Coupled axial-flexural buckling of shear deformable columns using an exact stiffness matrix

Flexural-torsional buckling analysis of columns is widely covered in the literature. By contrast, there are hardly any corresponding publications on axial-flexural buckling. This is because there appears to be a commonly held view that in a column, the axial deformation is perceived to be small and therefore its coupling with the flexure can be neglected when predicting its critical buckling load. This paper counters this view by focusing on the buckling behaviour of axial-flexural coupled columns. The usefulness for this research stems from the fact that there are many practical columns which have cross-sections that exhibit axial-flexural coupling as opposed to flexural-torsional coupling, and thus, the axial-flexural coupling is likely to have significant effects on buckling behaviour. The problem does not appear to have been adequately addressed by investigators. Starting from the derivation of the governing differential equation with the inclusion of shear deformation, the stiffness matrix of an axial-flexural coupled column is derived in an exact sense, and subsequently applied through the implementation of the Wittrick-Williams algorithm as solution technique to determine the critical buckling load of some illustrative examples. The results are validated by alternative methods. Finally. some conclusions are drawn.