-c)h kH k1 k2 . . . . . . . kn h ch 2 k1 k2 k3 k4 k5 k6 3 1 x1 x Modeling Criteria k1 & k6 Stiffness of boundary columns k2 - k5  Stiffness of tributary web areas kH Shear stiffness (Horizontal spring simulates shear deformations)

  3. Modes of Deformation (1-c)h h ch FlexuralandShear Deformations of the MVLEM areuncoupled Relative Rotation around a point on central axis at height “ch” c depends on expected curvature distribution

  4. RW2 P=0.07Agf`c Lateral Load (kips) Top Displacement (in.) Experimental Calibration • Cyclic Tests performed on RC and Steel RC hybrid shear walls with rectangular and T-Shaped cross sections. RC Wall Tests Thompsen and Wallace (1995)

  5. Linear Analysis: Pre-Cracking (1-c)h k1 k2 . . . . . . . kn kH h ch k1 k2 k3 k4 k5 k6 Stiffness of vertical bars Stiffness of horizontal spring G0: initial shear modulus E0: initial tangent modulus A’ : effective shear area

  6. P+ RW2 P=0.07Agf`c Lateral Load (kips) (Klat)experimental Top Displacement (in.) Pre-cracking range : } (Klat)experimental 100 kip/in. (Klat)analytical 140 kip/in. 40% deviation Pre-cracking Lateral Stiffness

  7. Data Assessment/Reliability Concrete Strain Gages : P (csg)1 csg Mcsg = (P)(d1) (csg)2 d1 d2 LVDT’s : (LVDT)1 (LVDT)2 7LVDT’s LVDT (LVDT)7 MLVDT = (P)(d2) Embedded Concrete Strain Gages

  8. Concrete Strain Gages Experimental Results: LVDT’s EIuncr Concrete Strain Gages : (EI)uncr  100*106 kip-in2 (Klat)uncr 95 kip/in Moment (kip-in) EIuncr LVDT’s : (EI)uncr  65*106 kip-in2 (Klat)uncr  65 kip/in Curvature Lat. Load - Top Defl. : (Klat)uncr 100 kip/in Data Assessment/Reliability Analysis Results: (EI)uncr = 160*106 kip-in2 (Klat)uncr= 140 kip/in

  9. Nonlinear Analysis • 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.

  10.  Steel Hysteretic Constitutive Relations  Concrete  F • Shear Model to be improved • Coupling shear deformations • with flexural deformations d Shear Spring

  11. 40 Quasi-Static P+ 30 Pushover Lateral Load (kips) 20 10 0 -10 -20 -30 -40 -4 -3 -2 -1 0 1 2 3 4 Top Displacement (in) Nonlinear Analysis Results • Pushover Analysis • Pseudo – Static Analysis • Nonlinear Dynamic Analysis

  12. Correlation with Experiments

  13. 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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