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

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Problem

Dynamic Testing

Static Testing

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.

Outline Assumptions Cross Sectional Fiber Analysis Nonlinear Pushover Analysis Results Discussion

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

Outline Assumptions Cross Sectional Fiber Analysis Nonlinear Pushover Analysis Results Discussion

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

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.

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

Outline Assumptions Cross Sectional Fiber Analysis Nonlinear Pushover Analysis Results Discussion

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

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

Dynamic Test

Static Test

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

Predicted Bar Fracture

Predicted Bar Fracture Location

Outline Assumptions Cross Sectional Fiber Analysis Nonlinear Pushover Analysis Results Discussion

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

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

Actual Predicted

Predicted Bar Fracture Actual Bar Fracture Predicted Bar Fracture

The rest of the story… Catenary Action Prediction Cutoff

Outline Assumptions Cross Sectional Fiber Analysis Nonlinear Pushover Analysis Results Discussion

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

“And the structure stands…” Questions? “And the structure stands…”