Stress analysis on cold-formed C-purlins subjected to wind suction load considering the effective stiffness of anti-sag bar

• Solution for the effective stiffness of anti-sag bar considering the local deformation of section is proposed.
• Effect of the bracing stiffness of anti-sag bar on the behaviour of cold-formed C-purlins is investigated.
• The stress distributions over the whole span for the cold-formed steel purlins containing one anti-sag bar are studied.
• New solutions for the maximum tensile and compressive stresses in C-purlins with one anti-sag bar are proposed.

The anti-sag bar is frequently adopted as an effective solution to enhance the lateral stiffness of cold-formed steel purlins. In many existing methods (e.g. EC3 method), the anti-sag bar is treated as the rigid lateral bracing for cold-formed steel purlins, which may overestimate its bracing efficiency due to the local deformation of purlin web near the position connecting the anti-sag bar, which may significantly reduce the effective stiffness of anti-sag bar. This paper presents an investigation on the effective stiffness of anti-sag bar in bracing the cold-formed steel purlins accounting for the effect of the local deformation of purlin web, based on which an accurate approximation is also proposed. The influence of the effective stiffness of anti-sag bar on the out-of-plane bending moment over the purlin span is then studied using the analytical model presented in EC3. Subsequently, new solutions for the maximum compressive and tensile stresses for purlins with one anti-sag bar at their mid-span section are then proposed with the influence of the effective stiffness of the anti-sag bar taken into account. The results of the proposed solutions are verified by comparing their predictions with the results from the finite element (FE) analysis. Comparisons with FE results made in this study also indicate that the predictions of the EC3 solution may significantly overestimate or underestimate the controlling stresses of cold-formed steel purlins with anti-sag bar in many cases.