_Article_  
Local Buckling and Resistance of Continuous Steel  
Beams with Thin-Walled I-Shaped Cross-Sections  
[PERSON]*\({}^{\text{\textregistered}}\) and [PERSON]  
Faculty of Civil Engineering and Architecture, Kielce University of Technology, al. Tysiaclecia Paristwa  
Polskiego 7, 25-314 Kielce, Poland; [EMAIL_ADDRESS]  
* Correspondence: [EMAIL_ADDRESS]  
Received: 8 April 2020; Accepted: 23 June 2020; Published: 28 June 2020  
**Featured Application: The research results included in the paper can be widely used in designing thin-walled steel elements for use in construction. The use of the presented calculation model for the calculation of continuous beams allows for more optimal and economical design of sections of this element class under resistance conditions. In this model, the real behavior of thin-walled beams under load was taken into account much more precisely in relation to the Eurocode. This made it possible to use the resistance reserves resulting from the effect of longitudinal stress variation and the elastic restraint of the thin-walled cross-section walls.**  
**Abstract:** In modern steel construction, thin-walled elements with Class 4 cross-sections are commonly used. For the sake of the computation of such elements according to European Eurocode 3 (EC3), simplified computational models are applied. These models do not account for important parameters that affect the behavior of a structure susceptible to local stability loss. This study discussed the effect of local buckling on the design ultimate resistance of a continuous beam with a thin-walled Class 4 I-shaped cross-section. In the investigations, a more accurate computational model was employed. A new calculation model was proposed, based on the analysis of local buckling separately for the span segment and the support segment of the first span, which are characterized by different distributions of bending moments. Critical stress was determined using the critical plate method (CPM), taking into account the effect of the mutual elastic restraint of the cross-section walls. The stability analysis also accounted for the effect of longitudinal stress variation resulting from the varied distribution of bending moments along the continuous beam length. The results of the calculations were compared with the numerical simulations using the finite element method. The obtained results showed very good congruence. The phenomena mentioned above are not taken into consideration in the computational model provided in EC3. Based on the critical stress calculated as above, \"local\" critical moments were determined. These constitute a limit on the validity of the Vlasov theory of thin-walled bars. Design ultimate resistance of the I-shaped cross-section was determined from the plastic yield condition of the most compressed edge under the assumptions specified in the study. Detailed calculations were performed for I-sections welded from thin metal sheets, and for sections made from two cold-formed channels (2C). The impact of the following factors on the critical resistance and design ultimate resistance of the midspan and support cross-sections was analyzed: (1) longitudinal stress variation, (2) relative plate slenderness of the flange, and (3) span length of the continuous beam. The results were compared with the outcomes obtained for box sections with the same contour dimensions, and also with those produced acc. EC3. It was shown that compared with calculations acc. EC3, those performed in accordance with the CPM described much more accurately the behavior of the uniformly loaded continuous beam with a thin-walled section. This could lead to a more effective design of structures of this class.  
**Keywords:** thin-walled I-section; continuous beam; local buckling; longitudinal stress variation; design ultimate resistance of the cross-section