Constrained optimization of anti-symmetric cold-formed steel beam-column sections

Flexibility in the manufacturing of cold-formed steel (CFS) cross-sectional shapes provides a unique opportunity to improve the load-carrying capacity of these elements, leading to more efficient and economic structural systems. This paper presents a practical constrained optimization methodology for pin-ended anti-symmetric CFS beam-columns members with different lengths subjected to various combinations of axial compression and bending moment. The optimization process is carried out using a Genetic Algorithm (GA) with respect to buckling resistance of CFS elements determined according to the Direct Strength Method (DSM). In total, 132 CFS beam-columns with three different lengths (1000, 2000 and 3000 mm) and eleven different cross-sections are optimized under concentrically compressive loads with different levels of eccentricities varying from 0 to 30 mm. Each cross-section is formed using a certain number of fold-lines of steel plate, while the length and angle of the constituent elements of the cross-section are considered as the main design variables. To provide more practical beam-column elements, end-use constraints as well as a range of practical manufacturing and construction limitations are imposed on the selected cross-sections during the optimization process. A standard commercially available anti-symmetric Z section is taken as a starting point of optimization and used to assess the efficiency of the optimized sections. The results show that, for the given plate width and thickness, the adopted optimization process can significantly increase the strength of beam-column members on average 62%, 92%, and 188% for the short, medium and long length elements, respectively, compared to those with the standard section. It is also demonstrated that using more complex cross-sectional shapes does not necessarily provide higher strength for beam-column members. Finally, to verify the efficiency of the optimized sections, detailed nonlinear finite element models are developed using ABAQUS software. The developed models should prove useful for the efficient design of CFS beam-column elements in practice.