Sectorial properties of straight thin-walled beams

Abstract

The sectorial method of analysis for thin-walled beams subjected to torsional loading offers many advantages. In particular it enables warping restraint effects due to non-uniform torsion to be incorporated into a general beam theory covering all solid, thick-walled and thin-walled beams of non-deformable cross-section. The distribution of warping restraint stresses around the section is defined in a similar way as for bending by a system of sectorial co-ordinates and several additional geometrical terms. A wider understanding and acceptance of this useful method of analysis is only hindered by difficulties in calculating the various sectorial functions. Solutions are readily available for open sections and regular single cell closed sections. For more complex sections, particularly asymmetric or multicellular sections or those with tapering walls, pierced walls or bracing, these calculations are often tedious. A general computer program is described which analyses any cross-section with open or closed parts. Examples are given of its application to the analysis of several straight thin-walled beams.