Influence of the fixing type in the optimization of trapezoidal roofing sheets

• The optimization of a trapezoidal sheet is carried out using genetic algorithms.
• Two cases of fixing of the sheet span ends are studied.
• There is a similar solution for positive and negative bending moments.
• The structural performance is inferior for fixing at compression flanges.
• The covering area should not be increased by extending the fixing flanges.

The steel profiled sheets are fit to close large openings without too much increase of load over the cladding system structures. In this regard, these structural components become an economical alternative for roofing and siding in industrial buildings, hangars and other kinds of pavilions. Trapezoidal sheets are specifically a good alternative to close this kind of structures. The opening span that cold-formed sheets are able to cover can be determined through the serviceability displacement limit state. Beyond that, steel sheets are characterized by the high slenderness of the cross-section elements and, as a result, the susceptibility to undergo local buckling must be considered. This study attempts to evaluate the best alternatives for trapezoidal-shaped cross-sections to be used in roof cladding, considering pure bending and different boundary conditions. The analyses are carried out by using three-dimensional shell finite element models combined with optimization routines based on Genetic Algorithms. The profiles to be obtained are the ones that show lowest displacement and highest critical elastic buckling load, at the same time the roof covering area is maximized. The different configurations of the sheet fixing to the purlins lead to different cross-sectional geometries. The obtained optimum profiles are compared to a commercial profile. Finally, a sensitivity study of the objective function in relation to the design variables is carried out, that makes easier to understand the structural behavior of trapezoidal roofing sheets.