## 8 Summary and Conclusions  
The new calculation model presented in this paper for the local stability loss of the first continuous beam span, consisting of separate local buckling analysis for the span segment (loaded with a non-linear \"convex\" bending moment distribution) and the support segment (in which the \"concave\" moment distribution was approximated by a linear distribution) was successfully verified by numerical simulations using the finite element method. To improve the accuracy of the calculation of the critical resistance of a continuous beam with a Class 4 cross-section (in which large stress gradients in the longitudinal direction are found), it was necessary to take into account both the effect of the mutual elastic restraint of the cross-section component plates, and the longitudinal stress variation. The use of the critical plate method (CPM) according to Reference [10] to determine the \"local\" critical resistance and the design ultimate resistance of a thin-walled I-section led to a more optimal design of such elements. In this method, a more accurate calculation model is used, which takes into account both the effect of mutual elastic restraint of the cross-section component plates and the effect of longitudinal stress variation. The increase in the resistance that occurs in this case, compared to the EC3 calculation, results from a more faithful representation of the behavior of the thin-walled structural member in the engineering calculation model. At the same time, it should be noted that taking into account the above effects has only a minor impact on the complexity of calculations, which can be easily algorithmized and presented as relatively simple spreadsheets. This is due, among other things, to the simplified identification of the so-called critical plate and the definition of the so-called \"zero\" cross-sections [10]. Such assumptions allow for a slightly conservative assessment of the cross-section resistance. In this sense, the CPM can be used both for preliminary design or verification of FEM calculations and, in many technically important cases, for basic design. The \"local\" critical resistance defines the range of pre-critical behavior of a section and constitutes the limit of validity of the thin-walled bar theory with a rigid cross-section contour (the Vlasov theory), assuming unlimited elasticity of the material. To determine the design ultimate resistance of a thin-walled cross-section, the effective width method applied to the individual plates can be used along with the additional assumptions formulated in Section 5, Step 12. The relative slenderness of the component plates is determined from the respective critical stresses. For CP, these are stresses determined by taking into account the restraint coefficient and longitudinal stress variation. For the RP, simple support and a constant stress distribution along the length can be assumed on the same edge. Such assumptions allow for a technically precise and sufficient calculation of the resistance of a thin-walled cross-section. In the case of a continuous beam under uniform load, the segment that determines the resistance of the structure is the support segment (\(M_{s}\)) of the first span, where the \"local\" critical resistance is first achieved, followed by the design ultimate resistance. For the analyzed continuous beam made of a welded section I-300\(\times\)5\(\times\)250\(\times\)5 and calculated according to CPM (Section 7.2), a 121% increase in the critical resistance \(q_{cr}\) was determined, which translated into a 23% increase in the design ultimate resistance \(q_{eff}\) in relation to the calculations done according to EC3. In the case of the same continuous beam but made of a compound section 2C-250\(\times\)250\(\times\)4 and calculated according to CPM, there was a 158% increase in the critical resistance \(q_{cr}\), which translated into a 22% increase in the design ultimate resistance \(q_{eff}\) in relation to the calculations done according to EC3.