# Probability of Plastic Collapse Failure

*by*James L. Jorgenson,

John E. Goldberg,

**Serial Information**:

*Journal of the Structural Division*, 1969, Vol. 95, Issue 8, Pg. 1743-1761

**Document Type:**Journal Paper

**Abstract:**The probability of a plastic collapse failure for a structure of random material strength acted on by random loads can be evaluated considering that failure may occur by any one of the possible failure mechanisms for the structure. A single-bay single-story structure acted on by wind and snow loads is considered. Probability distributions are selected for the loads and for the yield strength of the structural material. The probability of failure for the frame can be closely approximated by using the sum of the probabilities of failure for the individual mechanisms for those frames in which a single failure mechanism has considerably higher P

_{F}than P

_{F}for the other possible failure mechanisms. For the case in which two or more individual failure mechanisms have near equally high probabilities of failure, the P

_{F}for the frame can be closely approximated by the sum of the P

_{F}for individual mechanisms minus the probabilities of the intersection of those events that have individually high probabilities of occurring.

**Subject Headings:**Structural failures | Failure analysis | Probability | Material failures | Strength of materials | Snow loads | Structural strength | Frames

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