# Global Buckling Resistance of Cold-Formed Steel Beams with Omega-Shaped Sections
## 6 Conclusions  
The objective of this study was to assess the bending moment resistance to the global buckling of Cold-Formed Steel (CFS) omega-shaped profiles. Current design codes emphasize the importance of the elastic critical lateral-torsional buckling moment in evaluating the resistance to global buckling, ensuring the safety of steel members. To investigate this parameter's impact, we conducted a comparative analysis involving numerical simulations with various computational tools, namely ABAQUS, GBTUL, and CUFSM, as well as the analytical expression proposed in ENV 1993-1-1:1992 [19]. Our study focused on a selection of cold-formed omega-shaped profiles, chosen based on their height and thickness. When assessing the sectional bending moment resistances, we observed consistency among the European, Brazilian, and American standards. However, variations emerged when evaluating the bending moment resistance to global buckling. These discrepancies were linked to differences in assessing the critical lateral-torsional moment through various approaches, albeit to a lesser extent. Specifically, the bending moment resistance calculated according to Eurocode 3, using an analytical expression proposed in the past for hot-rolled profiles, exhibited a significant overestimation compared to numerical methods. Therefore, we draw a key conclusion regarding the inadequacy of using the standard analytical equation for evaluating the critical lateral-torsional buckling of laminated steel beams when predicting the critical moment of CFS omega-shaped profiles. The agreement \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Profile 70 \(\times\) 1.5 (L = 4.0 m)**} \\ \cline{2-7}  & \multicolumn{3}{c}{\(\mathbf{M_{b,Rd}}\) [2] (kN.m)} & \multicolumn{3}{c}{\(\mathbf{M_{Rd}}\) [4,6] (kN.m)} \\ \cline{2-7}  & **(Equation (3))** & **(GBTUL)** & **(CUFSM)** & **(ABAQUS)** & **(GBTUL)** & **(CUFSM)** & **(ABAQUS)** \\ \hline \(\Psi\) = 1.0 & 2.01 & 0.22 & 0.23 & 0.22 & 0.23 & 0.26 & 0.22 \\ \(\Psi\) = 0.5 & 2.13 & 0.29 & 0.29 & 0.28 & 0.30 & 0.29 & 0.29 \\ \(\Psi\) = 0.0 & 2.21 & 0.38 & 0.37 & 0.37 & 0.40 & 0.39 & 0.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Resistant bending moment to global buckling for the 70 \(\times\) 1.5 profile. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Profile 170 \(\times\) 2.0 (L = 6.0 m)**} \\ \cline{2-7}  & \multicolumn{3}{c}{\(\mathbf{M_{b,Rd}}\) [2] (kN.m)} & \multicolumn{3}{c}{\(\mathbf{M_{Rd}}\) [4,6] (kN.m)} \\ \cline{2-7}  & **(Equation (3))** & **(GBTUL)** & **(CUFSM)** & **(ABAQUS)** & **(GBTUL)** & **(CUFSM)** & **(ABAQUS)** \\ \hline \(\Psi\) = 1.0 & 12.13 & 0.78 & 0.74 & 0.78 & 0.78 & 0.74 & 0.78 \\ \(\Psi\) = 0.5 & 12.51 & 1.01 & 0.91 & 1.01 & 1.03 & 0.92 & 1.03 \\ \(\Psi\) = 0.0 & 12.84 & 1.38 & 1.20 & 1.38 & 1.42 & 1.23 & 1.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Resistant bending moment to global buckling for the 170 \(\times\) 2.0 profile. between GBTUL, CUFSM, and ABAQUS critical moments suggests their reliability for estimating the elastic critical lateral-torsional buckling moment. Certainly, GBTUL stands out for its simplicity, ease of application, and capability to incorporate various types of loading, rendering it a favorable option for evaluating this parameter. It is important to note that this study did not account for the beneficial effect of cladding sheets. These sheets are typically positioned beneath metal purlins to provide points of lateral restraint. Consequently, the bending moment resistance calculated using GBTUL, CUFSM, and ABAQUS may underestimate, in some cases, the capacity of CFS omega-shaped beams. To gain a comprehensive understanding, further experimental studies should consider more realistic loading and boundary conditions. Conceptualization, L.M., J.L.R.P. and J.M.C. ; Methodology, L.M., J.L.R.P. and J.M.C. ; Software, J.C. and J.A.E. ; Formal analysis, R.P., J.C. and J.A.E. ; Writing\(-\)original draft, R.P., J.C. and J.A.E.