Effect of warping shape on buckling of circular and rectangular columns under axial compression

摘要

The structural stability of a column with rectangular and circular cross-section under axial compression is studied based on various higher-order shear deformation beam theories. This paper has two-fold objectives. One is to introduce a transition parameter to describe the direction of axial load from Engesser's hypothesis to Haringx's one, then a unified method is presented to determine the critical load. The other is to introduce new cross-section warping shapes of rectangular and circular columns, then the buckling loads are exactly calculated and compared for various warping shapes. A governing equation for buckling of a column under axial compression is first derived. The buckling loads of a prismatic column with typical ends such as clamped-clamped, pinned-pinned, and clamped free columns are determined and an explicit expression is obtained in terms of the Euler buckling load. The effects of the warping shape of the cross-section on the buckling loads are analyzed. The Haringx buckling load is greater than the Engesser buckling load that gives a conservative estimate of the critical load. A comparison of these buckling loads with Euler loads is made. The obtained results indicate that Euler buckling loads are both significantly overestimated for short columns or those with weak shear rigidity. The buckling loads are nearly not affected for very slender columns or those with high shear rigidity. The Euler loads are recovered from the present ones for columns in the case of shear locking. The buckling loads are also dependent on the warping shape of the cross-section. (C) 2020 Elsevier Inc. All rights reserved.