# Overview of FEM-Based Resistance Models for Local Buckling of Welded Steel Box Section Columns
## 5 Evaluation of the Numerical Results  
### Comparison to Different Calculation Methods  
The primary objective of this research is to investigate the ultimate resistance of local buckling failure of square-welded box sections subjected to pure compression and analyze the difference between the experimental and computed buckling resistances. Four approaches were studied: (i) analytical expression provided by EN1993-1-5 [4], (ii) alternative analytical calculation based on Annex B of EN 1993-1-5 [4], (iii) numerical model utilizing equivalent geometric imperfection (b/200) to cover the residual stresses and initial geometrical imperfection together, and (iv) advanced computation model which incorporates residual stress patterns and realistic geometric imperfections using the models analyzed in Section 4. The ultimate resistance provided by all calculation methods was compared to the experimental specimens available [1,3,5,5,10,11,12,14,21]. The results of the ultimate resistances ratios for 124 test results are shown in Table 10. The obtained data points are also plotted in function of relative slenderness in Figure 13. The vertical axis of the first four diagrams shows the results of the experiments and the horizontal axis shows the buckling resistance calculated by the four different design methods (two analytical and two numerical methods). The diagram e and f compares the standard-based resistances to the FEM-based values. Figure 11: Load–displacement curve for 100 \(\times\) 3.05 mm square section, experimental data is from [1]. Figure 12: Load–displacement curve for 200 \(\times\) 6 mm square section, experimental data is from [6]. Figure 13: Resistance ratios in function of relative slenderness: (**a**) experiment compared to EN 1993-1-5 [4], (**b**) experiment compared to advanced FEM, (**c**) experiment compared to EN 1993-1-5. Annex B [4], (**d**) experiment compared to FEM with equivalent imperfection, (**e**) EN 1993-1-5 [4], compared to advanced FEM, and (**f**) EN1993-1-5 Annex B [4] compared to advanced FEM. Comparing Figure 13a,b, results show that for slender sections, EN1993-1-5 [4] are always on the safe side and for stockier sections the calculated resistance is a good approximation of the average resistance. The advanced FEM effectively provides the expected value of the real resistance for every slenderness region within a \(\sim\)10% range. The results shown in Figure 13c prove that the application of the Annex B curve is more on the safe side than the Winter-type buckling curve of the EN 1993-1-5 code [4] and the application of this buckling curve leads to a generally safe side resistance, especially for slender cross-sections. Figure 13d shows that the application of b/200 as equivalent geometric imperfections leads to safe side resistance for stocky plates and unsafe side values for slender columns. This observation proves that the value of the equivalent geometric imperfection needs to be revised and its accurate value should be slenderness-dependent. Comparing Figure 13e,f, results indicate the local buckling resistance determined by EN1993-1-5 [4] is conservative when it is compared to the resistance values obtained using an advanced computational model for the entire range of plate slenderness analyzed. Conversely, the computational approach outlined in EN1993-1-5 Annex B [4] demonstrates similar resistance to the values obtained by advanced computational models for stocky plates, while exhibiting a reduction in resistance capacity for slender plates. Utilizing the data gathered throughout this project, Figure 14 displays the normal distribution of the ultimate local buckling resistance ratio from the analyzed methods for welded square box sections. The results show that GMNIA modeling incorporating geometric imperfection based on the Somodi_mod model (see Equation (19)), and the residual stress pattern based on 2021_mod model (see Equation (21)), provide the most accurate prediction for the load capacity, with a smaller standard deviation compared to the other methods analyzed.