Effects of Engesser’s and Haringx’s Hypotheses on Buckling of Timoshenko and Higher-Order Shear-Deformable Columns

Abstract

This article investigates the structural stability of prismatic columns with elastically restrained ends under axial compressive force. An emphasis is placed on the analysis of the effect of Engesser’s and Haringx’s hypotheses on buckling. Based on the Timoshenko beam theory and a higher-order shear-deformable beam theory, simple characteristic equations were derived for buckling of an axially loaded elastic column with two ends linked to translational and rotational springs. By introducing orientation factor α, a buckling load falls between those corresponding to Engesser’s (α=0) and Haringx’s (α=1) models. For freely standing, simply supported, and clamped columns, explicit expressions for each critical load were obtained. The effects of Engesser’s and Haringx’s hypotheses as well as of the translational and rotational spring stiffnesses at the elastically restrained end on buckling loads are analyzed in detail. Obtained results indicate that Engesser’s and Haringx’s hypotheses hardly affect buckling loads for a column with strong shear rigidity, and they have a significant influence on buckling loads for a column with weak shear rigidity. The effect of translational spring stiffness on buckling loads is more pronounced than that of rotational spring stiffness.