Buckling of thin-walled girders under compound load

A theoretical study of the local buckling kof thin-walled girders with closed polygonal cross-sections is presented. The load of the girder consists of compression, asymmetrical bending and shear. The parabolic distribution of shear stresses in webs is included in the theoretical considerations. The energy method is employed and sine and polynomial series are applied to describe the deflections of any wall. A sample of the results of numerical calculations is presented for a girder with rectangular cross-section subjected to bending and shear. Some results for a girder under asymmetrical bending are also included.     

Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method

The details of an application of the finite strip method to the elastic buckling analysis of thin-walled structures with various boundary conditions and subjected to single or combined loadings of longitudinal compression, transverse compression, bending and shear are presented. The presence of shear loading is accounted for by modifying the displacement functions which are commonly used in cases when shear is absent. A program based on the finite strip method was used to obtain the elastic buckling stress, buckling plot and buckling mode of thin-walled structures and some of these results are presented.     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

Lower bound estimation of load-carrying capacity of thin-walled structures with intermediate stiffeners

The design of thin structures must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with the interactive buckling of thin-walled structures with central intermediate stiffeners under axial compression and/or a constant bending moment. The structures are assumed to be simply supported at the ends. The lower bound estimation of load-carrying capacity on the basis of the post-buckling behaviour of thin-walled structures with imperfections is studied when the distortional deformations are taken into account. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed using the transition matrix method. The present paper is a continuation of previous work by the authors (Int. J. Solids Struct. 32 (1995) 1501; 33 (1996) 315; 37 (2000) 3323), where the interactive buckling of thin-walled beam-columns with central intermediate stiffeners in the first- and the second-order approximation were considered. In the solution obtained, the transformation of buckling modes with an increase in the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The results obtained are compared with data reported by other authors.     

弯剪共同作用下不锈钢薄腹梁承载性能试验研究

为研究不锈钢薄腹梁在弯矩和剪力共同作用下的承载性能,进行了6根焊接工字形截面不锈钢梁的试验研究.结果 表明,所有梁试件的破坏形态为结合了腹板剪切屈曲和受压区板件局部鼓曲的弯剪联合屈曲.建立精细有限元数值模型对试验过程进行模拟,同时考虑了不锈钢材料、几何双非线性,局部几何初始缺陷和焊接残余应力的影响.基于得出的试验和有限...     

Simulation of the behaviour of stiffened box girders with and without shear lag

A finite element program with large deformations and plasticity is used to analyse the behaviour of stiffened compression flanges of box girders. Simulations are performed for pure bending and for bending with shear in order to investigate the diminishing of the shear lag effect at collapse. It is concluded that at the actual ultimate load, shear lag has largely disappeared but that a design at ultimate load without consideration of the shear lag may entail an inelastic behaviour under service load. First yielding occurs in the centre of the stiffened panel for pure bending and in the middle of the unloaded edges when elastic shear lag becomes important. A substantial increase of the ultimate load can be expected from an increase of the stiffener rigidity.     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

Performance-based analysis of concrete-filled steel tubular beam-columns, Part I: Theory and algorithms

This paper presents a performance-based analysis (PBA) technique based on fiber element formulations for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam-columns with local buckling effects. Geometric imperfections, residual stresses and strain hardening of steel tubes and confined concrete models are considered in the PBA technique. Initial local buckling and effective strength/width formulas are incorporated in the PBA program to account for local buckling effects. The progressive local buckling of a thin-walled steel tube filled with concrete is simulated by gradually redistributing normal stresses within the steel tube walls. Performance indices are proposed to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam-columns under axial load and biaxial bending. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral axis in a thin-walled CFST beam-column section to satisfy equilibrium conditions. The analysis algorithms for thin-walled CFST beam-columns under axial load and uni- and biaxial bending are presented. The PBA program can efficiently generate axial load-strain curves, moment-curvature curves and axial load-moment strength interaction diagrams for thin-walled CFST beam-columns under biaxial loads. The proposed PBA technique allows the designer to analyze and design thin-walled CFST beam-columns made of compact or non-compact steel tubes with any strength grades and normal and high-strength concrete. The verification and applications of the PBA program are given in a companion paper.     

Coupled instability and negative shear lag phenomenon in box girders

The explanation of the negative shear lag phenomenon in linear analysis of box girders is reviewed. The extension of the analysis to include geometrical nonlinear effects in a compression flange, due to buckling in both classical and negative shear lag environments, is presented. It is shown that in interaction the buckling and the negative shear lag have opposite effects on longitudinal stress distribution across the flange and, depending on load level, both the effects are effectively damped out. However, the overwhelming significance of buckling near the peak load may be expected. The important influence of flange transverse stiffeners and the very unusual distribution of longitudinal stresses in box girder webs in the negative shear lag region are also mentioned.     

Modeling distortional shear in thin-walled elastic beams

In this paper, the theoretical background and the numerical analyses of an advanced beam finite element that relaxes the hypothesis of the cross-section non-deformability are presented. The corresponding new modes, called distortional modes, are added to the modes describing the behavior of a classical thin-walled beam: tension/compression, bending and torsion. For instance, a load acting in a cross-sectional plane of a beam is considered to induce not only bending and torsion but also distortion. The distortion produces non-uniform shear and axial stresses together with a non-uniform warping of the cross-section. These resulting effects, significant for very thin-walled open profiles (and thin-walled closed profiles with high distortional loadings), are shown in this paper to be important when compared to bending and torsion stresses even in simple loading cases.     

Thin-walled cold-formed sections subjected to compressive loading

The weakening effects of local buckling on the compressive load carrying capability of thin-walled cold-formed sections is examined and discussed. Theoretical results are presented for the pin-ended support condition and a study is made of the local buckling and overall bending interaction behaviour of compression members with different cross-sectional shapes. It is shown that singly symmetric plain channel sections exhibit considerably different interactive equilibrium characteristics to those of I-sections for which the shear centre and section centroid are coincident.

The theoretical results given have been obtained through the solution of a differential equation which governs, approximately, the overall bending behaviour of a locally buckled compression member. Both local and overall imperfections are considered in the theoretical approach and it is shown that the effect of these is to reduce the ultimate compressive carrying capacity of cold-formed sections.

An experimental investigation of the behaviour of concentrically loaded pin-ended I-section struts and columns is reported and the findings from this are compared with theoretical predictions. The theoretical predictions of load-deflection equilibrium behaviour and stress variations with load are shown to be in good agreement with those obtained from test.

The provisions made in the UK Code of Practice and the American Specification pertaining to the design of cold-formed compression members are briefly outlined and compared. It is shown that with regard to I-section struts and columns the American design procedure gives, in general, more conservative estimates of collapse.     

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。     

Out-of-plane stability of simply supported beams with knee braces

This paper investigates the buckling of thin-walled beams braced by horizontal knee angles, which is a new practice currently coming into use in Chinese industrial buildings with small and moderate overhead cranes of light or medium duty to improve the stability of simply supported crane runway girders. It was found that this technique increases significantly the elastic buckling capacity of thin-walled beams. The increase in elastic-plastic buckling capacity may also be as high as 40% compared with unbraced beams. Simple formulae are presented for buckling moments of the knee-braced beams. Compared with the results of finite element analysis, the proposed formulae have excellent accuracy in prediction of the critical loads of knee-braced beams under concentrated load at mid-span and uniformly distributed loads. The application of the formulae was explained through an example of a practical crane runway girder.     

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.     

Performance-based analysis of concrete-filled steel tubular beam–columns,Part II: Verification and applications

The theory and algorithms of a performance-based analysis (PBA) technique for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam–columns with local buckling effects were presented in a companion paper. Initial local buckling and effective strength/width formulas for steel plates are incorporated in the PBA program to account for local buckling effects. Performance indices are used in the PBA program to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam–columns. This paper presents the verification and applications of the PBA program developed. The axial load–strain curves, ultimate axial loads and moment–curvature curves for thin-walled CFST columns predicted by the PBA program are verified by experimental data. The PBA program is then utilized to investigate the effects of local buckling, depth-to-thickness ratio, concrete compressive strengths, steel yield strengths and axial load levels on the stiffness, strength and ductility performance of thin-walled CFST beam–columns under axial load and biaxial bending. The PBA technique developed is shown to be efficient and accurate and can be used directly in the performance-based design of thin-walled CFST beam–columns and implemented in advanced analysis programs for composite columns and frames.     

Interactive buckling and load carrying capacity of thin-walled beam–columns with intermediate stiffeners

The design of thin-walled beam–columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled beam–columns with central intermediate stiffeners under axial compression and a constant bending moment. The columns are assumed to be simply supported at their ends. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed by means of the transition matrix method and Godunov’s orthogonalisation. Instead of the finite strip method, the exact transition matrix method is used in this case. The most important advantage of this method is that it enables us to describe a complete range of behaviour of thin-walled structures from all global (flexural, flexural-torsional, lateral, distortional and their combinations) to local stability. In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure. The paper’s aim is to expand the study of the equilibrium path in the post-buckling behaviour of imperfect structures with regard to the second order non-linear approximation. In the solution obtained, the transformation of buckling modes with an increase of the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The calculations are carried out for a few beam–columns. The results are compared to those obtained from the design code and to the data reported by other authors.The results discussed in the present study represent the most important results obtained by the authors in earlier investigations devoted to central intermediate stiffeners (Int. J. Solid Struct. 32 (1995) 1501; Eng. Trans. 43 (1995) 383; Int. J. Solid Struct. 37 (2000) 3323; Int. J. Solid Struct. 33 (1996) 315; Thin Wall. Struct. 39 (2001) 649; Arch. Mech. Eng. XLVIII (2001) 29).     

Experimental collapse of thin cylindrical shells submitted to internal pressure and pure bending

A thin-walled pressurised cylindrical shell is sensitive to buckling phenomena when it experiences locally a compressive stress. It is often considered that its behaviour under bending is rather similar to pure compression, but very few are the experimental investigations that precise the real behaviour of a thin pressurised cylinder submitted to a bending load. A large amount of experimental results is presented here, obtained on thin shells (550<R/t<1450) of moderate length (L/R≈2). The evolution of the cylinders' behaviour that has been recorded when internal pressure increases is outlined. It is shown that one must distinguish between local buckling and global collapse of the structure. A comparison of our experimental data to design recommendations given by two standards (NASA SP8007 and Eurocode 3) is finally achieved, putting in advance safety margins provided by these codes.     

多弹性扭转支承开口薄壁杆的扭转屈曲

研究了截面形心和剪切中心重合的多弹性扭转支承开口薄壁杆在轴向压力作用下的扭转屈曲,把作用在开口薄壁杆上的弹性扭转支承去掉,代之以相应的未知扭矩,采用Laplace变换推导出了其扭转变形的位移函数,并求得了多弹性扭转支承开口薄壁杆在轴向压力作用下扭转的屈曲特征方程。     

Buckling of thin flat-walled structures by a spline finite strip method

A method of buckling analysis of thin flat-walled structures of finite length subjected to longitudinal compression and bending, transverse compression as well as shear is described. The analysis uses the spline finite strip method and allows for boundary conditions other than simply supported ends as required in the semi-analytical finite strip method of buckling analysis.Convergence studies with increasing numbers of section knots are described for plates in compression, bending and shear, and for long columns with different support conditions subjected to compression. A buckling analysis of a stiffened plate subjected to compression and shear is compared with results from a finite element analysis.     

Geometrically non-linear approximations on stability and free vibration of composite beams

Second-order formulations based on moderate rotations are often used in finite element models because this approximation facilitates their implementation. However, in some cases this approximation is not enough to obtain all couplings among bending, twisting and stretching deformations for a beam member. Therefore, a simplified second-order formulation may lead to the subsequent loss of some significant terms in the non-linear strains. Without these terms the beam model may predict inaccurate results when the effect of large rotations is important. The present paper investigates the influence of large rotations on the buckling and free vibration behavior of thin-walled composite beam. To carry out this analysis it is necessary to use a geometrically higher-order non-linear beam theory. A distinctive feature of the present study over others available in the literature is that this beam model incorporates, in a full form, the effects of shear flexibility (bending and warping shear). The numerical results show that second-order formulation overestimates the buckling load and natural frequency values when the effect of large rotation is important, and this effect depends on some factors such as load condition and stacking sequences.