Static and dynamic interactive buckling of isotropic thin-walled closed columns with variable thickness

The present paper deals with static and dynamic analysis of interactive buckling of thin-walled closed columns with variable thickness subjected to in-plane constant and/or pulse loading. This investigation is concerned with thin-walled structures with corners bevelled at the angle of 45° under axial compression. The plate model is adopted for the structures. The material, all plates are made of, is subject to Hooke's law. The structures are assumed to be simply supported at the ends. The differential equations of motion have been obtained from Hamilton's principle. In this paper the static solution has been obtained by Koiter's asymptotic method in the second-order approximation. The study is based on the numerical method of the transition matrix using Godunov's orthogonalization. The interaction of an overall mode with two local modes having the same wavelength has been considered (i.e. three-mode approach). The nonlinear equations of dynamic stability are solved with the Runge–Kutta method. The calculations are carried out for settled imperfections.     

Euler buckling of thin-walled composite columns

Pultruded composite structural members with open or closed thin-walled sections are being extensively used as columns for structural applications where buckling is the main consideration in the design. In this paper, global buckling is investigated and critical loads are experimentally determined for various fiber reinforced composite I-beams of long column length. Southwell's method is used to determine the critical buckling load about strong and weak axes. The experimentally determined buckling load is compared with theoretical predictions. A number of observations about testing methodology and data reduction techniques are presented.     

Dynamic buckling of thin-walled viscoplastic columns

The purpose of this paper is the analysis of strain-rate effect in dynamic stability of thin-walled orthotropic column of closed rectangular cross-section, subjected to in-plane pulse loading of finite duration. For the solution the first-order shear deformation theory displacement field is employed with the Green–Lagrange strain tensor application. The effect of strain rate sensitivity is included in the framework of the viscoplasticity constitutive Perzyna model for material behaviour under high strain rate loading. The numerical results are obtained with the finite element method application. In the performed analysis the strain-rate effect influence on the dynamic buckling load is examined as well as the initial imperfections of walls, pulse shape and the orthotropy ratio are considered. The results of dynamic criteria application are compared furthermore.     

Torsional-flexural buckling of open thin-walled columns with battens

A rational method for determining the torsional-flexural buckling load of thin-walled open sections with battens is presented. Theoretical results are compared with experimentally obtained buckling loads for a number of different cases. It is shown that torsional-flexural buckling behaviour is dependent on the number and spacing of the battens used and the torsional-flexural buckling load can be predicted with reasonable accuracy using a simple formula which is valid for both battened and unbattened columns.     

Global buckling and the interaction of initial imperfections of columns subjected to conservative loading

This paper deals with the problem of global instability of slender systems with imperfections. The inaccuracies in the systems are modelled assuming an initial curvature and the introduction of the eccentricity of an external load. Systems loaded by Euler’s load or by a force directed towards the positive pole are considered. The problem is formulated on the basis of an energetic method. Analysis of the global imperfections is carried out. The results of analytical, numerical and experimental research concerning the mutual relations between the introduced imperfections and their influence on the system behaviour are presented.     

Distortional buckling modes of semi-discretized thin-walled columns

This paper presents distorting buckling solutions for semi-discretized thin-walled columns using the coupled differential equations of a generalized beam theory (GBT). In two related papers recently published by the authors a novel semi-discretization approach to GBT has been presented. The cross section is discretized and analytical solutions are sought for the variation along the beam. With this new approach the general GBT equations for identification of a full set of deformation modes corresponding to both homogeneous and non-homogenous equations are formulated and solved. Thereby giving the (complex) deformation modes of GBT which decouple the state space equations corresponding to the reduced order differential equations.In this paper the developed semi-discretization approach to generalized beam theory (GBT) is extended to include the geometrical stiffness terms, which are needed for column buckling analysis and identification of buckling modes. The extension is based on an initial stress approach by addition of the related potential energy terms. The potential energy of a single deformation mode is formulated based on a discretization of the cross section. Through variations in the potential energy and the introduction of the constraints related to beam theory this leads to a modified set of coupled homogeneous differential equations of GBT with initial stress for identification of distortional displacement modes. In this paper we seek instability solutions using these GBT initial stress equations for simply supported columns with constrained transverse displacements at the end sections and a constant axial initial stress. Based on the known boundary conditions the reduced order differential equations are solved by using the trigonometric solution functions and solving the related eigenvalue problem. This gives the buckling mode shapes and the associated eigenvalues corresponding to the bifurcation load factors. Thus the buckling modes are found directly by the analytical solution of the coupled GBT-equations without modal decomposition. Illustrative examples showing global column buckling, distortional buckling and local buckling are given and it is shown how the novel approach may be used to develop signature curves and elastic buckling curves. In order to assess the accuracy of the method some of the results are compared to results found using the commercial FE program Abaqus as well as the conventional GBT and FSM methods using the software packages GBTUL and CUFSM.     

Local and distortional buckling of thin-walled short columns

This paper assesses the applicability of Eurocode 3 (EC3) to the prediction of the compression capacity of short fixed-ended columns with different cross-sections. This compression capacity is determined by combining the effective width of plane elements due to local buckling and the effective stiffener thickness due to distortional buckling. Numerical calculations have been carried out in order to compare alternative methods for determining the minimum elastic distortional buckling stress in compression. The method given in EC3 does not correlate as well as Lau and Hancock's method with the results given by Generalized Beam Theory (GBT). The end boundary conditions have a significant influence on the distortional buckling strength, and thus also on the compression capacity of short columns. Selected experimental results from compression tests on C-, Hat- and rack upright-sections are compared with the predictions given by EC3. The procedure in EC3 was modified by determining the distortional buckling stress using GBT, taking into account the actual column length and the end boundary conditions. This lead to better agreement between the experimental results and the theoretical predictions.     

冷弯薄壁卷边槽钢轴压构件畸变与局部相关屈曲试验研究

对卷边尺寸不同的两类腹板中间设置加劲卷边槽形截面,共18个冷弯薄壁型钢固支轴压试件进行畸变屈曲与局部屈曲相关作用的静力试验研究。得到试件的屈曲模式、相关屈曲行为、破坏模式以及极限荷载。试验结果表明：畸变屈曲与局部屈曲的耦合相关对试件的变形和极限荷载有不利作用;畸变屈曲与局部屈曲的耦合相关作用存有较大的屈曲后承载力;畸变屈曲与局部屈曲的耦合相关顺序,即畸变屈曲 局部屈曲耦合相关、局部屈曲 畸变屈曲耦合相关,对试件的变形、非线性平衡路径、破坏模式以及极限荷载的影响有所不同。采用ABAQUS有限元软件对试件进行模拟分析,计算结果与试验结果吻合良好。     

Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.     

Design of thin-walled plain channel section columns against flexural buckling

The paper presents a comparison of design strengths of thin-walled plain channel section columns, which have slender flanges and may undergo local buckling, with tests and analytical ultimate loads. The design strengths are obtained using the British, American and Australian specifications for cold-formed steel structure. The comparison is shown for fixed-ended and pin-ended columns.

A simple design procedure is presented for plain channel section columns. By introducing a ‘pin-ended stub column strength’, it is possible to calculate accurately the strength of concentrically loaded pin-ended columns without resorting to a beam-column design approach. It is also possible to account for the different effects of local buckling on the strengths of pin-ended and fixed-ended columns.     

Asymmetric effects of prop imperfections on the upheaval buckling of pipelines

Submarine pipelines often carry products which are much hotter than the surrounding seawater. The potential thermal expansion is restrained by friction between the pipeline and the seabed, causing the development of large compressive axial forces in the line, which can lead to buckling of the pipeline.

This paper takes a fresh look at the vertical buckling of a pipeline encountering a point irregularity on an otherwise perfectly flat seabed, the so-called ‘prop case’. Some approximations and assumptions in earlier work in this area are reexamined and their effects are calculated. Most importantly, the assumption that buckling is symmetric about the prop is tested. Asymmetric results are found, at a lower critical temperature than the symmetric mode, a fact which may have significant implications for design.     

Some aspects of dynamic interactive buckling of composite columns

The static and dynamic problem of interaction of global buckling modes in compressed columns with complex open cross-sections was considered in this paper. Columns made of laminate composites were assumed to be simply supported at both loaded ends. A plate model was adopted in the analysis. Within the frame of the first order nonlinear approximation, the dynamic problem of modal interactive buckling was solved by the transition matrix using a perturbation method. Distortions of cross-sections and a shear-lag phenomenon were taken into consideration. A modification of the Kleiber–Kotula–Saran quasi-bifurcation dynamic criterion [Kleiber M, Kotula W, Saran M. Numerical analysis of dynamic quasi-bifurcation. Eng Comput 1987;4:48–52.] was proposed. A comparison of the proposed modification to the Budiansky–Hutchinson criterion [Budiansky B, Hutchinson JW. Dynamic buckling of imperfection-sensitive structures. In: Goetler H, editor. Proceedings of the eleventh international congress of applied mechanics, Munich, 1966. p. 636–51.] was presented for rectangular pulse loading.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

Elastic and elasto-plastic buckling of thin-walled columns subjected to uniform compression

The problem of local stability loss in the elasto-plastic range of a thin-walled column, loaded by uniform compressive stresses, is examined on the basis of the J₂ deformation theory and the J₂ incremental theory of plasticity. The problem is solved in two different ways. Several types of closed and open cross-sections are considered. The results of numerical calculations are presented in graphical form, showing the relationship between the critical stress and the slenderness ratio for the column section. All possible buckling modes in the elastic range and local buckling in the elasto-plastic range are demonstrated in the case of a column of channel form cross-section.     

Numerical studies of interactive buckling in prestressed steel stayed columns

A steel column that is reinforced by prestressed stays generally has an increased strength in axial compression. In the past, greater emphasis was placed on obtaining its higher critical buckling load. However, detailed knowledge of the post-buckling behaviour is important to ensure the safety and the efficiency of the structure. Although a few studies into the post-buckling behaviour exist, interactive buckling behaviour has never been investigated. As interactive buckling can lead to more dangerous instabilities, the current work examines this for the most popular stayed column configuration using nonlinear finite element analysis. It is shown that interactive buckling becomes the worst case, with a commensurate decrease in the maximum load capacity, where a higher mode governs the critical buckling response.     

Buckling and post buckling of thin-walled composite columns with intermediate-stiffened open cross-section under axial compression

The thin-walled composite columns with an open cross-section reinforced by intermediate stiffener under axial compression have been considered. The finite element method is employed to study the buckling behaviour of the thin-walled composite column. Eigenvalue analyses are carried out first to predict the buckling load and buckling mode shapes of the column, and then the geometric nonlinear analyses are performed to investigate the nonlinear buckling properties and post-buckling behaviour of the thin-walled structures. The type of angle ply symmetric laminate is used. The investigation is performed over several values of ply arrangement angle and various values of stiffener parameter. The numerical results show a significant effect of the intermediate stiffeners and composite ply angle on loading capacity and buckling behaviour of the thin-walled composite column. The research provides insight into the thin-walled structure and composite laminate, which is employed to enhance the loading capacity of thin-walled composite structures.     

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).     

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.     

高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲性能研究

建立了考虑材料和几何双重非线性的550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲性能分析的有限元模型,并通过对两种厚度高强冷弯薄壁型钢轴压构件畸变屈曲试验已有结果的分析比较验证了其有效性;采用该模型进一步分析了厚度、长度、初始缺陷模式及幅值等参数对畸变屈曲轴压构件承载力的影响,并对轴压构件畸变屈曲发生机理进行了探讨。结果表明：厚度、长度和初始缺陷模式是影响畸变屈曲轴压构件承载力的主要因素,且卷边面内屈曲是槽形截面轴压构件发生畸变屈曲的主要原因。通过理论计算与试验结果的对比分析,表明可以采用建议方法计算此类复杂截面轴压构件的畸变屈曲承载力。