# 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  
To obtain a geometrical imperfection model, an initial comparison was made using the residual stress model of ECCS, ensuring force equilibrium in the plate. This modified model addresses stress equilibrium in the plates, maintaining a ratio of 1:1 between the lengths of the maximum tensile residual stress and the transition zone from the tensile zone to the compression zone. The comparison of realistic geometrical imperfections was conducted using values from academic works and design standards. Initial results of load resistances are presented in Table 3; the statistical evaluation of the results is presented in Table 4. The table shows the resistance ratios between the numerical model and the experiment, calculated using Equation (18):  
\[\text{Resistance ratio}=\frac{\text{Experimental resistance}(\text{F}_{ \text{EXP}})}{\text{Ultimate computed resistance}(\text{F}_{\text{FEM}})} \tag{18}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multicolumn{2}{c}{\({}^{-}_{\mathbf{\lambda_{p}}}\)**} & \multirow{2}{*}{**Experiment**} & \multirow{2}{*}{**b/125 [52]**} & \multirow{2}{*}{**2021 Model [50]**} & \multirow{2}{*}{**2023 Model**} & \multirow{2}{*}{**[PERSON]**} & \multirow{2}{*}{**[PERSON]**} \\  & & & & & & & & **et al. [51]** \\ \hline \multirow{4}{*}{[1]} & 0.47 & 5460 & 5290 & 5357 & 5357 & 5357 & 5357 & 5357 \\  & 0.84 & 8923 & 8072 & 8746 & 8605 & 8761 & 8589 & 8844 \\  & 1.20 & 7035 & 6831 & 6919 & 6863 & 7049 & 6991 & 7018 \\  & 1.56 & 7579 & 7891 & 7500 & 7510 & 7888 & 7891 & 7924 \\ \hline \multirow{4}{*}{[2]} & 0.72 & 182 & 151 & 174 & 150 & 164 & 171 & 177 \\  & 1.09 & 184 & 176 & 173 & 171 & 178 & 178 & 177 \\  & 1.45 & 184 & 197 & 176 & 179 & 197 & 197 & 196 \\  & 1.80 & 211 & 214 & 173 & 178 & 211 & 214 & 211 \\ \hline \multirow{4}{*}{[3]} & 0.83 & 1833 & 1446 & 1677 & 1560 & 1492 & 1613 & 1687 \\  & 0.80 & 506 & 426 & 480 & 437 & 439 & 454 & 470 \\  & 0.86 & 1280 & 1070 & 1206 & 1126 & 1098 & 1159 & 1215 \\  & 0.93 & 1651 & 1311 & 1403 & 1353 & 1297 & 1372 & 1403 \\ \hline \multirow{4}{*}{[11]} & 0.83 & 1608 & 1417 & 1572 & 1506 & 1491 & 1500 & 1557 \\  & 1.18 & 1510 & 1580 & 1510 & 1516 & 1587 & 1587 & 1588 \\  & 1.40 & 3101 & 3008 & 2972 & 2975 & 3010 & 3008 & 3004 \\  & 0.77 & 2909 & 2530 & 2942 & 2834 & 2435 & 2830 & 2947 \\ \hline \multirow{4}{*}{[21]} & 0.65 & 381 & 329 & 378 & 342 & 354 & 368 & 379 \\  & 0.98 & 433 & 383 & 395 & 382 & 390 & 389 & 390 \\ \cline{1-1}  & 1.15 & 442 & 401 & 389 & 389 & 403 & 402 & 404 \\ \cline{1-1}  & 1.23 & 150 & 139 & 132 & 131 & 139 & 139 & 139 \\ \cline{1-1}  & 1.44 & 160 & 144 & 129 & 130 & 144 & 144 & 143 \\ \cline{1-1}  & 1.64 & 159 & 153 & 151 & 152 & 151 & 153 & 151 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Resistance values with different imperfection models—in [kN]. The model with the mean resistances ratio closest to 1 was presented by [PERSON] and [PERSON] [42], since this model was developed for welded box sections facing local buckling failure and already incorporates upper bound following the BSI manual [52]. This model will be considered in the next validation step; the imperfection amplitude ranged from b/125 to b/533. The model with the second-best mean was presented by [PERSON] et al. [51]. The reason to choose these models was that based on the literature review, these proposals were the most recent models having significant research background (test-based and numerical model-based origins) according to the international literature. The imperfection models referred to in Tables 3 and 4 are introduced in Section 3.4.3. The given notations refer to the following equations: (i) b/125--Equation (15); (ii) 2021 model--Equation (11); (iii) 2023 model--Equation (16); (iv) [PERSON] et al. [51]--Equation (14); [PERSON] et al. [42]--Equations (12) and (13); 2021 mod--Equation (19). Although it provided acceptable results, this model was excluded from the further evaluation process.