Lateral Torsional Buckling Analysis Research Articles

Lateral-torsional buckling analysis of wood composite I-beams with sinusoidal corrugated web

Buckling instability refers to a significant limit on the structures with I-section members, which causes severe decreasing of critical buckling load. Many mechanisms and techniques have been developed to increase the loading capacity of I-section structures, e.g., using composite materials or changing web geometry. This study aims at theoretically investigating the effect of geometry on the buckling capacity of wood composite I-beams with sinusoidal corrugated web. Experiments and numerical simulations are carried out to validate the theoretical predictions. The presented model is also reduced to flat web to validate with an existing study. Good agreements are observed from the validations. Parametric study is conducted to indicate the effects of web geometry on the critical buckling load. A significant increasing of buckling load (minimum 17.7%) is obtained between flat and sinusoidal web I-beams. Sensitivity study is carried out to evaluate the influences of web thickness, beam length and beam height on the loading capacity of sinusoidal I-beams. Optimal design is conducted to investigate the impact of the ratios of wavelength-to-beam length (aL) and wave amplitude-to-flange width (AT) on the critical buckling load and volume of wood corrugated I-beams. The findings in this study can be further used as guidance for the design of composite I-beams with sinusoidal corrugated web.

Lateral-torsional buckling analysis of cantilever beam with tip lateral elastic brace under uniform and concentrated load

The studies on the lateral-torsional buckling of cantilever steel beam with tip lateral elastic brace are rarely reported. The total potential energy is first established for the lateral-torsional buckling of cantilever steel beam with tip lateral elastic brace under uniform and concentrated load. The modal trial function of the lateral displacement and torsional angle are expressed as trigonometric function combination with six terms. By introducing new dimensionless parameters, the analytical solution of the dimensionless buckling equation for the lateral-torsional buckling of cantilever steel beam with tip lateral elastic brace is obtained. With the help of 1stOpt software which is mathematical optimization analysis software, the non-dimensional critical moment formula of the lateral-torsional buckling of cantilever beam with tip lateral elastic brace is obtained. Then, the accuracy of the formula is verified by ADINA finite element software. The results show that the given critical moment formula is of high accuracy. It provides convenient and simple design method for practical engineering.

Lateral-torsional buckling resistance of unstiffened slender-web plate girders under moment gradient

The effect of moment gradient on the buckling moment resistance of I-beams can be taken into account by the use of an equivalent moment-gradient factor Cb. The Cb factors given by the previous researchers have been derived from elastic lateral-torsional buckling (LTB) analysis of compact I-beams. However, according to the available literature it is not known whether these factors can be applied to the LTB analysis of inelastic slender-web plate girders (SWPGs). The aim of this paper is to investigate the nonlinear LTB analysis of unstiffened SWPGs subjected to central loading. To this end, a 3D finite-element model using ABAQUS is developed for the inelastic nonlinear flexural-torsional analysis of SWPGs and used to evaluate the unbraced length and load-height effects (located at center, top flange and bottom flange) on their moment-gradient factor. It was found that the Cb factor given by AISC in Specification for structural steel buildings is generally unconservative for the elastic and inelastic SWPGs under the considered point load cases. Also, it was observed that the moment resistance versus unbraced length (M–L) relationships for the elastic SWPGs are not significantly affected by the applied load height.

Upper and lower bound solutions for lateral-torsional buckling of doubly symmetric members

A family of three finite elements is developed for the lateral-torsional buckling analysis of thin-walled members with doubly symmetric cross-sections. The elements are based on a recently derived variational principle which incorporates shear deformation effects in conjunction with a special interpolation scheme ensuring C1 continuity. One of the elements is developed such that it consistently converges from above while another element is intended to consistently converge from below. The third element exhibits fast convergence characteristics compared to other elements but cannot be guaranteed to provide either an upper or a lower bound solution. The formulation incorporates the ability to enforce any set of linear multi-point kinematic constraints. The validity of the solution is established through comparisons with other well-established numerical solutions. The elements are then used to solve practical problems involving simply supported beams, cantilevers and continuous beams under a variety of loading conditions including concentrated loads, linear bending moments and uniformly distributed loads. The effect of lateral and torsional restraints and the location of lateral restraint along the section height on lateral-torsional buckling capacity of beams are also examined through examples.

Finite element formulation for lateral torsional buckling analysis of shear deformable mono-symmetric thin-walled members

A shear deformable theory and a computationally efficient finite element are developed to determine the lateral torsional buckling capacity of beams with mono-symmetric I-sections under general loading. A closed-form solution is also derived for the case of a mono-symmetric simply supported beam under uniform bending moments. The finite element is then used to provide solutions for simply supported beams, cantilevers, and developing moment gradient factors for the case of linear moments. The formulation is shown to successfully capture interaction effects between axial loads and bending moments as well as the load height position effect. The validity of the element is verified through comparisons with other established numerical solutions.

Assessment of existing analytical models for the lateral torsional buckling analysis of PVB and SG laminated glass beams via viscoelastic simulations and experiments

Due to the large increase of structural glass applications, the lateral torsional buckling behavior of glass beams actually represents a topic of great interest for researchers. Although several analytical models and design approaches exist in literature, various aspects complicate the realistic prediction of their typical out-of-plane response, especially if composed of two (or more) laminated glass sheets. Based on viscoelastic numerical results and predictions of a large experimental campaign of lateral torsional buckling tests performed on PVB and SG beams, the paper investigates the accuracy of existing analytical models in the prediction of the elastic critical load and load-lateral displacement path of these elements.

Finite-Element Formulation for the Lateral Torsional Buckling of Plane Frames

AbstractA finite-element formulation is developed for the lateral torsional buckling analysis of plane frames with moment connections consisting of two pairs of welded plate stiffeners. The finite element provides a realistic representation of the partial warping restraint provided by the joint to the adjoining members. The element consists of two nodes with four generalized buckling degrees of freedom per node and is thus devised to interface with two classical beam buckling elements connected at right angles. The new finite element extends the functionality of the classical beam finite element to predict the lateral buckling load for noncollinear structures, such as portal frames. A comparison with results based on shell finite-element analysis demonstrates the ability of the new formulation to reliably predict the lateral buckling resistance of plane frames at a fraction of the computational and modeling cost of shell-based finite-element solutions.

Lateral–torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects

In this paper, lateral–torsional buckling behavior of open-section thin-walled beams is investigated based on a geometrically nonlinear formulation, which considers the effects of shear deformations. A finite element numerical solution along with an incremental-iterative solution procedure is adopted to trace the pre-buckling as well as the post-buckling equilibrium paths. Formulation is applicable to a general type of open-section and load position effects are also included. Numerical results are validated through comparisons with experimental results and those based on other formulations presented in the literature. Comparisons have also been made between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Examples illustrate the influence of beam slenderness and moment gradient on the effects of pre-buckling deformations in predicting bucking loads.

Elastic lateral-torsional buckling analysis of permanent means of access structure

International Maritime Organization (IMO) adopted a new regulation to request permanent means of access (PMA) for a regular inspection of ship structure. Horizontal platforms for an inspector to walk on should be provided at specified locations. The platform is attached perpendicular to longitudinal bulkheads or side shell like a common longitudinal stiffener. Since the platform is much wider than ordinary stiffeners, a mid-flat-bar is welded in the middle of the platform. The wide platform (i.e. the tall web plate) makes PMA structure prone to lateral torsional buckling prior to overall flexural Euler buckling subjected to axial compression. This study employs the Rayleigh–Ritz method to treat the elastic lateral-torsional buckling of the PMA structure. The deformation of the cross-section can be expressed using six independant parameters. Compared to the previous research for an ordinary stiffened plate ( Hughes and Ma, 1996a), two additional parameters are employed to model the deformation of the mid flat bar. This study also proposes a new strain distribution of lateral bending introducing two respective neutral axes for the flange and the mid-flat-bar. Two mathematical models are developed for two cases; one without associated plating, and the other with both the plating and its rotational restraint. In the former, the coupling between the lateral torsional buckling (“tripping”) and the Euler buckling is investigated. In the latter, a plate rotational spring constant is suggested based on extended deformed shape of the plating. For each model, the validity of the proposed method is verified by a comparison with a number of linear buckling analyses carried out using the NASTRAN finite-element program.

Lateral bracing of I-girder with corrugated webs under uniform bending

Lateral–torsional buckling may occur in an unrestrained beam where its compression flange is free to displace laterally and rotate. This paper presents the results of the theoretical and finite element analyses of the lateral–torsional buckling of I-girders with corrugated webs and lateral bracing, under uniform bending. It is well known that an elastic lateral brace restricts partially the lateral buckling of slender beams and increases the elastic buckling moment. However, a full study of the effect of lateral braces on lateral–torsional buckling has not been made especially for I-girder with corrugated webs. This paper develops a three-dimensional finite element model using ANSYS [User’s manual, version 10.0] for the lateral–torsional buckling analysis of I-girder with corrugated webs and uses it to investigate the effects of elastic lateral bracing stiffness on the critical moment of simply supported I-girders with corrugated webs under pure bending. It was found that for plastic and inelastic I-girder with corrugated webs, the effect of bracing initially is increased to some extent as the lateral unbraced length increases and then decreased until the beam behaves as an elastic beam. In other words, the effect of bracing depends not only on the stiffness of the restraint but also on the modified slenderness of the I-girder. Also, the results show that Winter’s simplified method to determine full brace requirements cannot be applied to I-girders with corrugated webs. Therefore, a general equation is proposed to determine the value of optimum stiffness ( K o p t ) in terms of the I-girder’s slenderness.

Elastic flexural and lateral torsional buckling analysis of frames using finite elements

A stiffness matrix has been developed for the elements of framed systems which are under constant axial force and moment. A global stiffness matrix can be obtained by using this stiffness matrix and the classical finite element techniques. The constant axial force and moment which will be used in the element stiffness matrix are obtained from a preliminary solution. These internal forces are then increased proportionally and new element stiffness matrices are calculated. Due to the increasing external loads excessive displacements, rotations and finally change of directions of these displacements and rotations occur. The external load conditions for this phase, give us the critical buckling load of the system. Within this framework an application is presented for the critical flexural and lateral torsional buckling loads of second-degree parabolic arches. This buckling loads of arches are compared with the specifications of the Eurocode 3, Part 2, Annex D, design of steel structures ENV 1993-1-1 and given some interpretations about the linear and non-linear analysis.

Elastic, full plastic and lateral torsional buckling analysis of steel single-angle section beams subjected to biaxial bending

Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account.

Distortional buckling in monosymmetric I-beams

This paper deals with distortional buckling of simply supported monosymmetric I-beams under three types of load: a central point load, a uniformly distributed load and a uniform sagging moment. ABAQUS is used for the investigation. Top-flange and bottom-flange load positions are considered for the first two load cases. It is found that for comparatively short beams, buckling may be governed by distortion of the web. Moment modification factors are calculated based on the present analysis, which accounts for the distortion of web and these are compared with those based on SSRC Guidelines, which are based on lateral-torsional buckling analysis only. It is seen that for short beams, provisions in SSRC Guide-1998 seriously overestimate the critical load.

Lateral-torsional buckling of prismatic and tapered thin-walled open beams: assessing the influence of pre-buckling deflections

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz`s criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely () the minor-to-major inertia ratio, () the beam length, () the location of the load point of application and () the bending moment diagram shape.

Lateral-Torsional Buckling of Nonprismatic I-Beams

A finite-element formulation for the lateral-torsional buckling analysis of nonprismatic I-beams is developed. The formulation is capable of analyzing continuous I-beams with a linear or quadratic taper within acceptable accuracy. The influence of warping deformations of the section and location of the member loads at different cross-section points are included in the formulation. Finite-element solution convergence is studied based on available experimental and numerical results. A parametric study on the lateral-torsional buckling strength is carried out for different forms and degrees of taper, loading, and support conditions for single-span and two-span continuous beams. The buckling strength of beams with various degrees of taper and number of spans are also investigated.

Large displacement theory of thin-walled curved members and its application to lateral-torsional buckling analysis of circular arches

The purpose of this study is to establish a one dimensional large displacement theory for plane-curved members with thin-walled open sections. Consequently, this theory is applied in the analysis of lateral-torsional buckling of circular arches. Typical numerical examples are shown herein to illustrate how the ratio of different types of rigidities in non-dimensional form affects the buckling loads.