# Overview of FEM-Based Resistance Models for Local Buckling of Welded Steel Box Section Columns
## 4 Verification and Validation of the Numerical Model
### Model Validation and Evaluation of Imperfection and RS Models
#### 4.2.2 Evaluation of Realistic Geometric Imperfection Models
This decision was made because the model was developed to be used in combination with a global imperfection factor. Additionally, investigation does not provide specifications about the hollow sections' manufacturing process nor consider residual stress distribution; values ranged between b/91 and b/1056. The model with the third-best result was presented by [PERSON] et al. [50]; since this model was developed considering welded sections under pure axial loading process and stress patterns generated during the manufactured process, it will be considered in the next validation step. Values ranged between b/670 and b/1223. The model presented by [PERSON] et al. in 2023 (pending publication) considers hybrid girders manufactured by the welding process, taking only a type 3 plate arrangement (see Figure 1); it will not be considered due to the specificity of that research. Finally, the value from BSI manual [52] was considered as the upper bound. The models used to establish a realistic geometric imperfection should be adjusted to narrow the range of the values provided by the mathematical expressions. It is evident that the magnitude of the initial geometric imperfection parameter cannot take values too high, because of the manufacturing tolerances. Therefore, it is necessary to set an upper bound. Computational analysis of the data using this limit was performed; results are given in Table 4.  
Since the model presented by [PERSON] and [PERSON] [42] considers a separated computing processes to set a value for NSS and HSS members, modification of them cannot be performed without a deep analysis of the process they used. The model presented by [PERSON] et al. [50] does not specify an upper limit value, but they do for the lower one. The adjustments of the model were to fix a new value for both the upper and lower bound. The actual lower limit was replaced by b/1000, and the upper limit was taken as b/125 from the BSI manual [52]. The rearrangement of the expression is shown in Equation (19). The new version of the model presented by [PERSON] et al. [50] was labeled as \"2021 mod\" and tested with the same data to compare the results to the original expression and to the other models in Table 4. This comparison was conducted to proceed with the validation of residual stress distribution models. Although the \"2021 mod\" model provides the best mean of the ultimate resistance ratio, this model and the model presented by [PERSON] and [PERSON] [42] will be tested further using different residual stress distribution patterns to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **b/125 [52]** & \begin{tabular}{c} **2021** \\ **Model [50]** \\ \end{tabular} & \begin{tabular}{c} **2023** \\ **Model** \\ \end{tabular} & \begin{tabular}{c} **[PERSON]** \\ **et al. [51]** \\ \end{tabular} & \begin{tabular}{c} **[PERSON]** \\ **et al. [42]** \\ \end{tabular} & \begin{tabular}{c} **2021\_mod** \\ \end{tabular} \\ \hline \hline \
\begin{tabular}{c} Mean \\ value \\ \end{tabular} & 1.095 & 1.070 & 1.100 & 1.076 & 1.052 & 1.039 \\ \hline
\begin{tabular}{c} Standard \\ deviation \\ \end{tabular} & 0.094 & 0.069 & 0.074 & 0.087 & 0.064 & 0.057 \\ \hline Min. & 0.933 & 0.989 & 0.996 & 0.937 & 0.933 & 0.941 \\ \hline Max. & 1.268 & 1.241 & 1.229 & 1.272 & 1.203 & 1.176 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of realistic geometric imperfection models. check if the ultimate resistance ratio, between numerical and experimental results, remains close to 1. \[\frac{\text{e}}{\text{b}}=\frac{-0.0513\times\left(\frac{\text{b}}{\text{t}} \right)+2.6131}{1000}\text{ with the assumption of }125\leq\frac{\text{e}}{\text{b}}\leq 1000 \tag{19}\]