# Global Buckling Resistance of Cold-Formed Steel Beams with Omega-Shaped Sections
## 1 Introduction  
In steel constructions, the use of Cold-Formed Steel (CFS) profiles in beams is a well-established and widely adopted practice. CFS profiles offer numerous advantages, including a high strength-to-weight ratio, versatility in manufacturing across a diverse range of cross-sectional shapes, reduced material consumption, and straightforward on-site installation. These characteristics collectively make CFS a popular and sustainable choice for various construction applications. CFS beams feature a variety of cross-sectional shapes, with the most common being the channel section, Z section, and hat section. The latter is particularly noteworthy due to its ability to achieve larger clear spans compared to other sections. Additionally, by bending the flanges and the depth of the section, it is possible to significantly enhance its stiffness. A specific type of the hat section is the omega-shaped section, which incorporates multiple bends, enabling even larger structural spans and reduced vertical displacements. CFS members have been extensively investigated due to their inherent slenderness, featuring thin-walled open or closed cross-sections. This characteristic makes them highlysusceptible to various instability phenomena, including local (I), distortional (D), shear (S), and global (G) flexural or flexural-torsional buckling, as well as couplings between them (e.g., L-D, L-G, D-G, or L-D-G mode coupling/interaction). These instability phenomena significantly impact the overall structural response and ultimate strength of CFS members, justifying their inclusion in CFS specifications. Consequently, CFS members have played a crucial role in the development and widespread adoption of the Direct Strength Method (DSM) [1]. Traditionally, thin-walled steel members were designed against local buckling using the Effective Width Method (EWM), an approach still embedded in current versions of certain codes, such as Eurocode 3 [2; 3]. However, the evolution of increasingly complex cross-sectional shapes, coupled with the recognition of distortional buckling as a potential failure mode for cold-formed thin-walled members with lipped cross-sections, paved the way for the development of the DSM. In response to unsuccessful attempts to efficiently predict distortional failures using methods based on an \"effective cross-section\", a more rational approach was sought. This research effort led to the standardization of the DSM, initially in North America [4], and almost simultaneously included in the Australian/New Zealand Standard [5]. A few years later, the DSM approach was also incorporated into the Brazilian standards for CFS structures [6]. Numerous researchers have made substantial contributions to the development of the DSM. More recently, [PERSON] et al. [7] reported on the buckling and failure of cold-formed steel simply supported beams under uniform bending, considering three cross-section shapes: (i) lipped channels bending about the major axis, (ii) zed-sections under tilt bending, causing uniform flange compression, and (iii) hat-sections subjected to either major-axis or minor-axis bending. This study revealed that the current DSM design curve fails to adequately predict the failure moments of some analyzed beams. To address this, the authors proposed novel DSM strength curves, offering better predictions of all available numerical failure moments. In a subsequent study, [PERSON] et al. [8] introduced two DSM design approaches to account for local-distortional (L-D) buckling modes interactions for cold-formed hat-sections, demonstrating that the DSM is current suitable for evaluating the buckling modes of this type of section. Additionally, several recent studies have been conducted to experimentally assess instability modes in steel elements subjected to bending loads. [PERSON] et al. [9] and [PERSON] et al. [10] numerically investigated the elastic critical lateral-torsional buckling of steel beams under bending loads using the finite element software ABAQUS.