# Global Buckling Resistance of Cold-Formed Steel Beams with Omega-Shaped Sections
## 1 Introduction
[PERSON], [PERSON], and [PERSON] [11] analyzed the structural behavior of cold-formed steel hat-section beams under non-uniform bending, using GBTUL and ABAQUS. [PERSON] et al. [12; 13] numerically evaluated the buckling behavior of hat-shaped sections with holes along the section. [PERSON], [PERSON], and [PERSON] [14] and [PERSON] et al. [15] conducted four-point bending tests on cold-formed steel beams with different innovative cross-sectional shapes to assess their potential instability modes. Furthermore, [PERSON] and [PERSON] [16] presented an extensive review of recent advancements in the design and analysis of cold-formed steel (CFS) under bending, highlighting the benefits of including intermediate reinforcements at the flange/web junction. The buckling behavior of cold-formed hat-shaped sections under bending has been experimentally investigated by [PERSON] et al. [17] and [PERSON] et al. [18]. However, despite the recent surge in popularity of CFS omega-shaped beams, the buckling behavior of these hat-section types, characterized by additional stiffeners along the section, has not yet been reported in any study, revealing a significant gap in the available scientific knowledge. The main goal of this study is to contribute to filling this gap, aiming to enhance the understanding of the structural behavior of CFS omega-shaped beams. Specifically, the focus is on evaluating the global buckling phenomenon as it represents a prominent failure mode in thin-walled elements with large spans. The primary objective of this study is to investigate the behavior of omega-shaped sections, specifically focusing on the global buckling phenomena. The assessment of bending moment resistance to global buckling is made using the European [2], Brazilian [6], and North American [4] standards. In the context of the European [2] provisions, the evaluation of global moment resistance relies on the effective elastic section modulus, determined using the method of effective widths, and a buckling resistance factor. This factor is a function of the normalized slenderness, which, in turn, depends on the critical elastic lateral-torsional buckling moment. Notably, the European code lacks an equation to estimate the critical moment for CFS members. As a common practice, engineers often resort to using the expression from ENV 1993-1-1:1992 [19], recommended for evaluating the critical lateral-torsional moment of hot-rolled profiles. The Brazilian [6] and North American [4] standards adopt the DSM. This method involves calculating the critical elastic local, distortional, and global buckling moments through an elastic buckling analysis, typically conducted using CUFSM [20; 21; 22]. The characteristic resistant bending moment is then determined as the smallest value calculated for global, local, and distortional buckling. If the profile does not exhibit local and distortional buckling modes in the analysis, the respective resistance corresponds to global buckling resistance, which is, again, directly related to the critical lateral-torsional moment. Therefore, assessing the bending moment resistance to global buckling in CFS omega-shaped profiles depends on evaluating their critical moments. To achieve this, we conducted a comprehensive comparative study involving numerical analyses, using different computational tools, namely ABAQUS [23], GBTUL [24], and CUFSM v5.05 [15], and the analytical expression proposed in ENV 1993-1-1:1992 [19]. The ABAQUS model served as our reference, validated against results obtained from an experimental campaign. Additionally, this campaign enabled us to compare the profiles' sectional resistance with the values derived from the European [2], Brazilian [6], and North American [4] standards.