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。     

薄壁组合箱梁的自由振动

研究薄壁叠加组合梁的自由振动。建立了适用于薄壁组合箱梁截面动力性能的一般分析模型。该模型基于古典叠加理论，考虑任意层压板叠合次序情况下弯曲和扭转的耦合，也就是非对称和对称以及各种边界条件。对薄壁组合梁，建立基于位移的一维有限元模型以预测自振频率和相应的振型，并由Hamilton原理派生出运动方程；考虑薄壁组合梁纤维角度、模数比、振动频率的边界条件以及组合形式的影响，得出计算结果。     

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.

     

Shear-flexible thin-walled element for composite I-beams

A shear-flexible finite element based on an orthogonal Cartesian coordinate system is developed for the flexural and buckling analyses of thin-walled composite I-beams with both doubly and mono-symmetrical cross-sections. Using the first-order shear deformable beam theory, the derived element includes both the transverse shear and the restrained warping induced shear deformations. Governing equations are derived from the principle of minimum total potential energy. Three different types of finite elements, namely, linear, quadratic and cubic elements are developed to solve the governing equations. The geometric stiffness for the buckling analysis of axially loaded, thin-walled composite beams is developed. The resulting linearized buckling problem is solved using a shifted inverse iteration algorithm. A parametric study of the effects of the aspect ratio and the fibre orientation on the tip displacement is presented. The convergence of the elements is also investigated. The elastic buckling loads for mono- and doubly-symmetric I-beam cross-sections are compared with other results available in the literature and with solutions using shell elements in a commercially available finite element program.     

Dynamic response of axially loaded monosymmetrical thin-walled Bernoulli–Euler beams

The dynamic bending–torsion coupled vibrations of elastic axially loaded slender thin-walled beams with monosymmetrical cross-sections are investigated by using normal mode method. The Bernoulli–Euler beam theory is employed and the effects of warping stiffness and axial force are included in the present formulations. The theoretical expressions for the displacement response of axially loaded slender thin-walled beams subjected to concentrated or distributed loads are presented. The method is illustrated by its application to two test examples to describe the effects of warping stiffness and axial force on the dynamic behavior of thin-walled beams. The numerical results for the dynamic bending displacements and torsional displacements are given. The proposed theory is fairly general and can be used for thin-walled beam assemblage of arbitrary boundary conditions subjected to various kinds of loads.     

Flexural–torsional behavior of thin-walled composite beams

This paper presents a flexural–torsional analysis of I-shaped laminated composite beams. A general analytical model applicable to thin-walled I-section composite beams subjected to vertical and torsional load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional responses for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric. Governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites under vertical and torsional loading, addressing the effects of fiber angle, and laminate stacking sequence.     

Behavior of biaxially-loaded rectangular concrete-filled steel tubular slender beam-columns with preload effects

In composite construction, rectangular hollow steel tubular slender beam-columns are subjected to preloads arising from construction loads and permanent loads of the upper floors before infilling of the wet concrete. The behavior of biaxially loaded thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns with preloads on the steel tubes has not been studied experimentally and numerically. In this paper, a fiber element model developed for CFST slender beam-columns with preload effects is briefly described and verified by existing experimental results of uniaxially loaded CFST columns with preload effects. The fiber element model is used to investigate the behavior of biaxially loaded rectangular CFST slender beam-columns accounting for the effects of preloads and local buckling. Parameters examined include local buckling, preload ratio, loading angle, depth-to-thickness ratio, column slenderness, loading eccentricity and steel yield strength. The results obtained indicate that the preloads on the steel tubes significantly reduce the stiffness and strength of CFST slender beam-columns with a maximum strength reduction of more than 15.8%. Based on the parametric studies, a design model is proposed for axially loaded rectangular CFST columns with preload effects. The fiber element and design models proposed allow for the structural designer to efficiently analyze and design CFST slender beam-columns subjected to preloads from the upper floors of a high-rise composite building during construction.     

Mode interaction in thin-walled equal-leg angle columns

This paper presents and discusses numerical results, obtained through Ansys shell finite element analyses, dealing with the post-buckling behaviour (mostly elastic, but also elastic–plastic), ultimate strength and failure mode nature of fixed-ended and pin-ended thin-walled equal-leg angle steel columns with coincident critical flexural-torsional and minor-axis flexural buckling loads (i.e., experiencing very strong coupling effects between these two global instability phenomena) – for comparative purposes, columns that are buckling in pure flexural-torsional and flexural modes are also analysed. Since the main aim of the work is to investigate the column imperfection-sensitivity, the analyses concern otherwise identical columns containing initial geometrical imperfections with different shapes and amplitudes, combining the competing critical buckling modes – particular attention is paid to the sign of the minor-axis flexural component. The results reported consist of column (i) elastic equilibrium paths and the corresponding peak loads and deformed configurations and (ii) elastic–plastic collapse loads and mechanisms, making it possible to assess how they are influenced by the initial geometrical imperfections.     

Buckling of shear deformable thin-walled members—I. Variational principle and analyticalsolutions

A variational formulation for the buckling analysis of thin-walled members is developed based on the principle of stationary potential energy. The formulation is based on non-orthogonal coordinates and captures shear deformation effects due to bending and warping. It is applicable to members of doubly symmetric cross-sections subject to general axial and transverse forces and naturally incorporates the effect of load position relative to the shear centre. Applying the conditions of neutral stability to the variational expression, the governing differential equations of neutral stability and associated boundary conditions are formulated. The resulting field equations are exactly solved for benchmark cases involving column flexural buckling, column torsional buckling, and lateral-torsional buckling for beams, and the results are compared to closed form solutions based on classical and other modern theories.     

Inelastic bifurcation of cold-formed singly symmetric columns

The paper describes a technique for determining the overall flexural and flexural–torsional bifurcation loads of locally buckled cold-formed channel columns. The method of analysis uses an inelastic geometric non-linear finite strip local buckling analysis to determine the flexural and torsional tangent rigidities of a locally buckled section. These tangent rigidities are substituted into the flexural and flexural–torsional bifurcation equations to calculate the inelastic overall buckling loads. The members are assumed to be geometrically perfect in the overall sense but can include geometric imperfections and yielding in the local mode. The bifurcation analysis is applied to cold-formed plain channel columns. The bifurcation loads and failure modes are compared with tests of fixed-ended columns and shown to be in good agreement with the tests. The effect of yielding is highlighted in the paper.     

A theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion

Results of a theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion are presented. The local critical bimoment, which generates local buckling of a thin-walled bar and constitutes the limit of the applicability of the classical Vlasov theory, is defined. A method of determining local critical bimoment on the basis of critical warping stress is developed. It is shown that there are two different local critical bimoments with regard to absolute value for bars with an unsymmetrical cross-section depending on the sense of torsion load (sign of bimoment). However, for bars with bisymmetrical and monosymmetrical sections, the determined absolute values of local critical bimoments are equal to each other, irrespective of the sense of torsional load. Critical warping stresses, local critical bimoments and local buckling modes for selected cases of thin-walled bars with open cross-section are determined.     

Elastoplastic buckling of circular annular plates under uniform in-plane loading

This paper deals with the elastoplastic buckling of a circular annular plate, with various axially symmetric boundary conditions and uniform axially symmetric in-plane radial loads on the inner and outer edge. The analysis is based on the standard linear buckling equations and the material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model of the material is considered. The solutions are obtained using the equilibrium approach where the governing differential equation is solved by the finite difference method which leads to the determination of eigenvalues of a homogeneous system of linear equations. Elastoplastic buckling loads for axially symmetric and asymmetric buckling shape modes with m waves in the circumferential direction are calculated and compared for both theories of plasticity. For one case, an experiment was performed and the results were compared with theoretical predictions.     

Local–global mode interaction in stringer-stiffened plates

A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global buckling mode and the strongly stable local buckling mode is highlighted. Highly unstable post-buckling behaviour and a progressively changing wavelength in the local buckling mode profile are observed under increasing compressive deformation. The analytical model is compared against both physical experiments from the literature and finite element analysis conducted in the commercial code Abaqus; excellent agreement is found both in terms of the mechanical response and the predicted deflections.     

剪切作用下冷弯槽钢的弹性屈曲

研究与腹板平行的纯剪切荷载作用下包含翼缘和卷边的整个槽钢截面的弹性屈曲,并给出了解决方案。采用样条有限条法(SFSM)对纯剪切作用下的薄壁槽钢进行弹性屈曲分析,以获得截面的弹性屈曲载荷(Vcr)。利用剪切屈曲载荷计算用于截面设计的腹板的剪切屈曲系数(KV)。主要变量为翼缘宽度、构件长度和卷边尺寸。边界条件为两端简支。根据分析结果绘制交互作用曲线,可作为设计指南,使得设计人员不用样条有限条法(SF-SM)软件也能够预测弹性屈曲剪切系数(KV)。给出了不同的翼缘宽度、构件长度和卷边尺寸下构件的典型屈曲模态。包括局部屈曲和翼缘屈曲,畸变屈曲和截面扭曲。     

Global buckling of thin-walled simply supported columns: Analytical solutions based on shell model

In this paper global buckling (i.e., flexural, pure torsional, or flexural–torsional buckling) of thin-walled columns is discussed. The considered problem is the most basic one: the column is simply supported and subjected to a uniform concentric compressive force. The column's cross-section is an arbitrary open thin-walled cross-section. For the critical forces of this problem classical analytical solutions are known. In the presented research alternative formulae are derived on the basis of modeling the member as a set of flat plane elements (or strips). As it is found, the derivations can be carried out in various ways, among which eight options are considered. The resulted critical force formulae are briefly discussed in this paper. Extensive numerical studies are also completed; these studies are summarized in a companion paper.     

多孔钢梁在组合屈曲模态下的非线性分析

讨论了一般强度和高强度多孔钢梁在组合屈曲模态下的非线性分析。建立一个考虑腹板和翼缘初始几何缺陷、残余应力和材料非线性等情况的多孔钢梁的三维有限元模型。用具有不同长度,不同截面,不同荷载条件和不同失效模态的多孔梁的试验结果验证了此有限元模型。该模型能计算多孔梁的失效荷载,跨中荷载-挠度关系和失效模态。用120根多孔梁的有限元计算数据进行了参数分析,研究截面几何尺寸,梁长和钢材料强度对多孔梁强度和屈曲性能的影响。参数研究结果显示:由于组合腹板的扭转和腹板后屈曲引起的多孔梁失效对承载力有很大的影响。对于长细比较小的多孔梁,应用高强度钢材料将能显著提高失效荷载值。将有限元计算得到的失效荷载与利用澳洲规范计算的多孔梁平面外屈曲计算结果进行了对比,发现规范的计算结果对于平面外屈曲的一般强度多孔梁是不保守的,而对于组合腹板扭转和腹板后屈曲的高强度多孔梁的失效则非常保守。     

Non-linear model for stability of thin-walled composite beams with shear deformation

A geometrically non-linear theory for thin-walled composite beams is developed for both open and closed cross-sections and taking into account shear flexibility (bending and warping shear). This non-linear formulation is used for analyzing the static stability of beams made of composite materials subjected to concentrated end moments, concentrated forces, or uniformly distributed loads. Composite is assumed to be made of symmetric balanced laminates or especially orthotropic laminates. In order to solve the non-linear differential system, Ritz's method is first applied. Then, the resulting algebraic equilibrium equations are solved by means of an incremental Newton–Rapshon method. This paper investigates numerically the flexural–torsional and lateral buckling and post-buckling behavior of simply supported beams, pointing out the influence of shear–deformation for different laminate stacking sequence and the pre-buckling deflections effect on buckling loads. The numerical results show that the classical predictions of lateral buckling are conservative when the pre-buckling displacements are not negligible, and a non-linear buckling analysis may be required for reliable solutions.     

轴心受压开口薄壁构件弹塑性屈曲荷载的统一计算方法

通过分析构件截面上应变与轴向力间的关系，以构件轴向应变为基本参数，提出了轴心受压开口薄壁构件的弹塑性屈曲荷载统一计算方法，给出了轴压构件的弯曲屈曲、扭转屈曲、弯扭屈曲等屈曲荷载的弦截法迭代格式，可应用于H形、T形、L形、十形截面等不同开口形式的轴压构件屈曲荷载计算，并可考虑具有残余应力的弹塑性本构关系。该方法以无残余应力的弹性屈曲荷载对应的轴向应变作为初始值，根据不同屈曲形式对应的非线性方程计算弦截区间点的函数值，进行弦截法迭代计算，得到弹塑性构件的临界轴向应变，进而获得屈曲荷载等信息。该方法采用的弦截法收敛速度快、计算量小、无需嵌套循环，可有效解决两端铰接轴心受压开口薄壁构件的弹塑性屈曲快速计算问题，便于工程应用。     

Torsional and flexural torsional buckling — A study on laterally restrained I-sections

Torsional and torsional–flexural buckling of columns under axial compression–as defined in the Eurocode 3-1-1(2005)–may practically occur in axially compressed I-sections, which are laterally restrained so that weak axis flexural buckling is prevented and buckling is initiated by torsional deformation about the axis of lateral restraint. The present study is focussed on the development and representation of specific buckling curves for this type of buckling mode. This is based on numerical simulations taking into account material nonlinearities as well as geometric imperfections and residual stresses. The study not only illustrates the typical buckling curves for torsional buckling, but also the transition from torsional buckling to main axis flexural buckling when the column length increases. It also shows that the use of weak-axis buckling coefficients for torsional buckling–as given in the rules of Eurocode 3-1-1–may lead to rather conservative results in many cases.     

内置薄壁H形钢-木组合梁受弯性能研究

为实现钢材与木材的高效组合,提高钢木组合梁受弯性能,提出了一种内置薄壁H形钢-木组合梁。为研究其破坏过程、破坏形态及组合受力性能,以翼缘木板宽度、抗剪连接栓钉间距、薄壁H形钢厚度、翼缘木板厚度、腹板木板高度和腹板木板厚度等为变化参数开展了受弯试验。并提出了可用于预测内置薄壁H形钢-木组合梁挠度和受弯承载力的计算公式,进行了有限元分析。结果表明：依据内置薄壁H形钢-木组合梁破坏过程及特征,可出现受拉翼缘木板受拉断裂、腹板木板受拉区开裂以及受压翼缘木板受压破坏或薄壁H形钢受压翼缘严重压屈和严重粘胶剥离的受压破坏三种破坏模式;在配置截面面积比约3.5%的薄壁H形钢的情况下,内置薄壁H形钢-木组合梁的受弯承载力、抗弯刚度、耗能和延性相对于纯木梁明显提高;腹板木板高度、翼缘木板宽度、翼缘木板厚度和抗剪连接栓钉间距等参数影响内置薄壁H形钢-木组合梁受弯性能较为明显,增加腹板木板的高度、翼缘木板的宽度、翼缘木板的厚度和减小抗剪栓钉间距可明显提高内置薄壁H形钢-木组合梁的受弯承载力;增加薄壁H形钢厚度,可使内置薄壁H形钢-木组合梁受弯承载力和刚度得到一定程度的提高;腹板木板的厚度对内置薄壁H形钢-木组合梁的受弯承载力影响不甚明显。所提出内置薄壁H形钢-木组合梁的挠度及受弯承载力计算式和有限元模型合理有效,计算结果与试验结果吻合良好。