Shape optimization of cold-formed steel columns

Abstract The objective of this paper is to demonstrate the application of formal optimization tools towards maximizing the compressive strength of an open cold-formed steel cross section. In addition, in the work presented here the cross section shape is not limited by pre-determined elements (flanges, webs, stiffeners, etc.), as is commonly required to meet the necessity of conventional code-based procedures for design that employ simplified closed-form stability analysis. Instead, by utilizing the finite strip method for stability analysis and the Direct Strength Method for the strength calculation, the full solution space of cold-formed steel shapes may be explored. In the analysis herein, a given width of sheet steel is allowed to be bent at 20 locations along its width, thus providing the ability to form nearly any possible shape. Three optimization algorithms are explored: the gradient-based steepest descent method and two stochastic search methods, genetic algorithms and simulated annealing. Compared with a standard cold-formed steel lipped channel the final optimized capacities are found to be more than double the original design. Steepest descent solutions are shown (as expected) to be highly sensitive to the initial guess, but they provide symmetrical and conceptually clean solutions. The stochastic search methods require significantly more computational capacity, explore the solution space more fully, and generate solutions that are largely insensitive to the initial guess. For long and intermediate length cold-formed steel columns the optimization methods identify two non-conventional alternative designs that maximize capacity. The future of this work lies in further integrating the optimization methods with additional manufacturing and construction constraints; for now, the method suggests several interesting alternative cross sections that are worthy of future study.