Effect of longitudinal stress gradient on the ultimate strength of thin plates

When thin-walled sections are subjected to a moment gradient, the plates that comprise the section are themselves subjected to a longitudinal stress gradient. This paper analyzes the effect of longitudinal stress gradient on the ultimate strength of thin plates. Two types of thin plates are investigated: (1) plates simply supported on all four edges; and (2) plates simply supported on three edges, and with one longitudinal edge free. These two cases illustrate the influence of longitudinal stress gradient on stiffened and unstiffened elements of cold-formed steel sections, respectively. Nonlinear finite element analysis (ABAQUS) was performed to determine the ultimate strength of thin plates under a longitudinal stress gradient. The results indicate that the longitudinal stress gradient increases the strength of both types of thin plates, but has significantly more influence on unstiffened elements than stiffened elements. The beneficial effect of longitudinal stress gradients can be accounted for in design by using a plate buckling coefficient modified to account for the longitudinal stress gradient, an example of the impact of this change on a common cold-formed steel channel is provided.