## 4 The Idea of the Critical Plate Method (CPM)  
The idea of the critical plate method [10] consists of determining the buckling stress of the weakest component plate of the cross-section, taking into account its elastic restraint in adjacent plates (walls),for which the buckling stresses are higher. In addition, the method allows the effect of longitudinal stress variation to be taken into account. In this computational model, the so-called critical plate (CP) must be identified, which determines the local buckling of the section in a given loading condition. The elastic restraint against longitudinal edge rotation of the CP results from the action of the adjacent restraining plate (RP). For example, for certain proportions of the bending I-section [10], the critical plate may be a compressed cantilever wall of the width \(b_{s}\) as a outstanding part of the flange width \(b_{f}=2b_{s}\), and the restraining plate will be a web of height \(h_{w}\). The buckling stress for the CP so determined is higher than that determined under the assumption of its simple support. This is especially true for cantilever plates, for which the elastic restraint against rotation of the longitudinal supported edge significantly affects the buckling stress values. The difference in plate buckling coefficients for an uniform compressed cantilever plate between a hinged support (\(k_{o}=0.43\)) [3] and a fully restrained support (\(k_{o}=1.25\)) [7; 19] is almost threefold. In References [19; 21], attention was paid to the additional phenomenon of the so-called mutual constraint of the component walls of the cross-section (affecting the increase of buckling stress), despite the fact that the theoretical critical stresses of individual walls (determined under the assumption of their hinged support) are equal. This was found to be due to the different buckling lengths of the internal and cantilever plates. Therefore, in Reference [21], approximation formulas for the local buckling half-wavelengths of the full cross-section were derived. This length is between the buckling length for a separate, simply supported, and fully restrained plate, on which the critical resistance of the full cross-section depends. Knowledge of local buckling half-wavelengths is useful for the direct definition of geometric imperfections in analytical and numerical models. On the other hand, in Reference [10], it was assumed that in a thin-walled section where thought-separated hinge-supported walls theoretically have the same buckling stresses, the effect of mutual constraint is insignificant (i.e., increases the buckling stress from 5 to 20%) and can be conservatively ignored. On this basis, so-called \"zero\" cross-sections were defined, in which the thought-separated hinge-supported plates have the same buckling stresses, and the resistance of such cross-sections can be calculated according to the standard procedure [1; 3]. The distinction between \"zero\" and \"non-zero\" cross-sections significantly simplifies the identification of the critical plate in the latter and allows for a slightly conservative (safe) estimation of the buckling stress. Therefore, the elastic restraint coefficient of the CP in RP can be estimated using Equation (3) [10]  
\[\kappa=1/(1+2D_{s}/b_{s}C_{\theta}), \tag{3}\]  
where \(C_{\theta}\)rotational spring stiffness equal to the bending moment created during rotation by unit angle (\(C_{\theta}=M/\theta\)), \(b_{s}\)--CP width, \(D_{s}\)--plate flexural rigidity according to the formula  
\[D_{s}=\frac{Et_{s}^{3}}{12(1-\
u^{2})} \tag{4}\]  
where for \(E=210\) GPa and \(\
u=0.3\), it can be approximately assumed that \(D_{s}=19,200t_{s}^{3}\), \(t_{s}\)--CP thickness. The restraint coefficient according to Equation (3) varies from \(\kappa=0\) for simple support to \(\kappa=1\) for full restraint. When the above-mentioned effects are taken into consideration, it is possible to determine the critical stress causing the cross-section local buckling in a more accurate way.