A method for the direct evaluation of buckling loads of an imperfect two-bar frame

Abstract

The pre-critical, critical, and post-critical nonlinear response of an imperfect due to loading eccentricity two-bar frame is thoroughly discussed. In seeking the maximum load-carrying capacity of this non-sway frame, it was qualitatively established that its loss of stability occurs through a limit point and hence, the case of an asymmetric bifurcation can be considered only in an asymptotic sense. After deriving the nonlinear equilibrium equations with unknowns for the two bar axial forces, we can consider such a continuous system as a two-degree-of-freedom model with generalized coordinates the above axial forces. Then, the equilibrium equations and the stability determinant of the frame can be determined in terms of the first and second derivatives of its total potential energy (TPE) with respect to the axial forces. The vanishing of the second variation of the TPE together with the equilibrium equations allows a simple and direct evaluation of the buckling load. Numerical examples demonstrate the efficiency and the reliability of the proposed method.