Approximate Analysis of Post‐Limit Response of Frames

Abstract

An approach to estimating the limit and post‐limit behavior of a framed structure from its geometrically linear response is presented. The method follows from a particular restatement of the weak form of the nonlinear differential equations governing the response of the structure, and is based upon the observation that geometric effects are insensitive to redistribution of the moment field in planar framed structures. The formulation gives insight into the relationship between important observed phenomena and the complex nonlinear governing equations. A novel derivation of Home's method for estimating the nonlinear response of frames is presented and extended to the important case of nonproportional loads. The role of the linearized geometric stiffness matrix, and the buckling eigenvalues is clearly demonstrated. Several examples are given to evaluate the validity of the inherent assumptions and to demonstrate the effectiveness of the approach.