冷弯薄壁型钢檩条两种稳定计算模式的比较

讨论国家规范GB50018-2002《冷弯薄壁型钢结构技术规范》“和欧盟规范EC3-1-3对冷弯薄壁型钢檩条承载能力的两种计算模式的差异：拉条和屋面板对檩条抗扭约束刚度及其整体稳定的重要影响,进行檩条畸变屈曲和翘曲应力的计算,评估工程实践中可滑动的卷边咬合式屋面板对檩条的抗扭约束刚度以及拉条的构造等对檩条的工况作用问题。对工程实践具有重要参考价值。     

Elastic flexural-torsional buckling of steel beams with rigid and continuous lateral restraints

A simple model of the elastic buckling of steel beams with rigid and continuous lateral restraints has been developed. It is based on a method of displacements that associate lateral restraint conditions. A numerical procedure for resolving the resulting partial differential equations is proposed in which rotations are approximated by trigonometric functions. The effects of moment distribution and continuous restraints on the elastic flexural-torsional buckling of beams are also studied and design approximations and procedures developed. This study also highlights that the restraint of the tensioned part of the beam is not sufficient to limit lateral buckling. The use of these solutions is demonstrated by two examples.     

Steel cantilever strength by inelastic lateral buckling

Methods used for the design of steel beams supported at both ends are not well suited for the design of cantilevers against lateral buckling. The end restraints are very different for cantilevers, and the maximum displacements and twist rotations take place at the free ends, instead of near mid-span. Consequently, their buckling modes are very different to those of supported beams. The methods of allowing for the effects of the moment distribution on the elastic and inelastic buckling of supported beams use a mean of the moment distribution, which is weighted to allow for the maximum deformations being near mid-span. These methods are clearly inappropriate for cantilevers whose deformations are greatest at the free ends.Lateral buckling design methods for cantilevers are modifications of the methods for supported beams, but are of doubtful accuracy, and may be over conservative. In some cases there is little or no design guidance.This paper summarizes information on the effects of the moment distribution and load height on the elastic buckling of cantilevers which can be used in the method of design by buckling analysis. It then extends a method of designing supported beams by inelastic buckling analysis to allow for the effects of the moment distribution on the inelastic buckling of cantilevers. This extended method is then used to provide improved design methods for cantilevers which are consistent with those for simply supported beams. A worked example is summarized.     

轻钢屋面檩间支撑体系探讨

檩间支撑在轻钢屋面系统中占有很重要的位置,它能有效地将檩条倾覆力传递给刚架,起到提高檩条侧向稳定与屋面整体刚度的作用。分析不同形式的檩间支撑及直拉条在不同受力情况下的支撑体系优缺点,并提出用C型钢作直拉条的檩间支撑体系。分析表明:C型檩间支撑刚度好,连接方便,而且有很好的经济效益,是值得推广的一种檩间支撑形式。     

Lateral, local and distortional buckling of I-beams

A theoretical study of the elastic buckling modes of I-section beams under various loading conditions is presented.

The analysis is based on energy considerations and the energy equations governing instability are derived using plate theory to allow for distortion of the cross-section. The resulting analysis is able to predict lateral, local and distortional buckling modes.

The results are compared with classical lateral buckling solutions based on beam theory.     

Inelastic buckling of columns partially restrained against sway and rotation

A computer program for calculating the buckling load and the buckling shapes of columns restrained at intervals against sway and/or rotation by elastic springs is described, Analysis beyond the elastic limit of the material is performed by introducing the tangential modulus in a procedure like Engesser-Shanley's for simple columns.The programme, which also takes advantage of an algorithm developed by Wittrick and Williams for elastic structures, is particularly suitable for a desk computer because of the very small amount of storage required. Some numerical results are also presented.     

Modelling of cold-formed purlin-sheeting systems-Part 2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its good correlation with experimental results.     

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.     

Modelling of cold-formed purlin-sheeting systems- Part 1: Full model

Purlin-sheeting systems used for roofs and walls commonly take the form of cold formed channel or zed section purlins, screw-connected to corrugated sheeting. These purlin-sheeting systems have been the subject of numerous theoretical and experimental investigations over the past three decades, but the complexity of the systems has led to great difficulty in developing a sound and general model. This paper presents a non-linear elasto-plastic finite element model, capable of predicting the behaviour of purlin-sheeting systems without the need for either experimental input or over simplifying assumptions. The model incorporates both the sheeting and the purlin, and is able to account for cross-sectional distortion of the purlin, the flexural and membrane restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The validity of the model is shown by its good correlation with experimental results. A simplified version of this model, which is more suitable for use in a design environment, is presented in a companion paper.     

A Study of the Buckling Behaviour of Horizontal Saddle Supported Vessels

Previous experimental work, by one of the authors, examined the behaviour of end supported cylindrical vessels loaded centrally. It was found that the vessels failed by buckling when the radius to thickness ratio (R/t) was greater than 150. These results provided the motivation for examining the buckling behaviour of such vessels when they are supported, in a more conventional way, by using two saddles. In the cases examined it was noted that the stresses that cause buckling behaviour are the longitudinal and circumferential membrane stresses. These occur at four vessel locations, i.e. the zenith and nadir (top and bottom) of both the vessel mid-span and the saddle centre profiles. Known buckling formulae based on simple loading patterns, such as an axially loaded cylinder and a cylinder under pure bending, will be utilized in determining the allowable buckling stress. Present British Code rules and European recommendations will also be discussed. The allowable buckling load will be compared with theoretical stresses obtained from a small displacement linear elastic analysis, using a Fourier series method. From these results a design method will be presented.     

关于门式刚架斜梁平面外计算长度的探讨

门式刚架中梁的平面外计算长度,在现行规程中无明确规定。对梁平面外计算长度的几种取法进行简单回顾,认为屋面横向支撑的相应位置应设置系杆,不宜用檩条兼作系杆;斜梁的平面外计算长度宜取屋面横向支撑间的长度。     

Elastic distortional buckling of continuously restrained I-section beam-columns

Doubly symmetric steel I-section members with thin webs and stocky flanges that have their tension flange restrained fully against translational and lateral rotational buckling deformations and elastically against twist rotation during buckling by the flexibility of a continuous restraint have been shown in previous studies to buckle in a so-called restrained distortional buckling (RDB) mode, involving distortion of the web of the I-section in the plane of its cross-section. These bifurcative buckling modes must necessarily occur in the negative moment region of composite T-beams and in half-through girder bridges. The present paper describes the elastic RDB analysis of a simply supported doubly symmetric I-section beam-column subjected to combined uniform axial force and moment gradient. The study adopts an energy method of analysis. The numerical solutions are used to develop a simple method of predicting the elastic RDB loads of beam-columns for use in design.     

冷弯薄壁型钢-混凝土组合梁局部屈曲性能研究

通过理论分析提出了冷弯薄壁型钢—混凝土组合梁钢梁腹板及翼缘的局部屈曲简化计算模型。继而在简化计算模型的基础上应用能量法分别求出了腹板及翼缘的弹性临界屈曲应力。结果表明,内填混凝土的存在有效地提高了腹板及翼缘的屈曲应力,改善了腹板及翼缘的局部屈曲性能。     

Numerical Studies of the Rotational Stiffness of Purlin–Sheeting System

In light-gauged steel purlin-to-sheeting roof systems, the attached sheeting can provide rotational restraints to the purlin. The magnitude of the additional rotational stiffness offered by the sheeting will affect the load bearing capacity of the purlin. The current design method in Eurocode3 (EC3) is less accurate in predicting the purlin–sheeting rotational stiffness as it neglects the effect of wall thickness of the purlin. An integral model is introduced based on the finite element method. Comparisons are made between numerical results and existing experiments and a good agreement is observed. Parametric studies are conducted based on the validated model to investigate the influences of geometric dimensions on the rotational stiffness. Two modified coefficients are proposed for calculating the rotational stiffness based on the codified formulae in EC3, where the effect of the wall thickness and the flange width of the purlin are both considered.     

轻钢压弯构件平面外支承长度的计算

对于轻钢结构压弯构件的平面计算长度的取值问题 ,在现有的设计标准中只是给出了原则性的规定 ,而在设计中符合什么样的条件才能为构件提供减少构件平面外计算长度的侧向支承点并没有提供依据。结合工程设计中常采用的檩条支承条件 ,通过采用能量法进行平面外有弹性支承的压弯构件弹性弯扭屈曲分析 ,得出可供设计时采用的分析结果。     

三边约束钢板的抗剪承载力

利用静力加载方法对4种宽厚比的三边约束钢板单元进行了试验研究,通过试验考察了三边约束钢板的破坏形态和抗剪极限承载力,分析了宽厚比对钢板抗侧性能的影响,试验结果表明:小宽厚比钢板的抗屈曲能力较强,但是对边界约束条件要求较高,易造成边界连接破坏.根据钢板破坏形态,对其抗侧性能进行了理论分析,建立了三边约束钢板的抗侧性能计算...     

Lateral buckling strengths of cold-formed rectangular hollow sections

Code rules for designing steel beams against lateral buckling which are based on data for hot-rolled I-sections are unnecessarily conservative when used for cold formed rectangular hollow section beams.Cold-formed rectangular hollow section beams have different stress-strain curves, residual stresses, and crookedness and twist. The effects of residual stress on the inelastic buckling of I-section beams are not nearly as pronounced for hollow sections with two webs, while the strengthening effects of pre-buckling deflections are greater for hollow sections. Simplistic code rules for top flange loading are very conservative when applied to hollow sections.This paper reviews elastic lateral buckling behaviour and the strength rules used to design steel beams. It develops realistic models for cold-formed rectangular hollow beams which are analysed to predict the effects of moment distribution, load height and yield stress on their strengths. The results of the analyses are used to develop improved design rules which remove much of the conservatism of present design rules.     

The effect of semi-rigid joints and an elastic bracing system on the buckling load of simple rectangular steel frames

A linear stability analysis for establishing the combined effect of joint flexibility and an elastic bracing system on the buckling load of steel plane frames is presented herein. Based on the beam-to-column model of Eurocode 3, the subsequent study shows that joint flexibility is a very important parameter that needs to be incorporated into the stability analysis of frames with semi-rigid connections. It was found that assuming flexible connections in such frames always leads to a reduction of their buckling load, which is proven to be significant in many characteristic cases. Numerical results for simple elastically braced or unbraced frames with semi-rigid connections, in tabular and graphical form, reveal the pronounced effect of joint flexibility and elastic bracing on their buckling load. The results presented herein can be readily used for the design of simple frames against buckling, while the flexible connection concept can be applied to all types of steel frames.     

Numerical modelling and design of LiteSteel Beams subject to lateral buckling

The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling.     

Numerical evaluation of the response in bending of an underground hard rock voussoir beam roof

The behaviour of a hard rock horizontally stratified roof, within a low primary lateral stress field, is investigated. The lowest roof stratum is modelled as a voussoir beam with three cracks, one at the midspan and one at each abutment. Its response in bending is computed, with the help of a distinct element computer code, for an ordered series of configurations. Two states of failure, i.e. buckling and crushing, are examined. The parameters of indeterminacy of the structure are investigated numerically and improved relations are derived for their evaluation. From the solution of the determined structure, deflections, strains and stability limits are evaluated analytically and validated numerically. Finally, in order to check against crushing, a chart is provided for the prediction of the lateral non-linearly distributed axial strain at the extreme fibre of the abutment.