On the Stresses in Thin-Walled Channels Under Torsion

Thin-walled channel beams such as cold-formed steel purlins are primarily used to withstand wind forces in the roofing and walling systems of buildings. Traditionally, these types of members are usually designed for bending moments, with the effects of torsion ignored. However, the loading on thin-walled channels can be much more complicated than simple bending actions. Because of the position of the shear centre outside the section, channels can undergo bending and torsion when subjected to vertical load on the top flange. The applied torsion may cause significant stresses in the channel, which may need to be accounted for in design. There appears to be no research on quantifying the effects of torsion on thin-walled channels subjected to a uniformly distributed load acting on the top flange. In this paper, a theoretical solution is derived for calculating the longitudinal stresses in thin-walled channels subjected to torsion caused by a uniformly distributed load acting on the top flange. The theory is validated by modelling the channels in a finite-element analysis. The theoretical results include calculations of the twist rotation, bimoment, sectorial coordinate and longitudinal stresses, while the results from the finite-element analysis include the twist rotation and longitudinal stresses. The results show that the longitudinal stresses caused by torsion can significantly exceed those caused by the bending moment. Practical advice is also given for engineers on how to minimize torsion in cold-formed steel purlins.