Modeling Progressive Collapse by Plastic Analysis

1. Modeling Progressive Collapse by Plastic Analysis Andrew Coughlin Ashutosh Srivastava Graduate Research Assistant Graduate Research Assistant The Pennsylvania State University The Pennsylvania State University Progressive Collapse Resistance Competition (PCRC) ASCE Structures Congress April 25, 2008 Vancouver, BC

2. Motivation Images are public domain distributed by wikipedia.org

3. Problem

5. Dynamic Testing

6. Static Testing

7. Approach Cross Section Fiber Analysis XTRACTTM Nonlinear Pushover Analysis CAPPTM Screenshots from XTRACTTM and CAPPTM, a collaborative effort between Imbsen and Associates and Charles Chadwell, Ph.D., P.E.

8. Outline • Assumptions • Cross Sectional Fiber Analysis • Nonlinear Pushover Analysis • Results • Discussion

9. Assumptions • Similitude: 1/8 scale model • 1/8th all lengths • 1/64th all forces • Same stress • Plastic hinge length d/2 • Axial deflections not considered • Fixed support conditions

10. Outline • Assumptions • Cross Sectional Fiber Analysis • Nonlinear Pushover Analysis • Results • Discussion

11. Cross Sectional Fiber Analysis • Material Models Cover Concrete Confined Concrete Reinforcing Steel Mander, J.B., Priestley, M. J. N., "Observed Stress-Strain Behavior of Confined Concrete", Journal of Structural Engineering, ASCE, Vol. 114, No. 8, August 1988, pp. 1827-1849

12. Cross Sectional Fiber Analysis Cover concrete Beam at joint Column Reinforcing steel Beam at cutoff Roof beam Confined concrete XTRACTTM Screenshots from XTRACTTM, a collaborative effort between Imbsen and Associates and Charles Chadwell, Ph.D., P.E.

13. Moment Curvature Screenshots from XTRACTTM, a collaborative effort between Imbsen and Associates and Charles Chadwell, Ph.D., P.E.

14. Outline • Assumptions • Cross Sectional Fiber Analysis • Nonlinear Pushover Analysis • Results • Discussion

15. Nonlinear Springs Screenshots from CAPPTM, a collaborative effort between Imbsen and Associates and Charles Chadwell, Ph.D., P.E.

16. Model • Elastic Beam Elements • Nonlinear Hinges • Where could they form? • Joints • Load points • Section changes (due to bar cutoff)

18. Dynamic Test

20. Static Test

21. 5 5 3 4 4 1 6 6 2 Plastic Hinge Formation

22. Predicted Bar Fracture

23. Predicted Bar Fracture Location

24. Outline • Assumptions • Cross Sectional Fiber Analysis • Nonlinear Pushover Analysis • Results • Discussion

25. Dynamic Results • Structure did not collapse • Max Deflection • Predicted = 0.96” • Actual = 0.21” • Permanent Deflection • Predicted = 0.87” • Actual = 0.20” • Sources of Error • Dynamic effects were not considered • Large change in deflection for little change in load • Material overstrength

26. Static Results • Maximum Load • Predicted = 1800 lb • Actual = 1800 lb (before catenary action) • Displacement at bar fracture • Predicted = 3.9” • Actual = 3.48”

27. Actual Predicted

28. Actual Bar Fracture Predicted Bar Fracture

29. The rest of the story… Catenary Action Prediction Cutoff

30. Outline • Assumptions • Cross Sectional Fiber Analysis • Nonlinear Pushover Analysis • Results • Discussion

32. Acknowledgements • Yang Thao of Imbsen and Associates • Educational Software Licenses • Prof. Charles Chadwell, Cal Poly • Modeling advice • Prof. Jeffrey Laman, Penn State • Review of submission • Prof. Mehrdad Sasani, Northeastern • Competition organization

33. Questions? “And the structure stands…”