Optimization of cold-formed steel beams under bending effects

Cold-formed steel profiles possess a high strength-to-weight ratio and are utilized in a variety of applications. Within the scope of this study, three cross-sectional profile types commonly employed in the construction sector were examined. Section optimization was conducted based on a design in which these profiles function as main and secondary beams within a flooring system. Analyses of the design were carried out in accordance with the AISI S100-16 North American Specification for the Design of Cold-Formed Steel Structural Members, following the Load and Resistance Factor Design (LRFD) methodology. Strength limit states and serviceability limit state checks were performed for each section. Among the strength limit states—yield strength, lateral-torsional buckling strength, local buckling strength, and distortional buckling strength—the smallest calculated moment capacity was selected as the design flexural strength (Mₙ). Subsequently, the required design moment (Mᵤ) was determined under dead and live load combinations. A MATLAB model incorporating the reduction factor φ was developed to iteratively adjust sectional properties, ensuring that the ratio of the reduced flexural capacity to the design moment (φMₙ/Mᵤ) remained close to—but did not exceed—unity. Iterations were performed within a 0.1% tolerance to identify the optimal section dimensions. The optimized sections were then evaluated for shear force, elastic shear buckling, and other combined shear-flexure limit states. Finally, deflection analyses were conducted to verify serviceability limit state compliance.