# 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
#### 4.2.4 Improvement in Residual Stress Models  
The residual stress distribution model with second-best ultimate resistances ratio is the ECCS [44] model, the lengths of the tensile and transition zone maintain the same-value relationship at any steel grade and plate dimension causing that the force equilibrium on the plate is not always fulfilled. Therefore, the aim of the next step is to obtain lengths of the zone, which ensure the equilibrium of the plates. The residual stress model of [PERSON] et al. [48] will not be considered in further analysis due to the model was developed for 690 MPa steel box sections and the elementary residual stress distribution (see Figure 5) cannot allow convenient adjustments. To extend the applicability of the residual stress distribution model presented by [PERSON] et al. [20], the limitations presented in that research will be modified. Restrictions are presented below followed by how they were modified. The steel grade used in the research ranged from S235 to S960. The yield strength of the base material is used to set the length of the tensile zone, parameter \"a\" in Figure 9. Table 7 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **ECCS [44]** & **[PERSON] et al. [20]** & **[PERSON] et al. [48]** & **ECCS\_Eq** & **Somodi\_mod** \\  & **+ 2021\_mod** & **+ 2021\_mod** & **+ 2021\_mod** & **+ 2021\_mod** & **+ 2021\_mod** \\ \hline Mean & 1.084 & 0.976 1 & 0.947 & 1.039 & 1.003 \\ \hline Standard Deviation & 0.078 & 0.056 1 & 0.080 & 0.057 & 0.056 \\ \hline \hline \end{tabular}  
* Values obtained by evaluating 36% of 22-specimen data pool, applying limitations of original RS model.  
\end{table} 
Table 6: Validation of RS distribution models using “2021_mod” geometric imperfection model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **ECCS [44]** & **[PERSON] et al. [20]** & **[PERSON] et al. [48]** & **ECCS\_Eq** & **Somodi\_mod** \\  & **+ [PERSON] et al.** & **+ [PERSON] et al.** & **+ [PERSON] et al.** & **+ [PERSON] et al.** & **+ [PERSON] et al.** \\  & **[42]** & **[42]** & **[42]** & **[42]** & **[42]** \\ \hline Mean & 1.097 & 1.003 1 & 0.976 & 1.052 & 1.032 \\ \hline Standard Deviation & 0.068 & 0.065 1 & 0.079 & 0.064 & 0.087 \\ \hline \hline \end{tabular}  
* Values obtained by evaluating 36% of 22-specimen data pool, applying limitations of original RS model.  
\end{table} 
Table 5: Validation of RS distribution models using the Radwan and Kövesdi geometric imperfection model. shows the computed expression to define it from the original model. To complete the table, it is necessary to consider steel grades out the studied range. For values below S235, Equation (20) is applied, which is an extrapolation of the values between S235 and S355. For values above S960, zero is considered, because the material composition does not allow to reach the yields strength in the vicinity of the welding toe. The adjustments are shown in Table 7.  
The thickness range used in that research was between 4 and 12 mm, and the b/t ratio ranged from 9.7 to 62.5. Both parameters were related to the magnitude of compressive residual stress and the transition zone length (parameter \"c\", as shown in Figure 9). An adjustment was made to avoid the limitation of the b/t ratio as it should restrict the applicability range for plate thickness at the same time. The intensity of compressive residual stress depends on the b/t ratio, as given in Equation (9). Therefore, the adjustment made is to fix limits to the compressive residual stress. These bounds are derived from ECCS [44] model, where limits are set according to the welding process and b/t ratio. To choose an adequate value, analysis of the actual residual stress measures was conducted, which showed that the magnitude of the compressive residual stress ranged between 8% and 51% of the yield strength. Consequently, the first and second row of Table 2 were ignored, because in the practice the plates of welded box sections do not reach those values.