Abstract
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.
Highlights
Lateral torsional buckling (LTB) of steel beams commonly used in general or industrial construction is an issue that has been examined by researchers for many years
Idealised boundary conditions of that type were taken into account to investigate the effect of the following: (a) the distribution of the bending moment over the beam length, e.g., [1,2,3,4,5,6], (b) the coordinates of the points of transverse load application over the height of the cross section, e.g., [1,7,8,9,10], (c) discrete restraint against displacement and/or the cross sections’ torsion over of the beam length, e.g., [11,12,13,14,15,16,17,18], (d) LTB of monosymmetric cross sections [2,4,8,19], (e) the use of complete and incomplete end plates [20,21,22], (f) coped beams [20,21,23,24,25,26,27], effect on the LTB critical moment, (g) modification of the energy equation leading to a nonlinear analysis of eigenvalue problem [28], and (h) interaction between buckling and LTB of beam columns [29,30,31,32]
In the analysis of elastically restrained beams, this approach causes difficulties when describing the degree of elastic fixity of beam support cross sections. In their previous studies [50,52,60], the authors utilised an alternative method for the description of beam displacements upon a loss of stability, namely employing power polynomials with a simple physical interpretation. This approach facilitates the description of the torsion angle function and beam lateral deflection when the conditions of its elastic restraint against warping and lateral rotation in the support nodes are taken into account
Summary
Lateral torsional buckling (LTB) of steel beams commonly used in general or industrial construction is an issue that has been examined by researchers for many years. According to the authors’ knowledge, apart from [23,57], the literature on the subject does not offer unambiguous analytical formulas for the LTB critical moment, which would simultaneously take account of the effect of elastic restraint against warping and elastic restraint against rotation relative to the major axis in support cross sections Such calculations can be performed using the finite element method, e.g., LTBeam or LTBeamN software employing finite bar elements, or by utilising more advanced 3D modelling, e.g., Abaqus software with shell or solid elements. In their previous studies [50,52,60], the authors utilised an alternative method for the description of beam displacements upon a loss of stability, namely employing power polynomials with a simple physical (static) interpretation As indicated before, this approach facilitates the description of the torsion angle function and beam lateral deflection when the conditions of its elastic restraint against warping and lateral rotation in the support nodes are taken into account. Beam Elastic Restraint against Warping and against Rotation in Its Bending Plane
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