Unconstrained shape optimisation of singly-symmetric and open cold-formed steel beams and beam-columns

• A Genetic Algorithm is used to optimise the cross-sectional shape of cold-formed steel beams and beam-columns.
• Fully restrained beams and unrestrained beams and beam-columns are investigated.
• Published automated rules for elastic axial buckling stresses accurately estimate elastic bending buckling stresses.
• Optimised cross-sections open widely in beams and progressively close up when the axial load increases in beam-columns.

This study aims to optimise the cross-sectional shape of singly-symmetric, open-section and simply-supported cold-formed steel (CFS) beams and beam-columns. No manufacturing or assembly constraints are considered. The previously developed augmented Lagrangian Genetic Algorithm (GA), referred to as the “self-shape” optimisation algorithm, is used herein. Fully restrained and unrestrained beams against lateral deflection and twist, as well as unrestrained beam-columns are optimised. Various combinations of axial compressive load and bending moment are analysed for the beam-columns. The Direct Strength Method (DSM) is used to evaluate the nominal member compressive and bending capacities. The accuracy of the automated rules, developed in the literature to determine the elastic local and distortional axial buckling stresses from Finite Strip signature curves, is verified herein to estimate the elastic bending buckling stresses. The optimised cross-sectional shapes are presented for all cases and the evolution of the unrestrained shapes from pure axial compression to pure bending is discussed.