Torsion of cold-formed steel lipped channels dominated by warping response

Abstract

The objective of this paper is to provide benchmark test results, explanatory shell finite element models, and preliminary Direct Strength Method prediction for cold-formed steel lipped channels undergoing torsion dominated by warping response. Although the elastic theory for the torsional response of a thin-walled cold-formed steel lipped channel member is well-developed, the extent to which warping torsion dominates the response of cold-formed steel members is not widely appreciated. Further, for cold-formed steel members in torsion little exists in terms of experimental benchmarks and even less on situations beyond the classic elastic theory, including geometric nonlinearity and post-buckling, and/or material nonlinearity from partial to full plastification of the section. Here, a typical cold-formed steel lipped channel member loaded experimentally in torsion exhibits significant strength beyond first yield. Shell finite element models of the testing correlate well with the experiments and indicate the extent of plastification as the thin-walled member undergoes torsion dominated by warping response. Idealized end boundary conditions are developed for the shell finite element model that is conservative with respect to the response, and in agreement with classical expressions in the elastic regime. The shell finite element model with idealized end boundary conditions is used to develop a parametric study on ultimate torsional capacity for members dominated by warping torsion. The results indicate that torsional slenderness may be used to predict torsional capacity and indicate that Direct Strength Method predictions for torsion for members dominated by warping torsion are possible. Preliminary design expressions for warping torsion strength prediction are provided.