Search Results (8)

The absence of analytical expressions in current codes for evaluating the critical moment for lateral–torsional buckling of cold-formed beams with omega-shaped sections presents a fundamental challenge when assessing their resistance to global buckling. In response to this challenge, a comparative study was conducted to explore various approaches for calculating the critical moment. This involved both analytical and numerical analyses, using different methods available in codes and computational tools. The analytical analysis followed the Effective Width Method, employing the expression proposed in ENV 1993-1-1:1992, which is commonly used for evaluating the critical lateral–torsional moment of hot-rolled profiles. Numerical analyses were then performed using the ABAQUS v6.13, GBTUL v2.0, and CUFSM v5.05 software packages. The ABAQUS model, validated with results obtained from an experimental campaign, serves as the reference model. Upon assessing the bending moment resistances according to European, Brazilian, and American standards, consistency was found among these standards. However, it became evident that using the analytical expression proposed for hot-rolled profiles is inadequate for evaluating the critical lateral–torsional moment of CFS omega-shaped profiles. Conversely, the agreement between the ABAQUS, GBTUL, and CUFSM results suggests their utility as reliable tools for estimating the elastic critical lateral–torsional buckling moment. Full article

Cantilever steel beams are an essential structural element in civil engineering fields such as bridges and buildings. However, there is very little research on the critical moment (M_cr) of cantilever beams subjected to a concentrated load (CL) or a combination of concentrated load and uniformly distributed load (CUDL) when the concentrated load is not limited to the free end. Therefore, the focus of the current paper is the calculation of M_cr for cantilever steel beams under CL and CUDL. This paper proposes a program and a simple closed-form solution for M_cr that are applicable to the elastic buckling analysis of cantilever I-beams under CL and CUDL. Based on the Rayleigh–Ritz method, a matrix equation and the corresponding procedure about M_cr under CL and CUDL are derived by using infinite trigonometric series for the buckling deformation functions. The value of M_cr and the corresponding mode of buckling can be obtained efficiently by considering the symmetry of the section, the ratio of two load values and the load action position. Experimental results and finite element calculations validate the numerical solutions of the procedure. A closed-form solution for M_cr is derived according to the assumption of a small torsion angle and the specific values of each coefficient in the closed-form solution of M_cr are calculated by the proposed procedure. The results show that the procedure and closed-form solution for M_cr presented in this paper have a high degree of accuracy in calculating the M_cr of the cantilever beam under CL and CUDL. The deviations between the results calculated by the proposed procedure and data from existing literature are less than 8%. These conclusions are capable of solving the calculation problem of M_cr for cantilever beams under CL or CUDL, which are both significant load cases in engineering. The study provides a reference for the design of cantilever steel beams. Full article

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. Full article

This study presents a numerical investigation of the elastic critical lateral-torsional buckling of a steel beam subjected to simultaneous transverse loading at the top flange and negative end moments. Here, the elastic critical buckling of the steel beam was estimated by utilizing the finite element software ABAQUS. In addition, the influence of the length-to-height ratio was taken into account. Additionally, the predicted values for elastic critical buckling when applying existing design codes and a previous study were also analyzed and compared to the numerical results of the finite element analysis. The result of the comparison revealed that the projected values from the design codes and the study are conservative for the majority of cases and have a tendency to be too conservative when the length-to-height ratio increases. Furthermore, a new equation with a factor considering the influence of the length-to-height ratio and transverse loading on the top flange is proposed, and the proposed equation shows sufficient accuracy and less conservative values for most cases. Full article

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. Full article

Tubular flange composite beams are increasingly applied in modern bridge structures. In order to investigate the overall stability behavior of doubly symmetric tubular flange composite beams with lateral bracing under concentrated load, the analysis of elastic lateral-torsional buckling is conducted by the energy variation method. The analytical solution of critical moment of doubly symmetric tubular flange composite beams with lateral bracing is obtained. Meanwhile, the simplified calculation formula of critical moment is fitted by 1stOpt software based on 26,000 groups of data, and the accuracy is verified by the finite element method. It is found that, the critical moment rises obviously with increasing lateral bracing stiffness, and adding lateral bracing to doubly symmetric tubular flange composite beams is beneficial to improve the overall stability in engineering practice. Finally, the influence of several parameters including concrete strength, span, steel ratio of flange and height-thickness ratio of web are studied. The results show that the concrete strength and the web height-thickness ratio have a weak influence on critical moment of elastic lateral-torsional buckling, while the influence of span-depth ratio and flange steel ratio is very significant. Full article

Structural glass beams and fins are largely used in buildings, in the form of primary load-bearing members and bracing systems for roof or facade panels. Several loading and boundary conditions can be efficiently solved by means of bonded composites that involve the use of laminated glass sections. Additionally, the so-obtained glass members are often characterized by high slenderness. To this aim, several literature studies were dedicated to the lateral–torsional buckling (LTB) behavior of laterally unrestrained (LU) glass elements, with the support of full-scale experiments, analytical models, or finite element (FE) numerical investigations. Standardized design recommendations for LU glass members in LTB are available for designers. However, several design issues still require “ad hoc” (and often expensive) calculation studies. In most of the cases, for example, the mechanical interaction between the structural components to verify involves various typologies of joints, including continuous sealant connections, mechanical point fixings, or hybrid solutions. As a result, an accurate estimation of the theoretical LTB critical moment for such a kind of laterally restrained (LR) element represents a first key issue toward the definition and calibration of generalized design recommendations. Careful consideration should be spent for the description of the intrinsic features of materials in use, as well as for a combination of geometrical and mechanical aspects (i.e., geometry, number, position of restraints, etc.). In this paper, the attention is focused on the calculation of the elastic critical buckling moment of LR glass beams in LTB. Existing analytical approaches of the literature (mostly developed for steel constructional members) are briefly recalled. An additional advantage for extended parametric calculations is then taken from finite element (FE) numerical analyses, which are performed via the LTBeam or the ABAQUS software codes. The actual role and the effect of discrete mechanical restraints are, thus, explored for selected configurations of practical interest. Finally, the reliability of simplified calculation approaches is assessed. Full article

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. Full article