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.     

Distortional buckling in braced-cantilever I-beams

This paper deals with distortional buckling of braced-cantilever monosymmetric I-beams under three types of load: a tip point load, a uniformly distributed load and a moment at the end. Top-flange and bottom-flange load positions are considered for the first two load cases. ABAQUS is used for the investigation. The effect of different types of bracing on buckling load is investigated. Results are compared with results from previous experimental investigations. It is also found that top lateral bracings are very effective for beam sections having larger bottom-flanges when a point load or a uniformly distributed load acts at the top-flange, and for the uniform moment case, except for the T-section or the inverted T-section cantilever beams. On the other hand, bottom lateral bracings are very effective for beam sections having larger top-flanges. When loads are placed at the bottom-flange, position of any kind of lateral bracing has practically no effect on the buckling capacity of a monosymmetric cantilever beam, except for the inverted T-section cantilever beams.     

装配式钢框架节点带Z字形悬臂梁段和削弱梁段连接的抗震性能研究

为研究装配式钢框架节点带Z字形悬臂梁段和削弱梁段拼接的抗震性能,采用拼接区和削弱梁段共同耗能设计了4个试件。对4个试件进行了低周往复加载试验以及单调及往复加载的有限元分析。通过对试件的破坏模式和拼接区的滑移情况进行了分析,研究了以梁端弯矩 转角表征的滞回曲线、骨架曲线、耗能能力、转动能力等。结果表明：试件主要利用削弱梁段的塑性变形和拼接区的滑移实现耗能;其失效模式为螺孔或者焊缝处撕裂、削弱梁段处局部屈曲和削弱梁段处弯扭失稳;为保证节点充分发挥耗能能力,应增大削弱梁段处的侧向约束,防止发生弯扭失稳;为满足现场安装方便的要求和应对工厂加工精度不足的现状,可以在悬臂梁段翼缘开大孔;为降低工厂加工难度,可以将方钢柱内隔板替换为三角形垂直加劲肋。     

Elastic lateral buckling of cantilever Litesteel Beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.     

Coupled static and dynamic buckling of thin walled beam by spline finite element

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.     

变截面悬臂钢梁稳定性分析

采用有限元分析软件MARC,对变截面悬臂钢梁进行了非线性屈曲分析,分析了不同约束情况下钢梁的极限承载力,从而为变截面悬臂钢梁的设计奠定理论基础。     

Lateral buckling of web-tapered I-beams: A new theory

This paper presents a new theory for the lateral buckling of web-tapered I-beams. Linear analysis is first conducted by taking account into the tapering effects of web-tapered I-beams, where the deformation compatibilities of the two flanges and web are considered in terms of the basic assumptions of thin-walled members. Subsequently, the total potential for the lateral buckling analysis of web-tapered I-beams is developed, based on the classical variational principle for buckling analysis. The lateral buckling loads of web-tapered cantilevers and simply supported beams of I-sections from the proposed theory are compared with those from the finite element (FE) analyses using two shell element models and two widely used beam element models. The two beam element models respectively represent the equivalent method using prismatic beam elements and the typical tapered beam theory in existing literature. These comparisons show that the results based on the total potential proposed in this paper are more accurate in predicting the lateral buckling loads of web-tapered I-beams than those in existing theories, indicating that the theory proposed in this paper is superior to existing theories. It is also found that the equivalent method using prismatic beam elements may yield unreliable buckling loads of tapered beams.     

Optimization of open cross section of the thin-walled beam with flat web and circular flange

This paper is devoted to cold-formed thin-walled beams with open cross section. The beam cross section is optimized for a fixed cross section area under strength and stability constraints. Optimal geometrical parameters of the cross section are determined with regard to maximal and safe bending moment. The strength condition is a classical condition applied to the theory of beams for assumed allowable stress. The stability condition serves also as a classical condition for lateral buckling, taking the warping torsion into account. Moreover, the thin-walled beams have been analyzed, for which the shear center, i.e. the main pole, is located in the centroid of the cross section. Results of the numerical analysis are given. Figures present examples of optimal cross sections of the thin-walled beams.     

Lateral distortional buckling tests of a new hollow flange channel beam

The LiteSteel beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. The LSBs are commonly used as flexural members in buildings. However, the LSB flexural members are subjected to lateral distortional buckling, which reduces their member moment capacities. Unlike the commonly observed lateral torsional buckling of steel beams, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist, and cross sectional change due to web distortion. An experimental study including more than 50 lateral buckling tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. It included the available 13 LSB sections with spans ranging from 1200 to 4000 mm. Lateral buckling tests based on a quarter point loading were conducted using a special test rig designed to simulate the required simply supported and loading conditions accurately. Experimental moment capacities were compared with the predictions from the design rules in the Australian cold-formed steel structures standard. The new design rules in the standard were able to predict the moment capacities more accurately than previous design rules. This paper presents the details of lateral distortional buckling tests, in particular the features of the lateral buckling test rig, the results and the comparisons. It also includes the results of detailed studies into the mechanical properties and residual stresses of LSBs.     

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.     

Finite element formulation for inflatable beams

The discretized nonlinear equations for bending and buckling of inflatable beams are written by use of the virtual work principle with Timoshenko's kinematics, finite rotations and small strains. The linearized equations around a pre-stressed reference configuration are then deduced, giving rise to a new inflatable beam finite element. The stiffness matrix contains the shear coefficient and the internal pressure. Use is made of the particular 3-node beam element to investigate the bending and the buckling of a cantilever beam, the deflection of a pinched torus and the buckling of a torus submitted to a radial compressive force. The numerical results obtained with the beam element are shown to be close to analytical and three-dimensional (3D) membrane finite element results. The validity of the numerical results is discussed, in connection with the concepts of the crushing force or the wrinkling pressure of the inflated beam.     

Analysis of equal leg single-angle section beams subjected to biaxial bending and constant axial compressive force

Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure.     

短悬臂斜拉桥主梁正应力分布试验研究

宽跨比大于0.5或高跨比大于0.2的梁按简单梁理论计算的正应力误差较大,因而分析短悬臂主梁的受力性能时,应考虑横向弯曲效应。为了研究短悬臂斜拉桥主梁横向弯曲变形对正应力的影响,定义了正应力不均匀系数,并对宽跨比1∶1的有机玻璃节段模型进行荷载横向对称变位试验,采集索力及应变增量数据进行分析。试验和有限元数据对比,可知:荷载横向不同作用位置对索力及剪力滞的影响很小,其引起的顶板横向弯曲变形会改变加载截面附近正应力的大小和分布规律;横弯效应对正应力的影响往自由端逐渐衰减,往固定端先减小后增大;塔根附近主梁应力的大小及不均匀程度与无横弯影响的结果相差很大。     

能量法求解有侧移框架的弹性屈曲荷载

运用层模型能量法研究了有侧移框架弹性屈曲,根据框架失稳模式和边界条件,选择合适的位移函数,采用Timoshenko梁理论,建立结构总势能方程,利用势能驻值条件求解结构弹性失稳临界荷载,能量法简单实用,精度很高。     

A comparative study of continuous steel-concrete composite beams prestressed with external tendons: Experimental investigation

A comparative study of prestressed continuous steel-concrete composite beams is carried out based on an experimental investigation. Four full-scale continuous composite beams were tested, among which two were two-span beams and two were three-span beams. One of the two-span beams was a conventional non-prestressed composite beam, and the other was a composite beam prestressed with external tendons in both the positive and negative moment regions. One of the three-span composite beams was non-prestressed, and the other was prestressed only in the negative moment regions with external high-strength tendons. The cracking behaviors, distortional lateral and local buckling as well as the load carrying capacity of the beams were investigated experimentally. Full plasticity was developed at the mid-span section of each beam; however, the maximum moments attained at the internal supports were governed by local buckling, which is related to the slenderness of the composite section. It is found that in hogging moment regions, the ultimate moment resistance of a composite beam prestressed with external tendons is governed by either distortional lateral buckling or local buckling, or an interactive mode composed of distortional lateral and local buckling. The results show that exerting prestressing on a continuous composite beam with external tendons increases the degree of the internal force and moment redistribution in the beam. A design proposal based on moment redistribution to evaluate the load carrying capacity of continuous composite beams with external tendons is proposed.     

椭圆空心截面梁侧向失稳分析

分析椭圆空心截面(EHS)构件弯曲时的侧向稳定性。对8根截面(高厚比为2)的无侧限EHS梁进行三点弯曲试验,并记录试件的试验设备、材料性质、截面几何形状、残余应力以及荷载、变形响应。使用数值模拟方法对试验数据进行补充,并依据试验结果验证其正确性。数值分析用于评估截面高厚比和构件长细比对侧向稳定性的影响。基于结构特性相关数据建立椭圆空心截面梁的侧向扭转屈曲曲线。提出限制长度以下时,侧向扭转屈曲(LTB)可不考虑。     

体外预应力钢-混凝土组合连续梁的试验研究及有限元分析

与承受正弯矩的简支梁不同,连续梁中支座部分承受负弯矩,组成组合梁的钢板件受压力作用,其力学性能受稳定控制,不考虑稳定影响的规范简化塑性算法会带来不安全的结果.以Ⅱ类、Ⅲ类组合梁和是否配置预应力筋为参数,进行了两组共四根连续组合梁的单调加载对比试验.试验结果表明:无论预应力连续组合梁或是普通连续组合梁,最终破坏特征均为负弯矩区混凝土开裂,钢腹板局部屈曲,整个截面畸变失稳,正弯矩区混凝土板压碎;正弯矩区的承载能力可由简化塑性计算方法计算,而负弯矩区的受力性能由稳定控制,影响其承载能力的主要因素为板件的宽厚比所表征的截面种类,考虑屈曲的承载力计算方法与试验结果吻合.对各组合梁进行了有限元数值分析,分析考虑界面滑移、预应力、稳定等影响,结果和试验吻合较好.     

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.     

与刚性铺板相连的H形钢梁的整体稳定保证条件

通过能量法对与刚性铺板相连的H形钢梁的弹性整体稳定进行了分析,分析中考虑了在连续侧向约束条件下,由于梁端部负弯矩的存在,对梁整体稳定承载力产生的不利影响。通过编制的有限元程序分析计算,得出了实际设计中考虑梁端部负弯矩影响时,保证梁整体稳定的控制条件。     

Buckling of frames braced by flexural bracing

This paper investigates the buckling of multistory frames braced by vertical beams. The sectional properties of the frames and the bracing beam are assumed to vary linearly along the height; the axial forces in the columns and the bracing beam are also assumed to linearly change along the height. A relationship between the buckling load and the bracing rigidity is established. The threshold rigidity for the vertical bracing beam which is just enough to make the frames buckle in a non-sway mode is obtained. The result may be used as a rational basis for classifying sway frames and non-sway frames after taking the influence of initial imperfections and lateral loads into account.