The study shows the results of theoretical investigations into lateral torsional buckling of bisymmetric I-beams elastically restrained against warping and against rotation in the plane of lateral torsional buckling (i.e., against lateral rotation) at the support nodes. The analysis accounted for the whole variation range of node stiffnesses, from complete warping freedom to full restraint, and from complete lateral rotation freedom to full restraint. It was assumed the beams are simply supported against bending about the major axis of the section. To determine the critical moment, the energy method was used. Both the twist angle function and the lateral deflection function of the beam were described using power polynomials with simple physical interpretation. Computer programmes were developed to make numerical and symbolic “computations”. General approximation formulas for the critical moment for lateral torsional buckling were derived. The formulas covered the basic and most frequently found loading diagrams. Detailed computations were performed for different values of the index of fixity against warping and against rotation in the plane of lateral torsional buckling. The critical moments determined using the programmes devised and approximation formulas were compared with the values obtained with LTBeam software (FEM). A very good congruence of results was found.

The study presents the results of theoretical investigations into lateral torsional buckling (LTB) of bi-symmetric I-beams, elastically restrained against warping at supports. Beam loading schemes commonly used in practice are taken into account. The whole range of stiffness of the support joints, from free warping to warping fully restrained, is considered. To determine the critical moment, the energy method is used. The function of the beam twist angle is described with power polynomials that have simple physical interpretation. Computer programs written in symbolic language for numerical analysis are developed. General approximation formulas are devised. Detailed calculations are performed for beams with end-plate joints. Critical moments determined with programs and approximation formulas are compared with the results obtained by other researchers and with those produced by FEM. Very good accuracy of results is obtained.

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.

This paper reports the results of the next stage of the authors’ investigations into the effect of the elastic action of support nodes on the lateral torsional buckling of steel beams with a bisymmetric I-section. The analysis took into account beam elastic restraint against warping and against rotation in the bending plane. Such beams are found in building frames or frame structures. Taking into account the support conditions mentioned above allows for more effective design of such elements, compared with the boundary conditions of fork support, commonly adopted by designers. The entire range of variation in node rigidity was considered in the study, namely from complete freedom of warping to complete restraint, and from complete freedom of rotation relative to the stronger axis of the cross section (free support) to complete blockage (full fixity). The beams were conservatively assumed to be freely supported against lateral rotation, i.e., rotation in the lateral torsional buckling plane. Calculations were performed for various values of the indexes of fixity against warping and against rotation in the beam bending plane. In the study, formulas for the critical moment of bilaterally fixed beams were developed. Also, approximate formulas were devised for elastic restraint in the support nodes. The formulas concerned the most frequent loading variants applied to single-span beams. The critical moments determined in the study were compared, with values obtained using LTBeamN software (FEM). Good compliance of results was observed. The derived formulas are useful for the engineering design of this type of structures. The designs are based on a more accurate calculation model, which, at the same time offers simplicity of calculation.