Shear deformability of thin‐walled beams with arbitrary cross sections

Formulas for the computation of the shear deformability of thin‐walled prismatic beams can be found in the technical literature only in the special case of symmetric cross sections. In order to fill this gap a formulation of the flexural behaviour of thin‐walled beams taking into account transverse shear deflections is developed in the present paper. On this basis, the general expression of the shear centre location and the shear deformability tensor for open and closed sections of arbitrary shape are given and their properties discussed. In the case of polygonal, circular and arc‐shaped cross sections explicit formulas, which can be suitably implemented for automatic computations, are provided. For the sake of completeness, the expression of the stiffness tensor for prismatic beams, previously obtained by the first two authors in a co‐ordinate‐free version, is reported. Finally, a numerical example is carried out and comparisons with the results given by Cowper 1 for symmetric cross sections are presented.