Elastic distortional buckling of tee-section cantilevers

The paper presents the results of a finite element study of the elastic distortional buckling of tee-section cantilevers, which can be thought of as beams fully braced at one end and unbraced at the other. The finite element procedure is described briefly, and then three loading cases, viz., a tip moment, a tip load and a uniformly distributed load are considered. All of these loading cases place the unstiffened or free edge of the stem or web into compression. The effects of distortion are quantified for the three loading cases, as are the effects of fully restraining the top flange against lateral deflection and twist by a discrete brace positioned anywhere along the cantilever. It is shown that the effects of distortion during buckling cannot be ignored in a tee-section cantilever with even a moderately slender web.     

Lateral-distortional buckling of I-beams and the extrapolation techniques

Various extrapolation techniques are utilized for predicting the critical buckling load of structural members undergoing lateral buckling. For the application of these methods it is only necessary to have data relating load to a deformation characteristic. In order to obtain an experimental comparison of the Southwell, Modified, and Massey Plot methods, these have been applied on lateral deflections and web transverse strains of four full-scale simply supported I-beams subjected to a central concentrated load with an effective lateral brace at the midspan of the top flange, undergoing inelastic lateral-distortional buckling. Although there is some scatter due to the application of various deformation variables and extrapolation techniques, the agreement between the extrapolated and the maximum test loads is generally good. The smallest discrepancy is found in the case of the Modified Plot. Moreover, in addition to demonstrating direct coupling between the lateral deflections and the web transverse strains representing web distortion, it is also shown that good predictions are provided by applying the Meck Plot on these deformation variables.     

Distortional buckling of castellated beams

In previous studies of the structural behavior of castellated steel beams, different possible failure modes of these extensively used structural members have been identified and investigated. On the other hand, during the past 25 years or so, a proliferation of research work has been undertaken on the distortional buckling of steel members. Nonetheless, no studies are found in the literature on the distortional buckling of castellated beams. Accordingly, tests of six full-scale castellated beams are described, in which the experimental investigation of distortional buckling was the focus of interest. In addition to the test strengths, the accurate critical loads of the beams have been obtained using some extrapolation techniques, and ultimately a comparison has been made between the obtained test loads and some theoretical predictions.     

Lateral-Torsional buckling of end-restrained beams

The influence of semi-rigid joint action on the behaviour and strength of laterally unsupported beams has been investigated using a finite element approach. The ultimate strength analysis allows for the effects of initial deflections, residual stresses and the gradual development of yielded zones. Connection behaviour is modelled with a multi-linear representation of in-plane moment-rotation (M-φ) behaviour. The validity of the program has been verified by checking against both analytical and experimental results. A parametric study has been conducted to assess both the importance of end-restraint effects and the sensitivity of the beam's strength to variations in the main problem variables. Studies of the spread of yield have been employed to explain the various phenomena observed. The results have been used as the basis for an assessment of the methods used to allow for end restraint in the new UK steelwork code.     

Lateral-torsional buckling resistance of coped beams

The lateral-torsional buckling resistance of beams depends on the support conditions. In floor structures for buildings coped beams are often used. A numerical model was developed to investigate the influence of copes on the lateral buckling resistance. This model is described in a companion paper [Maljaars J, Stark JWB, Steenbergen HMGM, Abspoel R. Development and validation of a numerical model for buckling of coped beams. Journal of Constructional Steel Research 2005;61(11):1576-93]. In this paper results of a parameter study carried out with the numerical model are presented. Based on these results recommendations for design rules are given. The study is restricted to (coped) beams with end plates.     

Interactive buckling of beams in bending

A discrete model involving a limited number of degrees of freedom is presented, for analyzing the interaction between overall lateral-torsional buckling and local flange buckling, qualitatively. The results are compared with experiments and show a good qualitative agreement. The results suggest that a quantitative numerical analysis based on Koiter's asymptotic approach may have a wide range of validity.     

钢——混凝土组合梁的侧向扭转屈曲

通过对工字型钢-混凝土组合梁劁向失稳形式的理论分析,提出工字型组合梁稳定性分析的计算模型,并根据计算模型推导了组合梁负弯矩区受压下翼缘劁向屈曲的临界弯矩,然后通过与现行工字型组合梁的稳定理论和计算方法比较,确定了工字型组合梁负弯矩区稳定设计的修正方法和建议意见。     

Elastic shear buckling characteristics of LiteSteel beams

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam. The unique LSB section is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. To date, limited research has been undertaken on the shear buckling behaviour of LSBs with torsionally rigid, rectangular hollow flanges. For the shear design of LSB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the flange and web elements. Therefore finite element analyses were carried out to investigate the elastic shear buckling behaviour of LSB sections including the effect of true support conditions at the junction between their flange and web elements. An improved equation for the higher elastic shear buckling coefficient of LSBs was developed and included in the shear capacity equations of Australian cold-formed steel codes. Predicted ultimate shear capacity results were compared with available experimental results, both of which showed considerable improvement to the shear capacities of LSBs. A study on the shear flow distribution of LSBs was also undertaken prior to the elastic buckling analysis study. This paper presents the details of this investigation and the results including the shear flow distribution of LSBs.     

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.     

Flexural-torsional buckling behavior of aluminum alloy beams

This paper presents an investigation on the flexural-torsional buckling behavior of aluminum alloy beams (AAB). First, based on the tests of 14 aluminum alloy beams under concentrated loads, the failure pattern, load-deformation curves, bearing capacity and flexural-torsional buckling factor are studied. It is found that all the beam specimens collapsed in the flexural-torsional buckling with excessive deformation pattern. Moreover, the span, loading location and slenderness ratio influence the flexural-torsional buckling capacity of beams significantly. Secondly, besides the experiments, a finite element method (FEM) analysis on the flexural-torsional buckling behavior of AAB is also conducted. The main parameters in the FEM analysis are initial imperfection, material property, cross-section and loading scheme. According to the analytical results, it is indicated that the FEM is reasonable to capture mechanical behavior of AAB. Finally, on the basis of the experimental and analytical results, theoretical formulae to estimate the flexural-torsional buckling capacity of AAB are proposed, which could improve the application of present codes for AAB.     

Interaction of local buckling and lateral torsional buckling of T-shaped cantilevering beams

The structural resistance of T-shaped cantilevering beams is governed by combined stability phenomena of lateral torsional buckling and local buckling. The aim of this paper is to show the applicability of the “general method” [1], to the prediction of the combined stability behaviour for single symmetric cross-sections. Since the approach is based on the modal shape and modal edge-moment distribution, it does not distinguish between local and lateral torsional buckling, but considers both phenomena in a single trail. A buckling curve for tapered T-shaped members is suggested and boundaries of applicability investigated.     

Interaction of buckling modes in castellated steel beams

This paper investigates the behaviour of normal and high strength castellated steel beams under combined lateral torsional and distortional buckling modes. An efficient nonlinear 3D finite element model has been developed for the analysis of the beams. The initial geometric imperfection and material nonlinearities were carefully considered in the analysis. The nonlinear finite element model was verified against tests on castellated beams having different lengths and different cross-sections. Failure loads and interaction of buckling modes as well as load-lateral deflection curves of castellated steel beams were investigated in this study. An extensive parametric study was carried out using the finite element model to study the effects of the change in cross-section geometries, beam length and steel strength on the strength and buckling behaviour of castellated steel beams. The parametric study has shown that the presence of web distortional buckling causes a considerable decrease in the failure load of slender castellated steel beams. It is also shown that the use of high strength steel offers a considerable increase in the failure loads of less slender castellated steel beams. The failure loads predicted from the finite element model were compared with that predicted from Australian Standards for steel beams under lateral torsional buckling. It is shown that the Specification predictions are generally conservative for normal strength castellated steel beams failing by lateral torsional buckling, unconservative for castellated steel beams failing by web distortional buckling and quite conservative for high strength castellated steel beams failing by lateral torsional buckling.     

工字钢-混凝土组合梁弹性约束畸变屈曲研究

约束畸变屈曲是不同于侧向屈曲和畸变屈曲的一类特殊的屈曲形式,通常发生在组合梁负弯矩区。基于弹性地基压杆方法对组合梁弹性约束畸变屈曲进行了研究。将Svensson压杆模型进行改进,考虑了腹板参与部分,并推导了两种基于改进压杆模型的变轴力稳定计算表达式。借助于有限元方法,分析了现有变轴力弹性地基压杆方法用于组合梁约束畸变屈曲的求解精度,研究结果表明：弹性地基压杆方法对组合梁作用纯弯矩及三角形负弯矩情况符合良好,但对非线性弯矩分布情况精度较差。对约束畸变屈曲引入等效弯矩假设,并对其适用性进行了分析,提出了约束畸变屈曲等效弯矩假设临界长度简化公式,进而通过三步简化实现了连续组合梁弹性约束畸变屈曲计算。图16表7参17     

钢梁稳定问题的有限元模拟

钢梁的稳定问题是一个重要的问题,通过有限元计算可以很好地对这一问题进行模拟,阐述了用有限元法求解钢梁稳定问题的过程,介绍了用ANSYS进行建模所需要注意的问题,最后计算了不同情况下的极限承载力,并和理论值进行了比较。     

Shear buckling characteristics of cold-formed steel channel beams

Cold-formed steel members are increasingly used as primary structural elements in the building industries around the world due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. For the shear design of LCB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of LCB web panels are determined by assuming conservatively that the web panels are simply supported at the junction between their flange and web elements. Hence finite element analyses were conducted to investigate the elastic shear buckling behavior of LCBs. An improved equation for the higher elastic shear buckling coefficient of LCBs was proposed based on finite element analysis results and included in the ultimate shear capacity equations of the North American cold-formed steel codes. Finite element analyses show that relatively short span LCBs without flange restraints are subjected to a new combined shear and flange distortion action due to the unbalanced shear flow. They also show that significant post-buckling strength is available for LCBs subjected to shear. New equations were also proposed in which post-buckling strength of LCBs was included.     

Semi-empirical design of complex metal beams by buckling analysis

Structural elements with complex geometries, boundary conditions and load patterns cannot be designed against buckling using empirical formulae because of uncertain elastic buckling moments or unknown buckling effective lengths, which are basic parameters for these equations. This article proposes a shell finite element procedure for buckling design of metal beams of complex configurations with codified initial imperfections assumed in the Perry–Robertson formula. The advantage of the proposed method lies in the use of elastic buckling moment with empirical design formulae for determination of design moment capacity of a beam; thereby eliminating the uncertainty of modelling initial imperfections. More importantly, the moment modification factor and assumption of effective length can be avoided because all second-order and yield effects have been considered in the computer model. Numerical examples demonstrate that the simplified method has a high level of accuracy, versatility and flexibility for the design of complex beams.     

Elastic interaction of local and lateral buckling in beams

A nonlinear finite strip method of analysis is described for the post-local buckling of geometrically imperfect plate assemblies. The method is used to provide an accurate alternative to the Winter effective width formula for obtaining the effective section of a simply supported I-beam in the post-local buckling range of structural response. The effective section of a locally buckled beam with thin flange outstands is used to investigate the resistance of the beam to flexural-torsional buckling. The analytical methods developed to assess the nonlinear interaction of local and lateral buckling are compared with experimental tests performed by Cherry.     

Optimal design of tapered beams for maximum buckling strength

This paper is concerned with the determination of the optimal linear taper of a narrow rectangular beam that will maximize the critical buckling load subject to a volume constraint. The beam considered is either cantilevered or simply supported and is under a uniformly distributed load or a point load. The solution to the problem is obtained by two independent approaches. Whilst one of the approaches is based on the Timoshenko energy technique, the other is based on a Lagrange multiplier and the gradient expression of problem.     

A study on local buckling behavior of hybrid beams

In this paper, the local buckling behavior of hybrid beams, with high-strength steel webs and mild steel flanges, is investigated. A wide-flange shaped member is essentially an assemblage of plate elements and then the plate buckling has a significant effect on the plastic deformation capacity of a beam, while the web provides the flange with some degree of rotational restraint against local buckling. The torsional restraint of the web against the flange inelastic buckling depends on the web stiffness, namely, the length of the plastic region in the web. A hybrid beam with high-strength steel webs and mild steel flanges is considered to be effective in carrying loads after the flange local buckling. The results of investigation are presented herein.     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.