Elastic Lateral-distortional Buckling Research Articles

Elastic lateral distortional buckling analysis of cantilever I-beams

A study of elastic lateral distortional buckling of cantilever monosymmetrical I-beams is presented. The method assumes that the flange cross-sections remain straight (undistorted) during buckling, but that the web is free to distort. Three different load patterns are considered: an end moment load, a uniformly distributed lateral pressure and an end point load. The study applied a Rayleigh–Ritz method that the authors previously developed for simply supported beams to cantilevers. The accuracy of the method is verified by comparing the results with a general finite element linear buckling analysis, using NX/Nastran. The method offers advantages over commonly used finite element analysis because it is mesh-free and requires only 6 × n degrees of freedom; therefore, the solution process is rapid and suitable for design space exploration. For doubly symmetric I-beams, a cubic transverse normal stress distribution, derived from the equation of equilibrium, was used in the total potential energy. The results were compared to the previous method which used a linear stress distribution.

Elastic lateral-distortional buckling of I-beams and the Meck Plot

Meck Plot is an adapted version of the well-known Southwell method to the case of lateral-torsional buckling, which indeed reflects the physical inter-dependence of lateral flexure (lateral displacement) and torsion (rotation) in the structure. In the recent reported studies, it has been shown experimentally and theoretically that lateral displacement of an I-beam undergoing elastic lateral-distortional mode of buckling is interestingly directly coupled with other various deformation characteristics such as web transverse strain, web longitudinal strain, vertical deflection, and angles of twist of top and bottom flanges, and consequently good results have been obtained as a result of application of the Meck`s method on lateral displacement together with each of the aforementioned deformation variables. In this paper, it is demonstrated that even web transverse and longitudinal strains, vertical deflection, and angles of twist of top and bottom flanges of an I-beam undergoing elastic lateral-distortional buckling are two-by-two directly coupled and the application of the Meck Plot on each pair of these deformation variables may still yield reliable predictions for the critical buckling load.

ELASTIC LATERAL AND RESTRAINED DISTORTIONAL BUCKLING OF DOUBLY SYMMETRIC I-BEAMS

Based on the energy principle, a theoretical study of the elastic lateral distortional buckling (LDB) and restrained distortional buckling (RDB) of I-beams is presented. First, because the existing potential energy expressions for LDB are not suitable for members under a transverse distributed load, a new general potential energy expression of I-beams for lateral buckling is derived by using the nonlinear elastic theory. The proposed expression is equivalent to the classical potential equation when web distortion is suppressed and caters for I-beams under transverse distributed load, transverse concentrated load, and end moments, and when the web is flexible. Then, an LDB equation for simply supported, doubly symmetric, I-beams under uniform distributed load is developed by invoking the Ritz method. In addition, an RDB equation for continuous composite beams is also deduced by using some simplifications. The corresponding simplifications and equations are verified by the finite element method. Suggestions for further study are also presented. The outcomes of the present paper have important theoretical and practical significance and provide a rational basis for practical design methods.

An Analytical Solution for the Elastic Lateral-Distortional Buckling of I-section Beams

Lateral-distortional buckling may occur in I-section beams with slender webs and stocky flanges. A computationally efficient method is presented in this paper to study this phenomenon. Previous studies on distortional buckling have been on the use of 3rd and 5th order polynomials to model the displacements. The present study provides an alternative way, using Fourier Series, to model the behaviour. Beams of different cross-sectional dimensions, load cases and restraint conditions are examined and compared. The accuracy and versatility of the method are verified by calibrating against the results of other published studies. The present method is believed to be a simple and efficient way of determining the buckling load and mode shapes of I-section beams that are susceptible to lateral-distortional buckling modes.

Inelastic lateral-distortional buckling of continuously restrained rolled I-beams

An energy method of analysis is presented which can be used to study the inelastic lateral-distortional buckling of hot-rolled I-sections continuously restrained at the level of the tension flange. The numerical modelling leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtainable, so as to enable a study of the factors that influence the strength of continuously restained I-beams to be made. Although hot-rolled I-sections generally have stocky webs and are not susceptible to reductions in their overall buckling loads as a result of cross-sectional distortion, the effect of elastic restraints, particularly against twist rotation, can lead to buckling modes in which the effect of distortion is quite severe. While the phenomenon has been studied previously for elastic lateral-distortional buckling, it is extended in this paper to include the constitutive relationship characteristics of mild steel, and incorporates both the so-called 'polynomial' and 'simplified' models of residual stresses. The method is validated against inelastic lateral-torsional buckling solutions reported in previous studies, and is applied to illustrate some inelastic buckling problems. It is noted that over a certain range of member slenderness the provisions of the Australian AS4100 steel standard are unconservative.

Flexural capacity of hollow flange beams

The hollow flange beam (HFB) is a unique cold-formed steel section developed in Australia for use as a flexural member. Research has identified that the HFB section's flexural capacity for intermediate span members is limited by lateral distortional buckling, which is characterized by simultaneous lateral deflection, twist, and web distortion. This buckling behaviour is mainly due to the unique geometry of the section, comprising two torsionally stiff triangular flanges connected by a slender web. This paper presents a finite element analytical model suitable for non-linear analysis of HFB flexural members. The model includes all significant effects that may influence the ultimate capacity of such members, including material inelasticity, local buckling, member instability, web distortion, residual stresses, and geometric imperfections. It was found to accurately predict both the elastic lateral distortional buckling moments and the ultimate capacities of HFB flexural members, and was therefore used in the development of design curves and suitable design procedures.

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.

Lateral Buckling Strengths of Cold-Formed Channel Section Beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed channel section (CFC) beams. Code rules for designing steel beams against lateral buckling that are based on data for hot-rolled I-section beams may be unsuitable for CFC beams, because they have different stress-strain curves, residual stresses, and initial imperfections. Distortion may reduce the resistance of a CFC beam to lateral buckling. In addition, because of the monosymmetry of the cross section, the effective shear center moves toward the web and the effective section becomes asymmetrical after yielding, so that a CFC beam under major axis bending is subjected to minor axis bending and twisting. Also, the minor axis bending and warping strain distributions, and therefore the strengths of CFC beams, are related to the twist rotation and minor axis deflection directions. This paper deals with these problems by developing an advanced finite element model to investigate the elastic lateral-distortional buckling, inelastic behavior, and strengths of CFC beams with residual stresses and initial imperfections. The results are used to develop improved design rules for CFC beams. The effects of moment distribution and load height on the strengths are also studied.

Lateral-Distortional Buckling of Hollow Flange Beams

While the flanges of cold-formed hollow flange beams (HFBs) are very stiff torsionally, their webs are comparatively flexible, and may allow web distortion effects to reduce their resistances to lateral buckling. There is no simple formulation for predicting the effects of web distortion on the lateral buckling of HFBs. As a result, structural designers are unable either to check or to extend the available elastic buckling predictions; thus code writers are not able to provide explicit formulations for the effects of distortion. The conversion from elastic buckling to strength for HFBs is also questionable, since cold-formed beams have different stress-strain curves, residual stresses, and geometrical imperfections from those of hot-formed beams. This paper deals with these problems, first by finding a simple but sufficiently accurate closed-form solution for the effects of distortion on the elastic lateral buckling of simply supported HFBs in uniform bending, and then by developing an advanced theoretical method of predicting the effects of the stress-strain curve, residual stresses, and geometrical imperfections on the strengths of HFBs that fail by lateral-distortional buckling. Such a method allows the development of a conversion from elastic buckling to strength, which is appropriate for HFBs. The use of this conversion together with the simple approximation developed here for elastic lateral-distortional buckling provides a rational basis for the lateral buckling design of unbraced HFBs.

Elastic distortional buckling of tapered composite beams

The overall buckling mode in a composite steel-concrete beam over an internal support is necessarily lateral-distortional, in which the bottom compressive range displaces laterally and twists, since the top flange is restrained by the nearly rigid concrete slab. An efficient finite element method is used to study elastic lateral-distortional buckling in composite beams whose steel portion is tapered. The simplified model for a continuous beam that is presented herein is a fixed ended cantilever whose steel portion is tapered, and is subjected to moment gradient, This is intended to give an insight into distortion in a continuous beam that occurs in the negative bending region, and the differences between the cantilever representation and the continuous beam are highlighted. An eigenproblem is established, and the buckling modes and loads are determined in the elastic range of structural response. It is found from the finite element study that the buckling moment may be enhanced significantly by using a vertical stiffener in the region where the lateral movement of the bottom range is greatest. This enhancement is quantified in the paper.