# Seismic Design and Ductility Evaluation of Thin-Walled Stiffened Steel Square Box Columns
###### Abstract
Research indicates that the ability of these piers to withstand severe earthquakes depends heavily on their strength and ductility [2; 15].To improve seismic performance, studies have explored incorporating stiffeners and diaphragms to enhance both strength and ductility [2; 6; 39; 40]. In response to the damage observed in steel bridge piers during the Kobe earthquake, a critical consideration in the seismic design and retrofit of steel tubular columns is to increase ductility while maintaining nearly unchanged ultimate strength [2; 31]. Therefore, understanding the cyclic inelastic behavior of thin-walled steel tubular columns is essential for developing rational performance-based seismic design methodologies and evaluating ductility. Finite element analysis (FEA) of thin-walled steel tubular columns has utilized both isotropic and kinematic hardening material models for cyclic analysis. The kinematic hardening model generally aligns better with test data compared to the isotropic hardening model [47; 49; 51]. However, it may overestimate strengths under cyclic loading [50]. To improve numerical accuracy, further investigation into additional material models, such as those implemented through ABAQUS-UMAT subroutines in FE ABAQUS 2023 software [52], is necessary. Recent advancements, particularly in Japan, have introduced  
Figure 1: The performance of the thin-walled steel box section bridge piers was during the Hyogoken-Nanbu earthquake near Kobe City, Japan, on 17 January 1995: (**a**) Collapsed thin-walled steel box column [32], (**b**) Tear-out of a weld-seam [32], (**c**) Damaged steel column [33]. alternative material models that better replicate test results, such as the fiber-based model with a failure segment [47]. FE analysis of cyclic behavior involves solving a system of non-linear equations derived from applied nodal forces and internal equivalent nodal forces [53; 54; 55]. The constitutive material model of structural steel is described using incremental plastic theory, which includes strength rules, yield criteria, flow rules, and criteria for plastic loading and unloading [56; 57; 58]. Accurate finite element methods are crucial for predicting the cyclic behavior of these structures. The modified two-surface plasticity model (2 SM), developed by [PERSON] et al. [6; 59; 58], which accounts for cyclic strain hardening and the reduction of the yield plateau and elastic range (Bauschinger effect) due to cyclic loading, was employed in the commercial software ABAQUS 2023 (ABAQUS-2 SM). This study aims to thoroughly investigate the stability behavior of cold-formed hollow steel box sections subjected to cyclic lateral loads combined with axial compression, focusing on local, global, and local-global interactive buckling phenomena. Thin-walled, stiffened steel square box columns are susceptible to damage from local buckling, global buckling, or a combination of both. Local buckling is influenced by the width-to-thickness ratio (\(R_{f}\)) of the flange plate, while flexural buckling is determined by the column's slenderness ratio (\(\lambda\)) [2]. Extreme seismic loads can cause significant damage or collapse due to these buckling modes [32; 33]. Large earthquakes generate substantial cyclic lateral loads, necessitating precise design parameters. This study employs ABAQUS-2 SM to validate the inelastic cyclic behavior of thin-walled, stiffened steel square box columns [45]. A parametric analysis assessed key design parameters, including steel material modeling, diaphragms, stiffeners, the width-thickness ratio for the flange (\(R_{f}\)), and the column slenderness ratio (\(\lambda\)). The study developed interaction equations for these parameters, facilitating a safe and cost-effective design approach for thin-walled, stiffened steel square box columns used in bridge piers.