Rafał Piotrowski

This paper presents the results of a further stage of the authors’ research into the lateral torsional buckling of hot-rolled bisymmetric I-beams, spatially elastically restrained at the support nodes, i.e., against: (1) warping, (2) rotation in the lateral torsional buckling plane and (3) rotation in the main bending plane M_y. The analysis considered the entire range of variation in node stiffness, from free support in bending M_y and full freedom of warping and rotation in the lateral torsional buckling plane, to full restraint of the beam at the nodes. The authors introduced a general approximation formula (AF) for the critical moment of lateral torsional buckling M_cr, simultaneously considering the three elastic fixity indexes for basic and frequently occurring loading schemes in engineering practice. In order to facilitate the calculations, the authors have included the full sequence of formulas for the successive components of the critical moment, derived in the authors’ previous papers. The ability to more accurately consider the actual conditions of the spatial elastic restraint of the beam at the nodes leads to a more accurate calculation of M_cr. The results obtained were compared with FEM (LTBeamN software, v. 1.0.3) by performing a large number of calculations and numerical simulations. The agreement of the AF/FEM results was achieved at a level sufficient from the engineering point of view (mean value 1.006, standard deviation 0.028, coefficient of variation 2.8%). Detailed calculations were carried out for different section types (I, H) and different combinations of fixity index values. The application of approximation formulas in practical calculations is demonstrated on an example. The formulas derived in the paper can be used, among other things, to verify the correctness of FEM calculations, including the correct modelling of elastic support restraints, which is important in design practice.

In this paper, a stability analysis was conducted of the lateral torsional buckling of the beam of a braced portal frame. The elastic critical resistance (ECR) of the frame was estimated for: (a) a volumetric 3D model (Abaqus/CAE 2017) including the interaction of the component members (beam, columns) in welded corner joints and (b) a simplified 1D bar model (LTBeamN, v 1.0.3) including the parameters of elastic restraint (at support nodes) for the so-called critical member extracted from the structure. In the case of the analysed portal frame, the critical member that determines the lowest elastic critical load of the frame was the transversely bent beam. The following parameters of the elastic restraint of the beam in the support members were taken into account: (1) restraint against warping, (2) restraint against lateral rotation, and (3) restraint against rotation in the bending plane M_y. The paper demonstrates that the use of a simplified model can enable an efficient and, from an engineering point of view, sufficiently accurate estimation of the ECR of the analysed braced portal frame. The underestimation of the calculated elastic critical resistance of the structure in the simplified 1D model (discrepancies of −10.3% to −18.8%) is compensated for by the lack of the need to prepare a relatively complex volumetric 3D model of the frame (Abaqus). Warping restraint, when neglected, reduces ECR by up to 25% for HEA300 columns.

This paper deals with the development of a new formula for the critical moment (Mcr) of lateral torsional buckling of a beam for extreme conditions of its support for bending My (i.e. simply support or complete restraint) and simultaneous occurrence of elastic restraint against warping (κω) and...

The aim of the study was to evaluate the impact of the location of the elastic bimoment stiffeners along the length of the main beam B-E of a simple H-type beam grillage on its elastic critical resistance (ECR) from the lateral-torsional buckling condition. The obtained ECR was compared with the critical resistance determined for the grillage without bimoment stiffeners. The greatest efficiency in increasing the ECR of the grillage (around +80%) was achieved by using elastic bimoment stiffeners shifted relative to joints B and E by approximately 21–25% of the main beam span.

In an experimental study of two-branched beams bent transversely about the major stiffness axis, the elastic critical load from the lateral-torsional buckling condition was determined. The tests were conducted on simply supported two-branch beam models with a built-up section consisting of two cold-formed channel members (2C) bolted back-to-back. The bolts were located at the mid-height of the built-up cross-section. Five groups of members differing in longitudinal bolt spacing were examined. The models were gravitationally loaded (using ballast) at the centre of the beam span. This approach eliminated the undesirable effect of the lateral support of the beam, e.g., by the actuator head. The critical load, measured by the concentrated transverse force (P_z,cr), was determined using the modified Southwell method. It has been experimentally shown that, in built-up beams, there is an influence of bolt spacing on the elastic critical load from the lateral-torsional buckling condition. The lowest critical load capacity and the most non-linear behaviour of the built-up member were observed in beams bolted with only three bolts (at the supports and in the middle of the span). However, the experimental results obtained in this study show that increasing the number of bolts above a certain level (in the case of the tested models, it was seven bolts) does not result in a further increase in the critical load, which is a surprising result. The obtained values were 15 to 23% lower than the critical load determined numerically by the finite element method (LTBeamN) for an analogous element with a uniform I-section.

Transversely loaded beam grillages are quite often used in industrial construction. In order to produce a safe design of such structures, it is necessary to account for the lateral torsional buckling phenomenon, which reduces load-bearing capacity. To be able to calculate the relevant reduction factor, the elastic critical load must be determined. As regards the existing design practice for such structures, simplified conditions are assumed for the mutual restraint of the component beams. However, this approach does not correspond to reality. This study discusses the results of numerical investigations and analytical calculations concerning the effect of the elastic action of simple beam grillage (SBG) joints on the critical load, which results from the lateral torsional buckling (LTB) condition. The SBG was defined as a flat system of interconnected beams, unstiffened laterally and loaded perpendicularly to the grillage plane. The analysis covered H-shaped grillages with different span ratios of component beams, in which the main (coupling) beam was decisive for instability. The effectiveness of the use of closed-section stiffeners at the grillage joints was also investigated. The grillage elastic critical resistances (ECR) were determined for two variants of joint stiffening. The computations were performed by means of FEM numerical simulations. The spatial models were discretised with the following elements: (1) solid ones in Abaqus, (2) shell ones in ConSteel, and (3) thin-walled bars in ConSteel. The LTB critical moments of the weakest beam (critical beam), elastically restrained against warping and against lateral rotation (in the LTB plane), were computed using the analytical methods developed by the authors. To this end, the methods were proposed to determine the indexes of the critical beam elastic restraint in the adjacent stiffening beams. In the study, it was demonstrated that (1) taking into account the conditions of mutual elastic restraint and interaction of the component beams provides a more accurate assessment of the grillage ECR, (2) the use of closed-section stiffeners in the grillage joints increase the ECR compared with classic flat stiffeners, (3) the grillage ECR can be estimated based on the critical moment M_cr of the weakest beam (critical beam) when the conditions of its elastic restraint in joints are accounted for.

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.

The paper deals with the analysis of lateral torsional buckling (LTB) of steel beams that are components of grillages. Such structures are constructed from primary substring beams and secondary coupling beams. One of the functions performed by secondary beams in grillages is point protection of...

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.