# Overview of FEM-Based Resistance Models for Local Buckling of Welded Steel Box Section Columns
## 1 Introduction  
Welded box section columns are used in many fields of the civil engineering industry; therefore, their appropriate design is crucial from economic and safety point of view. Welded box sections are commonly used in bridges, especially in steel arch bridges and for bracing systems. They are also commonly used for steel trusses in bridges and/or in buildings. In cases where steel sections are subjected to pure axial load, the plate slenderness emerges as a significant factor influencing the failure mode of steel member. It plays a crucial role in distinguishing between plastic failure and potential stability failures. A local buckling phenomenon limits the load-bearing capacity of the thin-walled sections based on the critical load. Additionally, stability problems are greatly influenced by residual stress patterns generated during the construction process and the geometric imperfections of individual plates and the entire structural element. The current design methods for calculating the reduction factor in local buckling have been subject to evaluation in academic research programs, revealing that they tend to yield outcomes that overestimate the load-bearing resistance. For instance, [PERSON]'s formula demonstrates an overestimation forplate slenderness values greater than 0.9, while for stocky plates with a plate slenderness below 0.9, it underestimates the values [1,2]. Similarly, the effective width approach tends to underestimate the resistance of square welded box section columns to local buckling within the stocky range, while it overestimates the resistance as slenderness increases [3]. Furthermore, the equivalent imperfection magnitude recommended in the EN1993-1-5 [4] provides conservative values for the ultimate load in thin-walled sections, especially in cases where stability interaction problems arise due to the consideration of residual stresses being double-counted. These findings and further research results show the need to improve the computational methods to design thin-walled cross-sections, while also maintaining their practicality and widespread applicability. In the context of local buckling, imperfections have a significant influence on the load-bearing capacity. Their magnitude and shape performs a pivotal role in determining whether the plate behaves in a column-like or plate-like manner, consequently affecting the ultimate buckling load capacity of the cross-section. Previous studies have demonstrated that high-strength welded steel box sections have a higher buckling load resistance than sections made using low-strength steel, even when the magnitude of residual stresses is higher [1,5]. In essence, it is the ratio of residual stress to yield stress that has more influence over the decrement of the local buckling load-bearing capacity than the magnitude of residual stresses themselves. Considering the substantial quantity of experimental results necessary for a comprehensive assessment of buckling phenomena, an expensive approach, the most suitable method of investigation involves the development of computational models that are properly verified and validated using existing experimental data. This approach opens a broad spectrum of possibilities for controlling the parameters that influence the buckling resistance. The aims of this paper are (i) to analyze and evaluate several residual stress and imperfection models to determine which combination of these gives the most accurate numerical model compared to test results, and (ii) to investigate which of the analytical resistance models give the best approach to the most accurate numerical results.