## 2 Computational Model for Local Cross-Section Buckling  
The Class 4 cross-section calculation model according to European standards EC3 [1; 2; 3] assumes that all component plates of athe cross-section are hinge-supported at their bonding edges. This means that the plates do not interact with each other, and the local buckling of the whole cross-section is determined by the weakest separated plate (cross-section wall).  
However, in many technically important cases this model is too conservative, which has been confirmed by numerous experimental studies, e.g., References [5; 12; 13; 14]; theoretical studies, e.g., References [4; 7; 15; 16]; and numerical simulations, e.g., References [17; 18; 19; 20; 21; 22; 23]. This is due to the fact that in real thin-wall cross-sections, there is an effect of mutual, elastic interaction of component plates (walls).  
Further, the standard computational model assumes that after determining the relative slenderness of the individual simply supported plates, their respective effective widths are determined, which determine the effective cross-section of the thin-walled member. In the calculation according to EC3, the effect of longitudinal stress variation, which often occurs in practice (e.g., in continuous beams), is also ignored.  
In References [19; 21], the effect of the mutual elastic restraint of thin-walled section walls was considered. Various load cases were taken into account, ranging from axial compression to pure bending relative to both axes of the section gravity, including interactive loads. Very large sets of simulation results were analyzed via the finite strip method using CUFSM software [18]. Calculations  
Figure 1: Static model of a continuous beam end span with thin-walled I-section.  
were made for many load cases and approximate analytical formulas were proposed for determining the plate buckling coefficient \(k\)[19] and the local buckling half-wavelengths [21] for various types of hot-rolled and welded sections. In Reference [22], in turn, approximation formulas of the \(k\) coefficient for hot-rolled sections under simple loads (axial compression, bending relative to the stronger and weaker axis of the cross-section) were given. However, the solutions obtained in References [19; 21; 22] relate only to constant stress distributions over the length of the structural member.  
In References [7; 24; 25], the impact of longitudinal stress variation in the compressed cantilever plate (which is, for example, a component of an I-cross-section) was taken into account, but only for extreme support conditions (hinge or full restraint).  
Meanwhile, in Reference [26], the approximation formulas of the plate buckling coefficient k for an axially compressed cantilever plate with any degree of elastic restraint of the supported edge and longitudinal stress distribution according to the linear function and \(2^{\circ}\) parabola were derived. At the same time, graphs of \(k\) coefficients were determined in References [27; 28] for elastically restrained and eccentrically compressed cantilever plates with longitudinal stress variation. Many technically important load cases have been considered.  
Reference [10] presents a more accurate computational model of the effect of local buckling on the resistance of thin-walled cross-sections. The critical plate method (CPM) takes into account the effect of both the elastic restraint of the cross-section plates and that of longitudinal stress variation.