Effect of Using Alternative Stress–Strain Definitions on the Buckling Load Predictions of Thin-Walled Members

Abstract

Thin-walled structural components are widely used in many industries including aerospace, building, aircraft, and shipbuilding. These types of structures are susceptible to buckling and it is important to predict their response accurately. Effect of shear deformation on buckling behaviour of thin-walled members can become significant, especially for short and stocky sections and/or when materials with relatively low shear modulus are used. There are two well-known approaches in the literature that produce contradictory results when elastic Hooke’s material is adopted for the shear deformable buckling analysis of columns. The first one is developed by Engesser and the second one by Haringx. The difference between the two methods has been attributed to different assumptions for the axial force orientation at the deformed state of the column. Engesser assumes that the axial force is parallel to the beam axis in the loading state whereas, in Haringx theory, the axial force is assumed to be perpendicular to the cross-section of the beam. This difference in the assumption of force directions can be traced down to the difference in the definitions of adopted stress–strain pairs within the Doyle-Ericksen family of strains. Although several shear deformable finite element formulations have been proposed for the buckling analysis of thin-walled beams, the differences that alternative stress–strain definitions might cause were not identified in the finite element context. In this paper, it is shown that alternative stress–strain definitions lead to changes in the geometric stiffness matrices of thin-walled beam finite element formulations. The effect of changes in the geometric stiffness matrix on buckling capacity predictions of thin-walled beams is illustrated through numerical tests on short FRP pultruded beams with low shear modulus.