A non-linear theory for the behaviour of thin-walled sections subject to combined bending and torsion

Thin-walled steel sections are extensively used in modern building either as purlins or as sheeting rails. Comparatively little is known about the effects of position and orientation with respect to the shear centre of the loading on the stability of such sections. The governing differential equations for the non-linear elastic behaviour of thin-walled sections subject to combined bending and torsion are developed in the paper. They include the non-linear contribution resulting from the movement of the point of application of the load. This is shown to have a significant influence on the behaviour of the member when the loads are inclined to the principal axes, as in the case of an asymmetrical section subject to gravity loading. Furthermore, it is shown that load resultants which pass through the shear centre but which are inclined to the principal axes of the section do not produce pure bending. They induce torsional moments in the section which are not accounted for in traditional theories. A finite-difference method is used to solve the equations, and the validity of the theory is assessed by comparing the results with those obtained from experiment.