Limit analysis of strain softening steel frames under pure bending

The present paper extends the classical limit analysis approach for steel structures to account for local strain softening behavior. As is well-known, the bound theorems underpinning the collapse load estimation of ductile structures require an assumption of perfect plasticity. They are invalid for the class of structures, such as those being considered here, that exhibit local softening. We propose a method, based on the same conditions governing the path-independent state problem, for capturing the maximum load multiplier characterizing the one parameter proportionally applied loading regime. The problem is cast as a special instance of the notoriously difficult to solve class of problems known as a mathematical program with equilibrium constraints (MPEC). Various solution approaches, all based on solving the MPEC as a standard nonlinear programming problem, are briefly presented. One of them, namely the penalty scheme, is used to solve the three numerical examples provided to highlight application of the proposed limit analysis approach.