1. Level (m-1 ) Level m h (1-c)h ch 1 2 3 4 5 6 Rigid Beam x1x1 x k1k1 k2k2 knkn kHkH....... RC AND SRC SHEAR WALL MACRO-MODELING l Multiple Vertical Line Element Model [MVLEM] RC Wall Model

2. Modeling Criteria (1-c)h h ch 1 2 3 4 5 6 x1x1 x k1k1 k2k2 knkn kHkH....... k1k1 k6k6 k2k2 k3k3 k4k4 k5k5 k 1 & k 6  Stiffness of boundary columns k 2 - k 5  Stiffness of tributary web areas k H  Shear stiffness (Horizontal spring simulates shear deformations)

3. 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

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

5. Stiffness of vertical bars E 0 : initial tangent modulus Stiffness of horizontal spring G 0 : initial shear modulus A’ : effective shear area (1-c)h ch k1k1 k2k2 knkn kHkH....... h k1k1 k6k6 k2k2 k3k3 k4k4 k5k5 Linear Analysis: Pre-Cracking

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

7. P 7 LVDT’s Embedded Concrete Strain Gages d1d1 d2d2 Concrete Strain Gages :  csg M csg = (P)(d 1 ) (  csg ) 1 (  csg ) 2 LVDT’s : Data Assessment/Reliability  LVDT M LVDT = (P)(d 2 ) (  LVDT ) 7 (  LVDT ) 1 (  LVDT ) 2

8. Analysis Results: (EI) uncr = 160*10 6 kip-in 2 (K lat ) uncr = 140 kip/in Moment (kip-in) Curvature Concrete Strain Gages LVDT’s EI unc r Concrete Strain Gages : (EI) uncr  100*10 6 kip-in 2 (K lat ) uncr  95 kip/in LVDT’s : (EI) uncr  65*10 6 kip-in 2 (K lat ) uncr  65 kip/in Lat. Load - Top Defl. : (K lat ) uncr  100 kip/in Experimental Results: Data Assessment/Reliability

9. l Iterative displacement-controlled nonlinear analysis scheme is applied. l 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

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

11. Nonlinear Analysis Results Pushover Analysis Pseudo – Static Analysis Nonlinear Dynamic Analysis P+ -4-3-201234 -40 -30 -20 -10 0 10 20 30 40 Top Displacement (in) Lateral Load (kips) Quasi-Static Pushover

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.