# 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
#### 4.2.5 Validation Using the Improved Residual Stress Model  
The 22-specimen data pool was tested with the new version of the residual stress distribution model. The results when using the initial imperfection model presented by [PERSON] and [PERSON] [42] are shown in Table 5, and the results from the new model for initial local imperfection developed in this work,\"2021_mod\", are presented in Table 6. In the case of the ECCS model, the adjustment made was to ensure the residual stress equilibrium. As shown in Table 2, lengths of the tensile and transition zones maintained a ratio of 1 without considering the grade of the material or plate dimensions. Table 8 shows the force equilibrium of each individual plate. For this comparison, experimental data collected were used, and for all of them, the magnitude of compressive residual stress was set to 0.29 fy. It is evident that the original model does not guarantee force equilibrium. Therefore, adjustment involved solving the equation system for force equilibrium. As specimens have a wide range of material yield strength and geometrical features, it is necessary to adjust the lengths of the zones one by one. Results are shown in Table 8. This modified model started from ECCS [44] model is referred under the name \"ECCS_Eq\". A sample data pool was tested using this new model. Table 5 contains the results from the model for geometric imperfection presented by [PERSON] and [PERSON] [42], and Table 6 contains the results when applying the realistic imperfection model \"2021_mod\". Both models, \"ECCS_Eq\" and \"Somodi_mod\", have more accurate results compared to the original versions. In order to take the definitive residual stress distribution model and realistic geometric imperfection model couple and to conclude the validation of the computational model, residual stress models were taken into consideration using the actual residual stress values presented in the academic investigations. The stress pattern was taken into consideration based on the corresponding residual stress models; the shape \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Research Work**} & \multirow{2}{*}{**b/t**} & \multirow{2}{*}{**f\({}_{\text{fy}}\) [MPa]**} & \multicolumn{4}{c}{**ECCS Model**} & \multicolumn{4}{c}{**ECCS\_Eq Model**} \\ \cline{4-9}  & & & & **a** & **b** & **Force-Remain** & **a** & **b** & **Force-Remain** \\  & & & & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[**N]** \\ \hline W72-0b & [PERSON] & (2004) [1] & 26.8 & 772.7 & 6.14 & 6.14 & \(-\)6213.71 & 8.21 & 8.21 & \(-\)4.4 \\ \hline \multirow{2}{*}{\#3} & [PERSON] et al. & (1998) [2] & 75.0 & 282.0 & 6.43 & 6.43 & \(-\)6136.38 & 12.06 & 12.06 & 1.6 \\ \hline T2A-T2B & [PERSON] et al. & (1967) [11] & 25.5 & 714.3 & 9.75 & 9.75 & \(-\)7309.76 & 12.39 & 12.39 & \(-\)6 \\ \hline S.52.10 & [PERSON] et al. & (1989) [12] & 53.4 & 353.0 & 9.15 & 9.15 & \(-\)4186.40 & 12.21 & 12.21 & \(-\)3.1 \\ \hline \end{tabular}
\end{table} 
Table 8: Force equilibrium on plates applying ECCS residual stress model. parameters needed for the residual stress model were computed using the actual input data. Results are shown in Table 9, which were obtained using all the specimens that present actual measures for a total of 22 specimens. The results show that the modified RS models always perform better than their original versions, and it can be seen that the 2021_mod is the geometrical imperfection model that provides the most accurate results if the RS values are considered based on the measured values. The accuracies were 1.012 and 0.993, respectively, for the ECCS_RS pattern and for [PERSON]'s RS pattern. An overview of the scenarios tested during in the validation process is presented in Figure 10.  
Based on the result, the best residual stress distribution model is the \"Somodi_mod\" that was developed in this work, paired to the geometrical imperfection model \"2021_mod\" that was also developed in this research.