Tracing Secondary Equilibrium Paths of Elastic Framed Structures

Abstract

For a framed structure that is subjected to bifurcation buckling, it may be useful to trace its secondary equilibrium path to gauge its sensitivity to geometric imperfections or to study the nature of load shedding from the buckled structure. For this purpose, a substantial number of branch-switching algorithms for tracing the secondary equilibrium paths of elastic structures have been proposed in the literature. However, virtually all of the published algorithms have heavy mathematical overtones that are not readily appreciated by practicing structural engineers. This paper presents a simple and efficient branch-switching algorithm that is explained in more easily understood terms. The proposed algorithm is demonstrated through numerical examples to be effective in tracing the secondary equilibrium paths of various framed structures with different types of postbuckling behaviors.