Modeling Progressive Collapse by Plastic Analysis

Andrew Coughlin Ashutosh SrivastavaGraduate Research Assistant Graduate Research AssistantThe Pennsylvania State University The Pennsylvania State University

Progressive Collapse Resistance Competition (PCRC)ASCE Structures CongressApril 25, 2008Vancouver, BC

Motivation

Images are public domain distributed by wikipedia.org

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 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

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

Cover Concrete Confined Concrete Reinforcing Steel

Cross Sectional Fiber Analysis

Beam at joint

Beam at cutoff

Column

Roof beam

Confined concrete

Reinforcing steel

Cover concrete

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

XTRACTTM

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

1. Elastic Beam Elements2. Nonlinear Hinges

Where could they form?1. Joints2. Load points3. Section changes (due to bar cutoff)

Dynamic Test

Static Test

Plastic Hinge Formation

6 6

2

1

3

4 4

55

Load Displacement Prediction of 1/8 Scale Model

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.5 1 1.5 2 2.5 3 3.5 4

Vertical Deflection (in)

Vert

ical

Loa

d (lb

s)

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 Predicted = 1800 lb Actual = 1800 lb

(before catenary action)

Displacement at bar fracture Predicted = 3.9” Actual = 3.48”

Load Displacement Prediction of 1/8 Scale Model

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.5 1 1.5 2 2.5 3 3.5 4

Vertical Deflection (in)

Vert

ical

Loa

d (lb

s)

Actual

Predicted

Predicted Bar Fracture

Actual Bar Fracture

The rest of the story…

Catenary ActionPrediction 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

Questions?

“And the structure stands…”