Optimum shape design of cold-formed thin-walled steel sections

The algorithm presented in this study obtains the optimum cross-sectional dimensions of cold-formed thin-walled steel beams subjected to general loading. It has the flexibility of considering different cross-sectional shapes such as symmetrical or unsymmetrical channel, lipped channel or Z-sections. The algorithm treats the cross-sectional dimensions such as width, depth and wall thickness as design variables and considers the displacement as well as stress limitations. The presence of torsional moments causes warping of thin-walled sections. The effect of warping in the calculation of normal stresses is included using Vlasov theorems. These theorems require the computation of sectorial properties of cross-sections. A general numerical procedure is presented for obtaining these properties. The optimum design problem of thin-walled open sections subjected to combined loading turns out to be a highly nonlinear problem. It is shown that optimality criteria method can effectively be used to obtain its solution. A number of design examples are presented to demonstrate the application of the algorithm.