Efficient Line-Element Method for the Second-Order Analysis of Steel Members with Nonsymmetric Thick-Walled Cross Sections

When designing steel members with nonsymmetric cross sections, it is essential to consider twisting effects when performing stability checks via second-order analysis according to the ANSI/AISC 360-22. Existing line-element formulations for nonsymmetric sections are mostly derived based on thin-walled assumptions, leading to an overestimation of member strength due to the inaccurate prediction of member behavior, especially when the cross sections have moderate wall thickness. This paper proposes an efficient line-element method for second-order analysis of steel members with nonsymmetric thick-walled sections considering the warping degree of freedom (DOF) and the twisting effects along with the transverse shear deformations. Additionally, a two-dimensional (2D) finite-element cross section analysis method employing the constant strain triangle (CST) element is developed to calculate the section properties for arbitrary cross sections, including the Wagner and the shear coefficients. The proposed method is implemented in the educational structural analysis software MASTAN2 and verified through two sets of examples.