## 1 Introduction  
Due to high strength of steel, beams of this material used in structures are characterized by small thicknesses of section walls. Therefore, they are susceptible to various forms of stability loss. One of the basic forms of general stability loss of beams in bending is the lateral torsional buckling. Consequently, in the design of steel beams, lateral torsional buckling should be taken into account, as it can significantly reduce load-bearing capacity and affect the safety of the entire structure. In such cases, bisymmetrical I-sections are the most commonly used. This happens because, compared with other profiles of similar heights (e.g., C or Z sections), I-sections show considerable stiffness in warping torsion [1], which increases the beam resistance to the lateral torsional buckling. Inmetal structures, single-span beams are the most common, which is related to, e.g., ease of assembly. In many technically important cases, beam static schemes are found, in which beams are freely supported in bending with respect to the stronger axis of the section. Additionally, they are elastically restrained against warping and rotation relative to the weaker axis of the section at the supports. As a result, the calculation model widely used for such beams so far (i.e., theoretical fork support) leads to a gross simplification. In contrast, the model proposed in the paper, which takes into account the beam elastic fixing at support nodes, allows a much more accurate representation of actual boundary conditions. This produces a more accurate value of the critical moment of beam lateral torsional buckling, and more optimal design of such elements. The literature on different issues related to lateral torsional buckling (LTB) of beams is vast, yet in a majority of cases it focuses on the determination of critical moments with the assumption that fork support is used. For such idealised support conditions, among others, the impact of the following was investigated: (a) distribution of the bending moment [2; 3; 4; 5; 6; 7], (b) points at which various transverse loads are applied over the section height [2; 8; 9; 10; 11], (c) elastic restraint against torsion over the beam length [11; 12; 13; 14; 15; 16; 17], (d) geometric ratios of monosymmetric sections [3; 5; 9], (e) coped beams and \"incomplete\" end plates [18; 19; 20; 21; 22; 14; 23], and (f) point lateral bracings [16; 17; 24; 25; 26; 27]. In real steel structures (e.g., grades, frames or framework structures), however, complex support conditions of beams and girders occur. In addition to the elastic restraint against rotation about the major axis of the section (i.e., in the plane of the beam greater stiffness), a restraint of warping and rotation with respect to the minor axis in the support sections is also found. Theoretical, e.g., [14; 18; 19; 21; 22; 28; 29; 30; 31; 32; 33; 34], and also experimental investigations [20; 23; 30] indicate that taking into account the actual conditions of beam support at the structure nodes can significantly affect the value of the elastic critical moment. The problem of the beam elastic restraint at the support sections was analysed, among other, in studies [14; 19; 28; 29; 30; 32; 33; 34; 35; 36], but in most cases, they dealt exclusively with the elastic restraint against warping. [PERSON] and [PERSON] [30] were concerned with theoretical and experimental determination of the critical loading of beams stiffened with end plates at supports. The authors derived a formula for the critical moment for lateral torsional buckling in which a limited freedom of warping of the support sections was taken into account. The effect of the thickness of end plates on the value of the critical moment was shown in the graphs. Then, in study [14], the impact of various constructional details on the critical moment and the ultimate resistance of beams was analysed.