# Overview of FEM-Based Resistance Models for Local Buckling of Welded Steel Box Section Columns
## 2 Literature Review
### Further Related Research Activities
Figure 1: Manufacturing possibilities for welded box sections (b is outer width, b\({}_{0}\) is inner width) [20]. Altogether, 124 unique experimental results were collected for basic square cross-sections; these are used and evaluated in Section 5. For 22 of the collected experiments, the actual residual stress patterns were also measured and published. These experimental data are used for the following:  
1. To validate the numerical model;
2. To evaluate the already existing models;
3. To develop a new proposal for improved imperfections and a residual stress pattern. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Total Number of Tests** & **Failure by Local Buckling** & **Section Type** & **f\({}_{\mathbf{y}}\) [MPa]** & **Loading Type** \\ \hline  & & & & 441.3 & \\  & & & & 471 & \\ [PERSON] (2004) [1]. & 49 & 24 & 1 & 772.7 & Quasi-static \\  & & & & 794 & Deformation-controlled \\  & & & & 1335 & \\  & & & 1350.7 & \\ \hline [PERSON] et al. & & & & & \\ (1998) [2]. & 11 & 6 & 2 & 282 & \begin{tabular}{c} Quasi-static \\ Displacement-controlled \\ \end{tabular} \\ \hline [PERSON] and & & & & & 561 & \\ [PERSON] (2015) [3]. & 32 & 8 & 2 & 610 & Quasi-static \\  & & & & 760 & Displacement-controlled \\  & & & & 991 & \\ \hline [PERSON] et al. & & & & 1100 & \\ (2018) [5]. & 12 & 12 & 1 & 1121 & no data \\ \hline  & & & & 562 & \\  & & & & 610 & \\ [PERSON] (2017) [6]. & 26 & 16 & 2 & 760 & Quasi-static \\  & & & & 980 & Displacement-controlled \\  & & & & 991 & \\ \hline [PERSON] and & & & & & \\ [PERSON] (1992) [7]. & 6 & 3 & 1 & 670 & \begin{tabular}{c} Quasi-static \\ Displacement-controlled \\ \end{tabular} \\ \hline [PERSON] et al. (2014) [8]. & 4 & 4 & 2 & 460 & Displacement-controlled \\ \hline [PERSON]. et al. (1987) [9]. & 13 & 13 & 3 & 248.6 & \
\begin{tabular}{c} Quasi-static \\ Displacement-controlled \\ \end{tabular} \\  & & & & 261.2 & Load-controlled \\ \hline [PERSON] (1981) [10]. & 13 & 12 & 3 & 743.8 & Load-controlled \\ \hline [PERSON], and [PERSON]. & & & & 273.1 & \\ (1967) [11]. & 8 & 8 & 2 & 266.1 & Displacement-controlled \\  & & & & 714.3 & \\  & & & & 799.8 & \\ \hline [PERSON] et al. (1989) [12]. & 6 & 6 & 3 & 268 & Static \\  & & & & 353 & Displacement-controlled \\ \hline [PERSON] et al. (1992) [14]. & 3 & 3 & 3 & 266 &
\begin{tabular}{c} Cyclic \\ Load-controlled \\ Displacement-controlled \\ \end{tabular} \\ \hline [PERSON], and & & & & 250 & \\ [PERSON] (1975) [21]. & 17 & 9 & no data 1 & 275 & no data 1 \\  & & & 312 & 403 & \\ \hline \hline \end{tabular}  
* Experimental values of [PERSON], and [PERSON] (1975) [21] were taken from the [PERSON] (2017) [6] research program.  
\end{table} 
Table 1: Summary table of experimental data. The current research program focuses on the square welded box section columns, where welding seams are in the four corners of the cross-section. An interesting research program on parallelogram-shaped hollow-section girders was reported by [PERSON] et al. in [22] and one on octagonally shaped tubular steel columns under uniaxial compression was reported by [PERSON] et al. [23]. There are also numerous research reports on the structural behavior of cold-formed hollow section columns, which have a significantly different manufacturing process, indicating different residual stress pattern and geometric imperfection magnitudes to the members. Comprehensive studies on this topic can be found in [24; 25; 26; 27; 28] in this topic, including the material properties and residual stress patterns, buckling capacity against local buckling and global buckling. The manufacturing method of the cold-formed sections can be different and several previous investigations have showed that the manufacturing process has a significant effect on the residual stress distribution and intensity. There are two common manufacturing methods for the cold-formed hollow sections, called in the international literature \"direct forming\" and \"continuous forming--indirect way from circular-to-square rolling\".