双轴对称楔形工字钢梁的弹性弯扭屈曲

本文利用基于板壳屈曲理论的有限元方法对楔形薄壁构件的弯扭屈曲进行了分析,对两种基于薄壁杆件理论的楔形工字钢梁弯扭屈曲分析方法进行了对比。基于较精确的楔形薄壁构件屈曲理论,对承受线性变化端弯矩作用的楔形梁的弯扭屈曲进行了大量分析,并提出了新的楔形工字钢梁临界弯矩计算公式。该公式形式与等截面梁的相同,便于工程应用。     

单轴对称工字钢梁的弹塑性稳定系数

工字钢梁在工业厂房中应用非常广泛,而平面外弯扭失稳是薄壁构件的主要失稳模式,比单独的扭转失稳和弯曲失稳要复杂的多。以往钢梁稳定研究主要集中在双轴对称截面,单轴对称截面的整体稳定性研究较少。为此,对承受跨中集中荷载和关于跨中对称的两点荷载的单轴对称工字钢梁进行了弹塑性弯扭屈曲分析,考虑初始变形和两种残余应力分布。通过算例分析得到不同截面尺寸和荷载作用点高度的稳定系数变化规律,以修正的ECCS公式为基础拟合得到了适用于单轴对称截面横向荷载作用下的弯扭屈曲稳定系数公式,该公式适用于的荷载作用点高度为剪心到上翼缘以上120mm,和截面宽高比为0.42~0.76范围内的单轴对称工字钢梁。与有限元计算结果对比表明,公式计算结果与有限元分析结果符合良好,且公式与有限元计算结果相比较为保守。     

局部封闭和开口薄壁压弯构件的弯扭屈曲

单轴对称开口薄壁压弯构件在荷载作用于对称平面内时有可能发生弯扭屈曲。在这种情况下,其临界荷载总是低于平面内弯曲失稳破坏荷载,如果在构件的开口边加上缀板,使之形成若干断续的封闭截面,则弯扭屈曲临界荷载将显著提高,并有可能使破坏模式由弯扭屈曲转化为平面内弯曲失稳。本文提出了一种计算薄壁压弯构件弯扭屈曲荷载的方法,这种方法对局部封闭和开口截面都能适用。曾经做了213根具有不同长细比、偏心距、缀板间距(或无缀板)的冷弯薄壁型钢压杆试验,其结果与理论符合较好。     

正六边形孔蜂窝钢梁的整体稳定研究

通过将双轴对称工字形截面的正六边形孔蜂窝梁的等效刚度代入当量实腹梁弯扭屈曲临界弯矩值的公式中,得到蜂窝梁的弯扭屈曲临界弯矩值公式。为考虑开孔引起的剪切变形对蜂窝梁弯扭屈曲临界荷载值的影响,并验证所得蜂窝梁弯扭屈曲临界荷载公式的正确性,通过与有限元软件计算同尺寸的蜂窝梁得到的弯扭屈曲临界弯矩相比较,证明了所推公式具有满足工程所需的精度。最后为方便工程应用,对蜂窝梁整体稳定性计算公式进行了改进。     

薄壁复合箱型梁的弯曲-扭转屈曲分析

对一轴心受压薄壁复合构件的屈曲进行研究。提出一个广义的分析模型,可用于分析轴心受压薄壁复合箱型梁的弯曲、扭转以及弯扭屈曲作用。此模型基于经典层压理论,考虑了任意层压堆积规律,结构的弯曲和扭转模式的耦合问题,如非对称以及对称和各种边界条件。采用一个基于位移的一维有限元模型来预测薄壁复合钢筋的临界荷载和随后的屈曲模式。从总势能的平稳值原则中推导出屈曲控制方程。轴心受压薄壁复合件的数值计算结果可用于估测纤维角、各向异性和边界条件对临界屈曲荷载和复合件模态的影响。     

薄壁复合箱型梁的弯曲—扭转屈曲分析

对一轴心受压薄壁复合构件的屈曲进行研究。提出一个广义的分析模型，可用于分析轴心受压薄壁复合箱型梁的弯曲、扭转以及弯扭屈曲作用。此模型基于经典层压理论，考虑了任意层压堆积规律，结构的弯曲和扭转模式的耦合问题，如非对称以及对称和各种边界条件。采用一个基于位移的一维有限元模型来预测薄壁复合钢筋的临界荷载和随后的屈曲模式。从总势能的平稳值原则中推导出屈曲控制方程。轴心受压薄壁复合件的数值计算结果可用于估测纤维角、各向异性和边界条件对临界屈曲荷载和复合件模态的影响。     

不等端弯矩作用下薄壁梁临界弯矩的计算分析

薄壁梁的弯扭屈曲分析是一个较为复杂的问题,在荷载作用下沿梁的弯矩为非均匀分布时．其屈曲方程的求解较为困难。根据梁柱杆端变形增量相关方程和改进后的CDC法,将薄壁梁的弯扭模型等效为拉弯模型,顺利的算出不等端弯矩作用下薄壁梁的临界弯矩,并提出建议公式。经计算与数值解比较,结果令人满意。     

复合荷载作用下钢梁弯扭屈曲临界弯矩研究

基于由完备的复合荷载作用下钢梁弯扭屈曲总势能方程推导的平衡微分方程,采用Galerkin法推导了考虑横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式,建立了等效弯矩系数的计算理论。依据等效弯矩系数的计算理论确定了7种常见工况的等效弯矩系数理论计算式并给出了6种特殊工况的Cb实用计算式,从Cb计算式的计算精度、适用范围和形式三个方面对国内外文献的Cb计算式进行对比,验证了等效弯矩系数理论的正确性并提出了Cb计算式的选用准则,最后通过2个数值算例验证了复合荷载作用下钢梁临界弯矩Mcr计算式的正确性和Cb计算式选用准则的合理性。结果表明：考虑了横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式形式简单、物理意义明确且便于计算;Cb实用计算式的适用范围广且精度高;等效弯矩系数的选用准则合理、有效。     

复合荷载作用下双轴对称工字形悬臂梁的弯扭屈曲分析

基于能量变分法,推导了均布荷载和端部作用集中荷载下的双轴对称工字形截面悬臂钢梁的弯扭屈曲总势能方程,其中截面弯扭屈曲变形的位移和转角分别选用一项和无穷项傅里叶级数来表达模态试函数.根据最小势能原理无量纲化后,获得复合荷载作用下悬臂钢梁无量纲的临界荷载的解析解;通过无穷级数形式解答的无量纲临界弯矩的解析解进行收敛性分析,...     

轴心受压杆件的弯扭屈曲

全面梳理了轴压杆弯扭屈曲的理论分析过程和工程应用方法。只有一个对称轴或无对称轴的截面,可能出现弯扭屈曲;当为双轴对称截面时,可能发生扭转屈曲;这时临界荷载可能小于通常的弯曲屈曲的欧拉临界荷载。根据弹性弯扭屈曲理论,GB 50017—2017《钢结构设计标准》给出了扭转屈曲和弯扭屈曲的设计公式。     

Elastic flexural-torsional buckling of thin-walled cantilevers

Previous studies by the authors revealed that the two representative theories with slight differences between, widely used in investigating the flexural-torsional buckling of thin-walled beams, have led to two different solutions in well-known literature for assessing critical loads of simply supported beams of monosymmetric cross section. With these two solutions, significant differences in critical loads may be found for these monosymmetric beams. Based on the classical variational principle for buckling analyses, a new theory on the flexural-torsional buckling of thin-walled members was proposed by the authors. In this paper, this new theory as well as the other two typical theories is employed to investigate the flexural-torsional buckling of cantilevers.This paper first gives a brief review and a careful comparative study on the flexural-torsional buckling of thin-walled cantilevers employing three different buckling theories. Differences between these theories are demonstrated with investigations on buckling of cantilevers under pure bending and two typical transverse loads. Explicit solutions, capable of considering variations of beam length and loading position along the vertical axis of cross section, are presented for predicting the critical loads of doubly symmetric cantilevers under two typical transverse loads. Advantages of presented solutions, such as good accuracy and ease of use, are exploited through the comparisons of critical results with those from existing solutions and finite element analyses.     

单轴对称双伸臂工形变截面钢梁整体稳定性分析

本文对简支单轴对称双伸臂工形变截面钢梁的整体稳定性进行了分析,采用能量法导出这种梁弯扭屈曲临界荷载的一般方程,计算结果业经编制成表,根据模型试验,对本文的计算进行了验证,计算值试验值基本符合。     

Buckling of elastically restrained beams with web distortions

An energy method is developed for studying the distortional buckling of monosymmetric I-section beams subjected to elastic restraints. The buckling solution is developed in terms of an eigenproblem for four by four symmetric matrices. The distortional buckling of monosymmetric I-beams with translational, minor axis rotational and twisting restraint applied to the smaller tension flange is considered, and the solutions are compared with predictions which assume non-distortion of the cross-section.     

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.     

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.     

Some thoughts on a surprising result concerning the lateral-torsional buckling of monosymmetric I-section beams

This technical note addresses a surprising result concerning the lateral-torsional buckling of monosymmetric I-section beams: amongst all bending moment diagrams caused by any combination of applied end moments and transverse loads acting at the shear centre, the lowest critical moment does not necessarily correspond to uniform bending, which is at odds with the “intuitive expectation” of most engineers that such bending moment distribution is the most unfavourable with respect to lateral-torsional buckling. It is shown, by means of several illustrative examples, that this may not be the case for I-section beams with unequal flanges (monosymmeric cross-section – symmetry with respect to the minor axis). Moreover, the critical inspection of the terms (i) associated with the cross-section monosymmetry and (ii) appearing in the beam potential energy expression and differential equilibrium equation provides the mechanical/mathematical explanation for this surprising behavioural feature.     

Analytical and parametric investigations on lateral torsional buckling of European IPE and IPN beams

Lateral torsional buckling is one of the main failure modes controlling the strength of the slender thin-walled members. A transversely or transversely and axially combined loaded member that is bent with respect to its axis of greatest flexural rigidity may buckle laterally and twist as applied load reaches its critical value unless the beam is provided with a sufficient lateral support. This study intends to present a unique convenient equation that it can be used for calculating critical lateral-torsional buckling load of simply supported European IPE and IPN beams. First, an analytical model is introduced to describe lateraltorsional buckling behavior of beams with monosymmetric cross-section. The analytical model includes first order bending distribution, load height level and monosymmetry property of the section. Then, parametric study is carried out using the analytical solutions in order to establish a simplified equation with dimensionless coefficients. The effect of slenderness and loading positions on lateral-torsional buckling behavior of IPE and IPN beams are studied. The proposed solutions are compared to finite element simulations where thin-walled shell elements and beam elements including warping are used. Good agreement between the analytical, parametric and numerical solutions is demonstrated. It is found out that the lateral-torsional buckling load of European IPE and IPE beams can be determined by presented equation and can be safely used in design procedures.

     

薄壁钢梁稳定性计算的争议及其解决

在规范修订过程中,对钢梁的整体稳定性计算,有学者对《钢结构设计规范》(GBJ17—88)所依据的临界弯矩计算公式提出了质疑,并提出了新的计算公式。本文对规范所依据的公式和新提出的公式所依据的理论进行了对比,对新公式所依据的理论提出了疑问。为避免薄壁构件理论引入的各种假设带来思辨上难以解决的争议,本文采用ANSYS通用有限元程序的三维板壳单元SHELL63进行了6组共36根梁的整体失稳分析。有限元分析结果表明,采用板稳定理论求得的梁临界弯矩与《钢结构设计规范》(GBJ17—88)所依据的公式符合较好,而与新提出的公式比较相差较大。本文根据薄壁梁弯扭稳定理论,推导了考虑非线性正应变和剪应变的梁失稳过程应变能的变化公式,从而解释了考虑非线性剪应变的理论与ANSYS分析结果不符的原因,并对传统的稳定理论得到的结果进行了肯定。     

Distortional buckling in monosymmetric I-beams: Reverse-curvature bending

This paper deals with distortional buckling in monosymmetric propped cantilever I-beams under two types of load: a central point load and a uniformly distributed load. Top-flange and bottom-flange load positions are considered. ABAQUS is used for the investigation. Moment modification factors are obtained and are compared with those based on Structural Stability Research Council Guidelines, which take into account lateral–torsion buckling only. It is seen that provisions in SSRC Guidelines seriously overestimate the critical load, especially for short beams.     

Buckling of monosymmetric arches under point loads

A finite element procedure is described for analysing the flexural-torsional buckling of arches of monosymmetric cross-section. First an inplane analysis is performed to obtain the distributions of axial force and bending moment in the arch. These are then substituted into the buckling equation for monosymmetric arches, and the resulting eigenvalue problem is solved numerically. Higher order quintic shape functions are used to describe the element displacement fields. The effects of the distances from the arch shear centre axis of point and uniformly distributed loads are also included in the analysis.

Flexural-torsional buckling tests on circular aluminium arches of monosymmetric I-section are also described. The test results for arches subjected to central concentrated point loads are compared with the finite element theory.