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Due to their thin-walled nature and complex geometry, cold-formed steel purlins are prone to a variety of instabilities. Sigma purlins are a family of cold-formed steel members with folding-lines along their webs. The non-straight geometry of their web is beneficial in terms of reducing the susceptibility of the web to local buckling, however, it increases their susceptibility to web crippling when the purlins are subjected to concentrated transverse loads and hence it may reduce their overall moment resistance. This paper reports a series of experiments on sigma purlins under the interiorone-flange (IOF) loading condition. Two different section geometries and three different bearing plate widths were examined. To investigate further the effect of web geometry on the IOF web crippling strength of sigma sections, an FE model was developed and validated against the reported test results. Following successful replication of the experimental observations, a comprehensive parametric study was performed, and several sigma sections covering a wide range of crosssectional geometries and slenderness were numerically modelled. Finally, a slenderness-based (or direct strength) design approach previously developed for the web crippling design of channel and hat sections is extended to sigma sections.

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This paper reports a numerical study on the optimization of the lip size of Z‐sections under gravity loads. Numerical models simulating the structural response of cold‐formed steel Z purlins partially restrained by cladding and angle struts and subjected to sagging moment were developed and validated against a total of nine previously reported experimental results on Z‐sections that failed in local or/and distortional buckling. Models of varying levels of complexity were generated and the key parameters affecting the structural response were determined by means of a sensitivity analysis. The investigated parameters included the magnitude, shape and combination of initial geometric imperfections pertinent to local and distortional buckling and the simplified or explicit modelling of test details such as struts and sheeting. Having determined the appropriate modelling strategy that yields the best balance between accuracy and computational cost, parametric studies were conducted to investigate the effect of decreasing or increasing the lip depth on the sections' moment resistance and corresponding failure mode. Based on the parametric study results, the optimal lip size which maximizes the moment/weight ratio for each section was determined.

Due to their thin‐walled nature and complex geometry, cold‐formed steel purlins are prone to a variety of instabilities. In most applications, purlins rely on the attached sheeting to restrain member buckling and hence their cross‐section is optimized to maximize their cross‐sectional resistance to local and distortional buckling caused by sagging bending moments under the action of a uniformly distributed load. Sigma purlins are a family of cold‐formed steel members with folding‐lines along their webs. The non‐straight geometry of their web is beneficial in terms of reducing the local slenderness of the web, however it increases their susceptibility to web crippling in case the purlins are subjected to concentrated transverse loads and hence it may reduce the overall moment resistance. This study reports a series of experimental tests on sigma purlins interior‐one‐flange (IOF) loading condition. The tested specimens employ two different section geometries and three different bearing plate widths. The test results show that all the specimens failed by web crippling, however two distinct failure modes and corresponding load‐deformation curves are observed depending on the section geometry. To investigate further the effect of web geometry on the IOF web crippling strength of sigma sections, an FE model was developed and validated against the reported test results. Following successful replication of the experimental observations, a comprehensive parametric study was performed and several sigma sections were numerically tested. Furthermore, the applicability of a novel slenderness‐based design approach previously proposed by Duarte and Silvestre for the web crippling design of channel sections is assessed and design recommendations are proposed.