## 1 Introduction  
In modern metal construction, thin-walled lightweight components that are sensitive to local stability loss are increasingly being used. Local buckling of a thin-walled member causes lateral (in relation to the direction of compressive stress) displacement of the component walls of the cross-section. This reduces the load capacity of the critical cross-section, which reduces the resistance of the entire structural member. In the European Eurocode 3 (EC3) [1; 2; 3] standards, cross-sections that are subjected to local buckling (in the elastic range) are included in Class 4 cross-sections. The classification of a steel cross-section into Class 4 is based on a comparison of slenderness (b/t) of separated component walls of the section with the limit values for Class 3. In the event the limits of at least one of the component walls being exceeded, the cross-section is qualified as Class 4, which implies the need to include the effects of local buckling in the calculation model. However, an interest in thin-walled members is currently growing due to a significant reduction in the weight of structural steel cross-sections. For example, hot-formed bisymmetric sections (e.g., IPE, HEB), much lighter cold-formed open sections (monosymmetric or compound cross-sections, e.g., two-branch cross-sections), or bisymmetrical box sections can be used for supporting elements of light halls, floor beams, trusses, columns, or purlins. This approach reduces the weight of the structure. The use of steels with ever higher strength as well as modern automatic welding technologies also affects the development of thin-walled welded I-sections. Such Class 4 bisymmetrical and monosymmetrical welded cross-sections are characterized by low weight, with an analogous degree of reliability of the structural member in relation to hot-formed members. From the point of view of the occurring instability phenomena, I-section beams may be subject to local buckling and lateral torsional buckling, including flexural-torsional loss of stability with the so-called forced rotation axis (e.g., wind suction purlin or from gravity loads in the supporting segment of continuous beams). This is due to the fact that thin-walled open cross-sections are characterized by low wall stiffness to local buckling and low rigidity of the whole cross-section to torsion [4; 5]. However, a forced rotation axis at lateral-torsional buckling, e.g., with a suitably rigid cover, results in a significant increase in critical moment and, in many cases, the adverse effects of lateral-torsional buckling can be neglected. Therefore, in the Class 4 thin-walled I-section beams, protected against lateral buckling, the influence of local stability loss remains, especially because thin-walled I-cross-sections are much less resistant to local buckling than, for example, box cross-sections [6]. This results from the fact that in such a cross-section there are cantilever walls, which are much less resistant to buckling in relation to internal walls [7; 8] or cantilever walls with a stiffening bend [9]. However, the use of I-sections (in relation to box sections) allows for simpler shaping of connections and nodes due to free and double-sided access, e.g., to bolt joints. Moreover, continuous beam systems, due to the favourable longitudinal distribution of bending moments, enable the effect of longitudinal stress variation to be used in local stability analysis [10]. The resistance of a thin-walled cross-section is determined using the effective width method [3]. This method consists of determining the critical stresses of local buckling (\(\sigma_{cr}=k\alpha_{E}\), where \(k\) is the plate buckling coefficient) for individual cross-section walls, assuming their hinged support and constant distribution of stresses along the member length.