Buckling Analysis of Frames with Semi-Rigid Connections using Power Series

Analyzing and investigating the elastic behavior of frames after buckling is complicated. When a frame is subjected to a force exceeding the critical load, it begins to undergo large deformations. In this case, the theory of small deformations is no longer valid for the structure and the theory of large deformations should be used. Post-buckling analysis of elastic structures always requires solving a set of nonlinear differential equations based on equilibrium equations. The present work deals with the effect of beam-column joint flexibility on the elastic buckling load of plane steel frames and proposes a simplified approach to the evaluation of the critical buckling load of frames with semi-rigid connections according to the assumptions of the Elastica theory. In this study, the equations are simplified using the power series. The elastic buckling load is found to be strongly affected by semi-rigid joints and reveals that the proposed model is computationally very efficient with the expressions presented being general. The paper makes reference to the other researchers in comparing the results.