半离散法分析薄壁柱的畸变屈曲

采用广义梁理论(GBT)的耦合差分方程解决了半离散法分析薄壁柱的畸变屈曲问题。作者近期发表的两篇文章对类似GBT的新型半离散分析方法进行了阐述。对横截面进行离散分析,寻找沿梁变化的解析解。采用新方法,利用齐次和非齐次方程建立确定梁全部变形的一般GBT方程并求解,从而使GBT的(复杂)变形方程变形为可降阶的微分方程。提出的半离散方法在广义梁理论(GBT)基础上增加了用于柱的失稳分析和失稳形态识别的几何刚度因素。通过势能的变化并在梁理论中引入约束条件,对初始应力下建立的GBT齐次微分方程进行修正,以分析其变形特性。对简支梁梁端施加横向位移和轴力,建立GBT初始应力方程,通过该方程寻求失稳的解决方法。根据已知的边界条件,利用三角函数关系式和求解特征值的方法求解这些可降阶的微分方程,使得屈曲形态和相关特征值与分叉荷载因素相符。因此,无需通过模态分解,可由耦合的GBT方程直接求得屈曲形态的解析解。通过实例分析了柱的整体失稳、屈曲变形和局部纵弯失稳,以及如何将新方法用于描述特征曲线和弹性屈曲曲线。将该方法的分析结果与ABAQUS、GBTUL和CUFSM软件的分析结果进行对比,验证了该方法的正确性。     

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.     

Design of thin-walled purlins for distortional buckling

Roof purlins and sheeting rails are generally loaded through the cladding members that they support and this provides both rotational and translational restraint. This restraint reduces the tendency to lateral torsional buckling and thus increases the importance of distortional buckling in the design procedure. This paper shows that the fundamental behaviour of restrained purlins under both downward and uplift load can be best understood with the aid of ‘Generalized Beam Theory’ (GBT). GBT also provides a yardstick by which approximate design methods can be assessed. The existing approximate methods are evaluated and an improvement is proposed. The proposed design approach is then validated by comparison with test results.     

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.     

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.     

Stabilität und Bemessung bisymmetrischer schlanker Stahlträger

The paper presents the influence of geometrical characteristics of the cross sections of beams upon their load capacity with the use of a simplified solution taking account of the influence of lateral torsional and local buckling. Bisymmetrical, simple supported steel beams loaded at ends by moments and by distributed or concentrated loads imposed in the centres of gravity of the cross sections have been analysed. The influence of local and global buckling of beams and interactive local and global buckling of flanges upon the load capacity of beams is assessed. For beams the local buckling capacities and reduced distortional buckling capacities are compared by approximate manners and according to Eurocode 3. The aim of the paper is to present the assessment of the influence of geometrical characteristics of beams, modes of load upon the ultimate load capacity of beams taking account of local and global buckling making use of approximate solutions and formulas given in Eurocode 3 and in the Polish Standard PN‐90/B‐03200.     

Inelastic buckling of channel columns in the distortional mode

Thin-walled channel sections may buckle in a distortional mode when subjected to compression. A variety of cold-formed channel columns were tested recently to study distortional buckling in the inelastic range. This paper describes a comparison of a theoretical method for predicting the inelastic distortional buckling strengths of thin-walled columns with the column tests. The method is based on a spline finite strip buckling analysis which takes into account the non-linear stress-strain behaviour of the steel making up the test sections, and the fix-ended test conditions. The inelastic buckling analysis is found to produce accurate estimates of the test failure loads and failure modes     

卷边槽钢梁柱的畸变屈曲有限元分析

对于卷边槽钢梁柱的畸变屈曲,文献1运用文献4的计算简化模型推导了畸变屈曲弹性计算公式。本文采用文献2的截面,运用有限元分析考虑了单一截面构件在不同参数时构件的弹性和弹塑性屈曲荷载和屈曲模式,并考虑了几何缺陷带来的影响,最后根据试验建立模型并将分析结果与试验结果进行对比。     

高强冷弯薄壁型钢卷边槽形截面轴压柱畸变屈曲试验研究

本文对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进行了试验研究,17根试件的试验结果表明:由于试件局部屈曲一般发生在畸变屈曲之前,促使畸变屈曲提前出现,这种相关作用减弱了构件整体刚度,降低了构件承载力;澳洲规范AS/NZS 4600:1996及北美规范NAS 2004中关于发生畸变屈曲构件承载力的计算方法没有考虑局部屈曲和畸变屈曲相关作用的不利影响。依据试验结果本文提出了一种修正直接强度法的建议计算方法,该法计算结果与试验结果较为接近且偏安全。     

高强冷弯薄壁型钢轴压柱畸变屈曲研究

550MPa高强冷弯薄壁型钢卷边槽形截面轴压柱发生畸变屈曲时会出现三种模式（O—O,O-I,I—I）,考虑材料和几何双重非线性的有限元法对三种畸变屈曲模式的构件承载力、变形模式、畸变屈曲应力、横截面应力的分布等相关性能进行比较分析,可看出三种畸变屈曲模式诸性能存在较大不同,同时畸变屈曲与局部屈曲、整体屈曲在相关性能方面也存在不同。采用直接强度法对畸变屈曲轴压柱极限承载力进行计算,计算结果与试验结果较吻合,故在计算畸变屈曲轴压柱极限承载力时建议采用直接强度法．     

基于广义梁理论的非线性材料薄壁受压构件屈曲荷载计算方法

提出适用于非线性材料的广义梁理论屈曲荷载计算方法,并对不锈钢薄壁受压构件屈曲荷载进行计算验证。通过定义材料非线性应力应变关系和瞬时弹性模量,对传统线弹性广义梁理论进行修正,建立非线性材料薄壁构件受压屈曲荷载计算方法,推导不锈钢薄板受压局部屈曲、冷弯薄壁不锈钢卷边槽形柱畸变屈曲及箱形不锈钢长柱弯曲屈曲荷载计算公式,并与既有试验数据对比。经验证,线弹性分析方法不适用于不锈钢材料;提出的修正GBT法具有较高精度,且本构关系采用变形法则结果偏于安全,可用于不锈钢等非线性金属材料薄壁构件受压屈曲荷载的确定,为研究和设计提供理论指导。     

Compression tests of high strength cold-formed steel channels with buckling interaction

This paper describes a series of compression tests conducted on cold-formed simple lipped channels and lipped channels with intermediate stiffeners in the flanges and web fabricated from high strength steel plate of thickness 0.6 and 0.8 mm with the nominal yield stress 560 MPa. A range of lengths of lipped channel sections were tested to failure with both ends of the column fixed with a special capping to prevent local failure of column ends and influence from the shift of centroid during testing. The high strength cold-formed steel channel sections of intermediate lengths generally displayed a significant interaction between local and distortional buckling. A noticeable interaction between local and overall buckling was also observed for the long columns. A significant post-buckling strength reserve was shown for those sections that showed interaction between local and distortional or overall buckling. Simple design strength formulas in the Direct Strength Method for the thin-walled cold-formed steel sections failing in the mixed mode of local and distortional buckling have been studied. The strengths predicted by the strength formulas proposed are compared with the test results for verification.     

Buckling mode identification of perforated thin-walled members by using GBT and shell FEA

The paper presents an original method based on the Generalised Beam Theory (GBT) whereby the general buckling modes, provided by the shell Finite Element Analysis (SFEA) of perforated thin-walled members, are expressed in terms of the fundamental (pure) buckling types (global, distortional and local). The contribution of each pure buckling mode to a coupled instability can be quantified, allowing a better understanding of the member buckling behaviour and post-buckling strength reserve. The main advantage of this method lies in using only the GBT cross-sectional pure deformation modes instead of member pure modal shapes. There are no restrictions regarding the element cross-sectional shape, loading and boundary conditions.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.     

冷弯薄壁卷边槽钢畸变屈曲承载力的计算方法比较

冷弯薄壁卷边槽钢在受力过程中除可能出现整体屈曲和局部屈曲外,还可能出现畸变屈曲。发生畸变屈曲会恶化构件的受力性能,从而降低构件的极限承载力。比较研究了5个国家或地区规范针对畸变屈曲的设计计算方法,并对最新的畸变屈曲承载力计算方法研究成果进行归纳,最后就既有的5种考虑畸变屈曲的承载力计算方法与有关试验进行对比分析,结果表明:北美规范采用的直接强度法适用范围广且精度相对较高。     

Selection of the initial geometrical imperfection in nonlinear FE analysis of cold-formed steel rack columns

This paper presents three methodologies to predict the load carrying capacity of cold formed steel rack columns via nonlinear finite element analysis (FEA). The column lengths are chosen in the range where the main failure is due to distortional buckling. It is demonstrated that for this range, to derive an accurate prediction of the ultimate load is more complex than for lengths where the main failure is local or global. The nonlinear analysis is carried out introducing an initial geometric imperfection on the upright. The three methodologies presented here allow for different imperfection shapes. The first one uses the critical mode shape (the first buckling mode). The second corresponds to an iterative methodology in which the shape that leads to the lowest ultimate load is used. These two first methodologies use exclusively the finite element method (FEM). The third one combines the finite element analysis with the generalised beam theory (GBT) in order to determine the modal participation of the FEM buckling mode and generate a particular combined geometric imperfection. To validate the predicted loads, the results of the three methodologies are compared with values obtained in experimental tests.     

Coupled instabilities with distortional buckling in cold-formed steel lipped channel columns

The paper addresses the elastic post-buckling behaviours of cold-formed steel lipped channel simply supported columns affected by mode interaction phenomena involving distortional buckling, namely local/distortional, distortional/global (flexural-torsional) and local/distortional/global mode interaction. The results presented were obtained by means of Abaqus shell finite element analyses adopting column discretisations into fine 4-node element meshes. In order to enable a thorough assessment of all possible mode interaction effects, the column lengths and cross-section dimensions were carefully selected to ensure similar local, distortional and/or global buckling loads. One analyses otherwise identical (elastic) columns having initial geometrical imperfections (i) with various configurations (combinations of the competing critical buckling mode shapes) and (ii) sharing the same overall amplitude.     

An experimental verification of the generalized beam theory applied to interactive buckling problems

Previous papers (Refs 1–4) have presented a method of analysis for any open unbranched thin walled section considering both rigid body movement and cross section distortion (including local buckling). Reference 1 described how the Generalized Beam Theory (GBT) can be used to calculate generalized section properties for all modes, including each of the four rigid body modes and the distortional modes. The additional section properties evolved from GBT were then used in Ref. 2 to consider second order elastic critical buckling problems.This paper compares the critical buckling predictions of GBT with the results obtained in two series of tests carried out on lipped and unlipped channels subject to a major axis bending moment. These predictions are then combined with the yield criteria of EC3 to allow a comparison with the analysis of these tests carried out by Lindner and Aschinger (Ref. 5). The paper concludes that the Generalized Theory is a powerful and effective analysis tool for the solution of interactive buckling problems where both local and overall buckling can occur.     

A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory

Generalized beam theory—GBT—is among the most adequate tools for the analysis of thin-walled prismatic elements. It enables the analysis of the distortion of the element cross-section and local buckling of individual walls in a unified manner that incorporates the results from classical bending theory. The basis of this theory was developed in the 1960s by Schardt for first and second order elastic behaviour of thin-walled members.Open and closed thin-walled members present the distinctive difference of the unknown shear flow that characterizes the latter. More specifically, shear strains must follow an elasticity law, as opposed to the simplifying assumptions for open cross-sections.It is the purpose of the present paper to present a unified energy formulation for the non-linear analysis of both open and closed sections in the framework of GBT, able to deal with all modal interaction phenomena between local plate behaviour, distortional behaviour and the more classical global (flexural, torsional and flexural–torsional) response. Finally, an application to the stability analysis of a compressed thin-walled column is presented and discussed.     

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。