1. 1 UH-Contribution Ravi Mullapudi Parnak Charkhchi Ashraf Ayoub NEES - Jan 23, 2008

2. 2 OUTLINE  Combined Bending/Shear  Modified Compression Field Theory (MCFT)  Rotating Angle Softened Truss Model (RA-STM)  Fixed Angle Softened Truss Model (FA-STM)  Soften Membrane Model (SMM)  Comparison between Models  Seismic Analysis – Numerical Results  Combined Torsion/Bending/Shear  Discretization of Section in 2D/3D Regions  3D Constitutive Models  Section Analysis  Numerical Results  On-Going Work  Beam Element under Combined Torsion/Bending/Shear  Seismic Analysis  OpenSees

3. 3 Modified Compression Field Model Rotating Angle- Softened Truss Model

4. 4 SOFTEN TRUSS MODEL -Principle  Shear stress along crack ≠ 0  V c  Biaxial Stress & Strain  Smeared Approach Concrete Element SOFTEN Membrane MODEL  Hsu/Zhu Poisson Ratio

5. 5 NUMERICAL RESULTS – USC Shear-Critical Column = 86 MPa Longitudinal yield stress = 510 MPa Transverse yield stress = 449 MPa Xiao and Martirossyan

6. 6 NUMERICAL RESULTS Effect of Different Models HC4-8L16-T6-0.1P Column Monotonic Analysis with different Elements

7. 7 NUMERICAL RESULTS HC4-8L16-T6-0.1P Column Hoop Strain Distributions

8. 8 NUMERICAL RESULTS – Cyclic Load Displacement Axial Load = 1068 kN USC Column Flexure Element  Flexure element is unable to predict the correct behavior

9. 9 NUMERICAL RESULTS – Cyclic Load Displacement Axial Load = 1068 kN USC Column Shear Element  Shear element is able to predict the correct behavior HC4-8L16-T6-0.2P Column

10. 10 NUMERICAL RESULTS Shear Element Load Displacement HC4-8L16-T6-0.1P Column Dynamic Shear Analysis

11. 11 NUMERICAL RESULTS – Earthquake Analysis – Load vs. Deformation HC4-8L16-T6-0.1P Column El Centro Record

12. 12 NUMERICAL RESULTS – Shear-Critical Column Aboutaha et al. = 22 MPa Longitudinal yield stress = 434 MPa Transverse yield stress = 400 MPa

13. 13 NUMERICAL RESULTS – Shear Element Load Displacement 48” Column Syracuse Column Axial Load = 0 kN  Due to weak axis loading, Pinching is high

14. 14 NUMERICAL RESULTS – Shear and Flexure Element 48” Column Syracuse Column Axial Load = 0 kN  Flexure element is unable to predict the correct behavior

15. 15 NUMERICAL RESULTS – Earthquake Analysis – Time History 48” Column Syracuse Column Shear Analysis Assumed Axial Load = 0.1 f c A g = 205.5 kN 2 * EL Centro (1940) record

16. 16 NUMERICAL RESULTS – Earthquake Analysis – Load vs. Deformation SC3 Column Shear Dynamic 2*El-Centro

17. 17 NUMERICAL RESULTS – Earthquake Analysis – Time History Syracuse Column Flexure and Shear Analysis Assumed Axial Load = 0.1 f c A g = 205.5 kN 2 * EL Centro (1940) record

18. 18 Longitudinal Reinforcement 2% Shell Region Core Region 406.4 mm Dia. Transverse Reinforcement 1% NUMERICAL RESULTS – UNR Column Vu Phan et al. 1829 mm EL Centro NS 36.3 N – S 2 /mm Axial Load = 355 kN

19. 19 NUMERICAL RESULTS – Earthquake Analysis UNR Column- 9F1 EL Centro (1940) record Experiment

20. 20 NUMERICAL RESULTS – Earthquake Analysis UNR Column EL Centro (1940) record

21. 21 NUMERICAL RESULTS Shear Element Load Displacement UNR Column 9S1 Deflection for 2.0*El Centro

22. 22 Torsion Basic Equations Equilibrium Compatibility

23. 23 Torsional Section Discretization 2D/3D Regions

24. 24 3D Constitutive Model – Vecchio and Selby Approach (1991)  No Complete 3D- Model available  Assuming the same relation ship for intermediate stress calculation  Implemented the 3D procedure to SMM

25. 25 Torsional Section Fiber Section Analysis

26. 26 Numerical Results Pure Torsion Box Section

27. 27 Numerical Results

28. 28 Numerical Results - Combined Torsion/Bending 24” 12” 5, #9 bars #4 hoops @ 5”

29. 29 ScheduleDeadline Finite element Analysis  Development of RC fiber beam- column element including torsion/bending/axial interaction  Calibration of the parameters of the developed element  Development of an OpenSees version of the developed element Jan 09- March 09 March 09-May 09 June 09-Aug 09 Schedule of On-Going Work