The main objective of this manuscript is to offer an optimization approach for the common thinwalled I, Z and channel-section beams subjected to direct torsion. The displacement limitations for the incident angle of twist are only considered: Using the Lagrange multiplier method, the mass of the supposed element is assumed to be the objective function, the deduced equations have solutions can represent the optimal values of the ratios between dimensions of the formed parts of the considered sections with respect to the global length of element.

Keywords : Direct torsion, Optimization Approach, Optimal dimensions, cold formed sections.