Should load remain constant when a thin-walled open-profile column buckles?

Abstract

This paper addresses the fundamental question of whether the applied load should necessarily be assumed to remain constant for bifurcation buckling analysis of thin-walled open-profile columns via the work-energy approach. The constant load condition has been recently used as a fundamental requirement for a valid analysis by Goto and Chen (1989, Int. J. Solids Structures25, 621–634) to dispute a theory proposed by Ojalvo (1989, ASME J. Appl. Mech. 56, 633–638). This paper establishes that neither constant load nor constant distance need be insisted upon for a valid analysis. It is permissible to assume either constant load or constant distance (or any other compatible configuration with second order changes in loads and distance) for a valid analysis. It is essential to ensure that the appropriate strain energy and work expressions are adopted.