Analytical study of flat and curved trapezoidal cold formed steel sheets by means of the yield line theory. Part 1: Flat sheets without transverse corrugations

Abstract

This article presents a study of self-supporting arched roofs made from cold-formed steel trapezoidal sheeting. The curved shape of the arches is achieved by press-forming a series of transverse corrugations into flat trapezoidal sheets. From the results of preliminary experimental tests, it is concluded that the study can be effectively dealt with by means of the Yield Line Theory (YLT). The main problem in using this approach is that YLT has, until now, never been applied to trapezoidal sheets subjected to pure compression or bending. Consequently, neither flat nor curved sheets have an available YLT formulation from which to derive their post-collapse behavior. The present article shows the first steps of the research, which are focused on the development of a YLT approach for flat trapezoidal sheets. It describes how a suitable YLT procedure can be derived from existing classical concepts and models of the Theory. Finally, the model proposed is capable to predict the behavior of the sheets satisfactorily, as it is verified by comparison with numerical and experimental test results. In the second part of the study, presented in a companion article, the YLT model will be adapted to the analysis of the curved sheets. By then it will be possible to see that YLT is an elegant and effective option for studying the effect of transverse corrugations on the behavior of trapezoidal sheets.