# Seismic Design and Ductility Evaluation of Thin-Walled Stiffened Steel Square Box Columns
## 7 Conclusions  
This study examined the cyclic behavior of prismatic thin-walled, stiffened steel square box columns, which model bridge piers, using finite element (FE) analysis with the commercial software ABAQUS, focusing on local, global, and local-global interactive buckling phenomena. The analysis employed the 2 SM model to capture material nonlinearity under cyclic loading. The 2 SM model offers a more accurate representation of the cyclic elasto-plastic behavior of structural steel compared to existing material models in ABAQUS. It effectively incorporates cyclic effects within the yield plateau, accounting for their reduction and eventual disappearance, as well as the cyclic strain hardening of the material. Key design parameters investigated included the width-to-thickness ratio (\(R_{f}\)), the slenderness ratio (\(\lambda\)), and the axial load ratio (\(P/P_{y}\)). The study led to the following conclusions:  
FE Analysis Accuracy: The FE analysis using ABAQUS and the 2 SM model (implemented via a UMAT subroutine) accurately captured column behavior under cyclic loading, closely matching experimental results. The thin-walled columns showed minimal variation when the FE model included a multi-linear kinematic hardening model. Local buckling was observed in thin-walled steel tubes, with geometric attributes influencing cyclic behavior more than material non-linearities, especially for thin-walled sections susceptible to local buckling. Significant differences in strength and ductility were found in compact columns when using different material models, as the material nonlinearity governs the column behavior in the absence of local buckling. Effect of Axial Loads: Axial loads up to 20% of the yield load (\(P_{y}\)) had a negligible effect on the ultimate strength of the columns. However, higher axial loads (exceeding 30% of \(P_{y}\)) significantly lowered buckling, post-buckling, and ductility of the impacted columns. Parametric Study Results: The ultimate lateral strength of thin-walled, stiffened steel square box columns was achieved when lateral displacement reached \(5\delta_{y}\). Beyond this point, strength decreased due to the local buckling of the component plates. Increasing both \(R_{f}\) and \(\lambda\) resulted in lower ultimate lateral strength and ductility. Design Equations: New design equations were introduced to predict ultimate lateral strength, maximum lateral displacement, and post-buckling displacement. These equations offer a practical approach for designing thin-walled, stiffened steel square box columns for bridge piers. Validation of Design Equations: To validate the proposed design equations, two columns were designed, and their ultimate lateral strength and displacement values were confirmed through FE analysis. The design equations achieved 95% accuracy in predicting ultimate lateral strength and 97% accuracy in predicting ultimate lateral displacements. The discrepancies between the FE predictions and experimental results were 5% for strength and 3% fortod ductility. Conceptualization, I.H.P.M. ; Methodology, I.H.P.M. ; Software, I.H.P.M. ; Validation, M.N. and I.H.P.M. ; Formal analysis, M.N. and I.H.P.M. ; Investigation, I.H.P.M. ; Resources, I.H.P.M. ; Data curation, M.N. and I.H.P.M. ; Writing--original draft, M.N. and I.H.P.M. ; Writing--review & editing, I.H.P.M. ; Visualization, M.N. and I.H.P.M. ; Supervision, I.H.P.M. ; Project