Analysis of laterally restrained cold-formed C-shape purlins according to Vlasov theory

• The results of research on purlins interacting with a cover made from corrugated sheets.
• Ideal cold-formed purlins and with geometric imperfections were investigated.
• Solutions subjected to bending and torsion were derived using the Bubnov–Galerkin method.
• The theoretical results were validated by experiments on models of a natural-scale.

This paper presents the results of theoretical and experimental research on channel purlins interacting with a cover made from corrugated sheets. Perfect (without pretorsion) cold-formed purlins and cold-formed purlins with geometric imperfections (permanent pretorsion or pointwise bracing with regard to torsion) were investigated. Appropriate solutions for the purlins subjected to simultaneous bending and torsion relative to a fixed axis of rotation were derived using the Bubnov–Galerkin method in both its full version and simplified (but sufficiently accurate for design purposes) version. As a result, direct relations for the linear and angular displacements of the purlins were obtained. The relationships can be used to calculate the forces and the strain in the purlins. The theoretical results were validated by experiments on a natural-scale roof fragment. Finally, practical conclusions were drawn from the research.