Simple Solutions for Lateral Buckling Loads of C-Section Purlins with Two or Three Anti-Sag Bars Under Wind Suction

Lateral buckling is the governing failure mode affecting the strength of cold-formed steel purlins. In industrial roofing systems, these purlins are frequently restrained by two or three anti-sag bars within their spans. Previous research by the authors indicated that under wind suction, the buckling behaviour of purlins with multiple anti-sag bars differs significantly from those with fewer restraints, primarily due to the semi-rigid nature of the bracing. This paper investigates the lateral buckling of C-section purlins with two or three anti-sag bars, explicitly accounting for lateral restraints provided by both the roof sheeting and the bars. Simplified analytical solutions are derived to facilitate practical design. Notably, a novel parameter is introduced to identify the controlling buckling mode, which significantly simplifies the calculation procedure. The proposed solutions show excellent agreement with results obtained from both commercial and custom-developed finite element codes.