This study develops a displacement-based finite element approach using one-element modeling to analyze the second-order inelastic local buckling of steel columns under axial compression. To account for local buckling, two new stress-strain relationships are proposed for steel using an energy method and assumptions from previous studies for both compact and slender cross-sections. Stress-strain curves of post-buckling regimes are modeled as nonlinear curves. Both geometric and material nonlinearity are considered in the buckling analysis. The effects of geometric nonlinearity are traced through stability functions. The tangent stiffness of steel members is continuously updated during the nonlinear analysis by updating the fiber behavior at monitoring cross-sections using the Gauss-Lobatto integration rule. The proposed stress-strain relationships accurately predict the ultimate strength, elastic, and inelastic local buckling behaviors of steel columns under axial compression, compared with ABAQUS and previous studies. The model accurately predicts elastic, inelastic, and ultimate strength behaviors, with post-buckling responses closely matching ABAQUS results (e.g. 0.881 (proposed with residual stress), 1.008 (proposed without residual stress) vs. 0.948 (ABAQUS) load ratio for HB3 specimen). This approach offers significant computational efficiency (~1.0 sec vs. 20–30 min for ABAQUS) and introduces adjustable constitutive models, enhancing practical design applications for steel structures. This study proves that the effects of residual stress on the local buckling cannot be ignored in the case of slender sections, since the differences of the ultimate load (with and without the initial residual stress) are equal to 63.3% for the HI4 specimen and 43.2% for the HS40-SH(B) specimen.
Nguyen et al. (Mon,) studied this question.