Failure Mode Identification for Structural Frames

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Abstract
A systematic approach is developed for the identification, enumeration, and description of multiple failure modes for structural frames. The procedure is based on a linear programming model of plastic analysis. The mathematical structure of the model is used to identify the failure modes as extreme points of an associated convex polytope, and an algorithmic procedure is used to find the failure modes in the ascending order of their collapse loads, The method automatically excludes all kinematically inadmissible modes and can generate a certain prespecified number of modes or all modes up to a specified level of significance, based on a safety measure. The modal collapse loads are obtained either as linear combinations of member resistances or as linear combinations of elementary mechanisms. Methods for finding bending moment distributions, modal correlations, and bounds on the number of failure modes are discussed. The approach is illustrated with an example.

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