Cold-Formed Cross-Sectional Folds with Optimal Signature Curve

A novel figure of merit based on the concept of signature curve for cold formed steel (CFS) cross sections is used to improve the structural member's overall behavior regardless of length and boundary conditions. The objective is defined as the area under the signature curve, plus a penalty function that ensures improved performance over standard sections at specified lengths. Charged system search (CSS), a meta-heuristic optimization algorithm, is used to search the design space. End-use and other geometrical constraints suggested by previous studies are considered to arrive at practical cross sections. This includes limiting the fold angles to minimize sharp corners in the optimized cross sections, which might result in residual stresses that diminish axial capacity. Such nonlinear constraints are also taken into account using penalty functions to facilitate integration with the heuristic optimization process. The proposed strategy is examined through a couple of illustrative examples and is shown to yield higher axial capacity at all points when combined with the proper penalization. The optimized cross sections are also analyzed in simple-simple and clamped-clamped boundary conditions showing improved axial capacity compared to the standard lipped-channel sections with the same coil width.