Optimization cross-sectional dimensions for cold-formed steel lipped channel columns

Abstract

Parametric optimization problem of cross-sectional sizes for cold-formed C-profiles subjected to central compression has been considered by the paper. Parametric optimization problem for cross-sectional sizes of cold-formed C-profiles has been formulated as follow: to define optimum cross-sectional sizes taking into account post-buckling behavior and structural requirements when stripe width and thickness as well as type of the cold-formed profile are constant and defined by the designer. Criterion of the profile load-bearing capacity maximization has been assumed as purpose function. The latter has been presented in the form of linear convolution of the resistance to central compression taking into account flexural, torsional and torsional-flexural buckling of thin-walled structural member determined according to the requirements EN 1993-1-3:2012 and EN 1993-1-5:2012. Searching for the optimum cross-sectional sizes has been performed taking into account a possibility of post-critical buckling behavior of the structural member based on the local buckling of the web and flanges and/or distortional buckling of the edge fold stiffeners. Formulated parametric optimization problem has been solved using software OptCAD. Update gradient method of the purpose function projection on the active constraints hyperplanes with simultaneous liquidations of the residuals in the constraints has been implemented by the software. As optimization results cold-formed C-profiles have been obtained. With the same stripe width optimum profiles have higher load-bearing capacity level taking into account buckling resistance under central compression comparing with the cold-formed C-profiles proposed by Ukrainian manufacturers. Besides, torsional-flexural buckling resistance of the cold-formed C-profile is determinative for all optimum cross-sectional decisions.