# Seismic Design and Ductility Evaluation of Thin-Walled Stiffened Steel Square Box Columns
###### Abstract  
This paper investigates the seismic performance of thin-walled stiffened steel square box columns, modeling bridge piers subjected to unidirectional cyclic lateral loading with a constant axial load, focusing on local, global, and local-global interactive buckling phenomena. Initially, the finite element model was validated against existing experimental results. The study further explored the degradation in strength and ductility of both thin-walled and compact columns under cyclic loading. Thin-walled, stiffened steel square box columns exhibited buckling near the base, forming a half-sine wave shape. The research also addresses discrepancies from different material models used to analyze steel tubular bridge piers. Analysis using a modified two-surface plasticity model (2 SM) yielded results closer to experimental data than a multi-linear kinematic hardening model, particularly for compact sections. The 2 SM, which accounts for cycling within the yield plateau and strain hardening regime, demonstrated enhanced accuracy over the multi-linear kinematic hardening model. Additionally, a parametric study was conducted to assess the impact of key design parameters--such as width-to-thickness ratio (\(R\)), column slenderness ratio (\(\lambda\)), and magnitude of axial load (\(P/P_{y}\))--on the performance of thin-walled stiffened steel square box columns. Design equations were then developed to predict the strength and ductility of bridge piers. These equations closely matched experimental results, achieving an accuracy of 95% for ultimate strength and 97% for ductility. thin-walled; stiffened; steel; square box section; multi-linear kinematic-hardening rule; modified two-surface model; cyclic loading; buckling; strength; ductility +
Footnote †: journal: Applied  
Acticle Seismic Design and Ductility Evaluation of Thin-Walled Stiffened Steel Square Box Columns Applied  
structures differ markedly from building columns, often failing due to local buckling in thin-walled members, irregular distribution of story mass and stiffness, strong beams and weak columns, low rise (one to three stories), and the need for residual displacement evaluations. Consequently, thin-walled steel box columns in bridge piers are particularly susceptible to damage from local and overall interaction buckling during severe earthquakes [31; 32; 33; 34]. For example, Figure 1 depicts the performance of thin-walled steel box section bridge piers during the Hyogoken-Nanbu earthquake near Kobe City, Japan, on 17 January 1995. The steel bridge piers with rectangular box sections experienced collapse, weld seam tearouts, and severe local buckling damage, as shown in Figure 1[32; 33]. Local buckling was observed near the base of the column (Figure 1c). Post-Kobe earthquake research has increasingly focused on steel tubular columns with various cross-sections subjected to constant axial loads and cyclic lateral loads in one or multiple directions. To enhance the seismic capacity of steel bridge piers with tubular box sections, researchers have investigated both experimentally and theoretically the stability and plastic ductility of steel tubular columns [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52]. The strength of these tubes is influenced by local buckling of the tube walls, which depends on the slenderness of the plate elements forming the tube. Local buckling patterns in rectangular or square bare steel tubes can include inward and outward buckles (see Figure 1c), which are considered in major steel design specifications. Thin-walled steel tubular columns typically experience local buckling near the base at heights corresponding to the diameter and width of circular and square thin-walled columns, respectively [2; 32; 33; 34; 35; 36].