An alternate method for the combined bending and torsion design of purlins restrained by screw-down systems

Cold-formed steel channel and Z-section purlins are widely used as secondary framing members in pre-engineered steel buildings. Under gravity and wind uplift conditions, the load transfer at screw-down locations induces a combination of bending and torsion in the purlins. Due to the inherently low lateral and torsional stiffness of thin-walled sections, accurate prediction of their deformation and strength becomes challenging. However, under gravity loading, the restrained flanges are subjected to compression, where instability is relatively less critical. In case of uplift loading, the unrestrained flanges are subjected to compression, making them more susceptible to instability. EN 1993-1-3 (2006) simplify the torsion effect through equivalent lateral flexure ‘( k h )’ and AISI S100 (2024) provided combined bending-torsion interaction and empirical R-factor approaches. However, these methods do not explicitly incorporate torsional effects in the design equations, often leading to overly conservative estimates of flexural capacity. To address this limitation, the present study proposes a direct bending–torsion interaction equation for purlins based on the concept of bimoment. The bimoment, primarily induced under wind uplift, is explicitly incorporated into the proposed formulation. The study first presents an analytical investigation of bimoment distribution and associated warping stresses, including the influence of sheeting without reducing the structural stability. Subsequently, an analytical model is developed to evaluate stress reduction factors. Based on these developments, a rational and efficient design methodology is proposed. The predicted flexural capacity is validated against the provisions of EN 1993-1-3 (2006) and further verified using an experimental database available in the literature. The results demonstrate that the proposed bimoment-based approach provides more accurate predictions of purlin strength.