On the numerical modeling of thin-walled cold-formed roof systems

Cold formed thin walled members are often used as purlins or girts in wall or roof systems. They are generally designed basing on the hypothesis that the roof or wall panel provides a strong lateral restraint to the purlin. Indeed, in the last years, the need for highly thermally insulated walls or roofs is leading the designers to solutions in which the purlin is more and more weakly restrained by the panel. The weak restraint, together with the need for the design forces to check the resistance of purlin-panel connectors and together with the local, the distortional and the global buckling phenomena that usually occurs in thin-walled members are, in the whole, a challenge for the designers, who are not supported by consolidated approaches for the analysis of this kind of structures. In fact, for example, Eurocode 3 in part 1-3 proposes a calculation method applicable to strongly laterally restrained roof systems, but requires more sophisticated analyses if the lateral restraint does not meet severe stiffness requirements. A straightforward modeling approach for these roof systems would be a three-dimensional finite element model of the whole system. This approach, although extremely accurate and detailed, is still not completely satisfactory in the current practice because of the difficulties in handling the three-dimensional model itself and the effort required to interpret the results. An alternative modeling approach relies on the development of one-dimensional finite element models based on higher order beam theories for the purlin, suitably combined with some continuous elastic restraint to take into account for the panel stabilizing effect. Some interesting results obtained with this approach, based on the Vlasov beam model, have been recently presented. Here, this one-dimensional modeling approach of the roof system is developed and critically examined with reference to the usage of the Generalized Beam Theory to model the purlin. The results of the analysis are naturally presented in this context in a clearly readable way, that takes advantage of the modal decomposition of the Generalized Beam Theory cross section analysis. The effects of different kinds of elastic continuous restraints are compared, showing that the results obtained by this modeling approach are in agreement for all the relevant aspects with more computationally expensive three-dimensional shell models. In particular, the correspondence of the results is shown to be satisfactory not only in terms of stresses and displacements in the purlin, but even for what concerns lateral distributed forces in the purlin-sheeting connectors.