# Global Buckling Resistance of Cold-Formed Steel Beams with Omega-Shaped Sections
## 5 Global Buckling Bending Moment Resistance  
In this section, the bending moment resistance to the global buckling of the selected Cold-Formed Steel (CFS) profiles is assessed according to the European [2], Brazilian [6], and North American [4] standards. Only negative moment scenarios have been considered. First, the critical elastic lateral-torsional buckling moment using Equation (3), provided by ENV 1993-1-1:1992 [14], is calculated, and then, through the numerical models developed in ABAQUS, GBTUL, and CUFSM. As mentioned earlier in this paper, Equation (3) is recommended for evaluating the critical lateral-torsional moment of hot-rolled profiles. Due to the absence of an analytical expression for CFS profiles in the European code, practitioners often resort to using this expression. Regarding the numerical models, ABAQUS [16] is considered the reference model since it was validated with the results of the experimental campaign. It should also be noted that the critical moment obtained through the CUFSM [15] program was used to determine the resistance moment to global buckling by the Direct Strength Method (DSM), considering the modification factor \(C_{\text{b}}\) from Equation (8). Tables 4-6 show the results associated with load cases \(\psi\) = 1.0, \(\psi\) = 0.5, and \(\psi\) = 0.0, as illustrated in Figure 20. The modification factor \(C_{\text{b}}\) was utilized in correlation with the \(\psi\) in these cases. For each profile, the results for two span lengths were analyzed. Figure 19: CUFSM analysis results for the CFS 170 \(\times\) 2.0 omega section under upward loading. The analysis of Tables 4-6 led to the following observations:  
* The critical moment values obtained with Equation (3) are significantly overestimated when compared to those derived from numerical analyses using GBTUL, ABAQUS, and CUFSM. This overestimation is more pronounced for smaller spans. * When comparing the results obtained with GBTUL, ABAQUS, and CUFSM, a good correlation between the three numerical approaches is observed, with ABAQUS generally providing lower values of critical moments. An exception is noted for the intermediate profile (170 \(\times\) 2.0), where CUFSM leads to slightly lower values than ABAQUS and GBTUL. Nevertheless, for this profile, the values of ABAQUS and GBTUL are practically coincidental. Tables 7 and 8 present the bending moment resistance to global buckling obtained for the 70 \(\times\) 1.5 and 170 \(\times\) 2.0 profiles, computed according to the European [2], Brazilian [6], and North American [4] standards. The values are based on the critical moments obtained for the higher span lengths (\(L\) = 4.0 m and \(L\) = 6.0 m). It is noteworthy that the results for the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Loading Cases**} & \multicolumn{4}{c}{**Profile 300 \(\times\) 2.5 (\(L\) = 4.0 m)**} & \multicolumn{4}{c}{**Profile 300 \(\times\) 2.5 (\(L\) = 9.0 m)**} \\ \cline{2-9}  & \(M_{\text{cr}}\) & \(M_{\text{cr}}\) & \(M_{\text{e}}\) & \(M_{\text{cr}}\) & \(M_{\text{cr}}\) & \(M_{\text{cr}}\) & \(M_{\text{e}}\) & \(M_{\text{cr}}\) \\  & **(Equation (3))** & **(GBTUL)** & **(CUFSM)** & **(ABAQUS)** & **(Equation (3))** & **(GBTUL)** & **(CUFSM)** & **(ABAQUS)** \\ \cline{2-9}  & **kN.m** & **kN.m** & **kN.m** & **kN.m** & **kN.m** & **kN.m** & **kN.m** & **kN.m** \\ \hline \(\Psi\) = 1.0 & 576.30 & 4.56 & 4.44 & 3.51 & 113.84 & 1.41 & 1.37 & 0.97 \\ \(\Psi\) = 0.5 & 754.95 & 6.01 & 5.55 & 4.65 & 149.85 & 1.86 & 1.72 & 1.28 \\ \(\Psi\) = 0.0 & 1020.05 & 8.40 & 7.40 & 6.54 & 201.49 & 2.55 & 2.29 & 1.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the uplift critical moments for the 300 \(\times\) 2.5 profile.