Elastic local post-buckling of elliptical tubes

The elastic local post-buckling behaviour of elliptical tubes under compression is analysed in this paper. A brief outline of the local, distortional and global buckling behaviour of EHS tubes is firstly provided, where it is shown that local buckling modes govern the stability of short to intermediate length tubes while distortional modes control the stability of intermediate length to moderately long tubes and global buckling dominates the behaviour of longer tubes. Following this, an in-depth numerical study employing shell finite element modelling, of the elastic local post-buckling behaviour of compressed elliptical hollow section (EHS) tubes is presented. It is concluded that EHS tubes with a low to moderate aspect ratio can support loads up to their limit loads but are imperfection sensitive (shell-type behaviour), while EHS tubes with a moderate to high aspect ratio can carry loads higher than their limit loads (plate-type behaviour) and are imperfection insensitive. The slope of the ascending post-buckling path increases with the EHS aspect ratio and can reach values up to 40% of the slope of the linear primary path. The bound imperfection amplitude concept, separating the imperfection amplitude ranges where the EHS tube is sensitive and insensitive, is proposed. It is also found that, for increasing EHS aspect ratio, the compressive stresses grow and accumulate near the zones of minimum radius of curvature while the zones of maximum radius of curvature possess an approximately uniform and relatively low compressive stress level. Therefore, it is expected that an approach based on the effective width concept widely used for the evaluation of the strength of flat plates may be adapted to the design of EHS tubes with moderate to high aspect ratios.     

A new formulation for distortional buckling stress in cold-formed steel members

Distortional buckling of compression members usually comprises rotation and translation of each flange and lip about the flange-web connection in opposite directions. The present procedures for the calculation of elastic distortional buckling stress in the literature are very complex, cumbersome and have long expressions. In this paper a new neural network (NN) based formula is proposed for the determination of the elastic distortional buckling stress of cold-formed steel C-sections with both end sections pinned. The focus of this study is on the distortional buckling, for which existing results are for sections subjected to pure compression and/or pure bending only. The data used for training and testing NNs is taken from Schafer’s report. The NN-based estimates are compared with the experimental, numerical and analytical results of different researchers and methods. It was found that the proposed NN based-formula is practical in predicting the elastic distortional buckling stress of cold formed steel C-sections.     

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.     

截面尺寸对冷弯薄壁槽形钢屈曲的影响

薄壁构件在轴向受压荷载作用下很容易由于屈曲而失效,但是冷弯薄壁型钢构件的屈曲又是一个复杂的过程。在此用有限条法分析了卷边C型截面钢构件的局部屈曲性能,较真实地反映了其受力的实际情况,得出了卷边C型截面钢构件各个截面参数变化对屈曲的影响。     

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．     

Study on distortional buckling performance of cold-formed thin-walled steel flexural Members with stiffeners in the flange

This paper presents a finite strip program CUFSM used to calculate and analyze the elastic distortional buckling of cold-formed thin-walled steel flexural members with stiffeners in the flange, which has different sectional geometric parameters. According to the classical buckling stress formula, the distortional buckling coefficient of the flange can be calculated so as to analyze the influence of changed sectional geometric parameters on it. On this basis, this study provides a simplified formula of distortional buckling stress to calculate 40 members with different sections which are selected from the Technical Code of Cold-Formed Thin-Wall Steel Structures of China but not contained in this paper. Compared with the analysis results of CUFSM, it shows that the two simplified formulas have quite high accuracy and wide applicability for general members provided by the specification. So it is suggested that they can be used for engineering design and standard revision.     

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。     

Analyses of distortional buckling of cold-formed sigma purlins using EN1993-1-3

This technical note presents a study on the calculation of the critical stress of distortional buckling of cold-formed sigma purlins using EN1993-1-3. The discussion is focussed on the determination of the spring stiffness of the stiffened element, a problem which has not yet been addressed in most design codes. Different support conditions at both the tension and compression ends of the web are employed and their influences on the critical stress of distortional buckling of sigma purlins are investigated. Comparison with finite strip analysis indicates that the model having a fixed support for the tension end and a roller support for the compression end of the web provides the best fit to the finite strip analysis.     

Distortional buckling tests of cold-formed steel compression members at elevated temperatures

In recent times, light gauge cold-formed steel sections have been used extensively since they have a very high strength to weight ratio compared with thicker hot-rolled steel sections. However, they are susceptible to various buckling modes including a distortional mode and hence show complex behaviour under fire conditions. Therefore, a research project based on detailed experimental studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. More than 150 axial compression tests were undertaken at uniform ambient and elevated temperatures. Two types of cross sections were selected with nominal thicknesses of 0.60, 0.80, and 0.95 mm. Both low (G250) and high (G550) strength steels were used. Distortional buckling tests were conducted at six different temperatures in the range of 20-800 ^°C. The ultimate loads of compression members subject to distortional buckling were then used to review the adequacy of the current design rules at ambient and elevated temperatures. This paper presents the details of this experimental study and the results.     

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.     

冷弯薄壁型钢卷边槽形截面构件畸变屈曲控制研究

基于部分加劲板件的畸变屈曲和局部屈曲的稳定系数比较,提出了冷弯薄壁型钢卷边槽形截面构件畸变屈曲发生于局部屈曲之后或畸变屈曲不发生的临界控制条件;给出了通过构件畸变屈曲计算长度控制畸变屈曲的临界条件;提出一种控制畸变屈曲的构造措施,即在卷边间加设缀板,并通过已有试验对其有效性进行验证,同时推导了卷边间缀板的刚度需求。结果表明：通过构件截面尺寸控制畸变屈曲不发生或发生在局部屈曲之后,可以不考虑构件畸变屈曲的影响,简化冷弯薄壁型钢卷边槽形截面构件承载力的计算;计算长度小于畸变屈曲半波长一半的构件不发生畸变屈曲;通过在卷边间加设缀板的构造措施能有效阻止部分加劲板件的转动,构件的畸变屈曲荷载和承载力都有很大的提高,缀板布置间距不同,构件承载力的提高幅度也不同,缀板间距越小,构件承载力提高幅度越大。算例分析表明,满足一定间距和刚度需求的缀板能够提高构件的畸变屈曲承载力或避免畸变屈曲的发生。     

Distortional buckling of monosymmetric I-beams

A finite element method which is applicable to studying the distortional buckling of fabricated monosymmetric I-beams is briefly described. The method is used to demonstrate the effects of web slenderness on a monosymmetric I-beam whose smaller flange is in compression. A study is also made of the effects of monosymmetry on the distortional buckling of an I-beam with a slender web in uniform moment and moment gradient. Based on parameter studies using the finite element method, a design equation is developed which may be used to determine the distortional buckling stress of a monosymmetric I-beam under moment gradient.     

Genetic programming-based formulation for distortional buckling stress of cold-formed steel members

The main purpose of the research is to develop formulations for estimating the Elastic distortional buckling stress (EDBS) of cold-formed steel member under compressive loading using Genetic programming (GP) which has not been applied so far. The required data used for the training and testing is collected from the literature. Two GP-based formulations are proposed to predict the elastic distortional buckling of cold formed steel C sections. The results of proposed GP formulations are compared with experimental and analytical results of different researchers and methods and found to be accurate. The results obtained from the formulas have shown that GP is a promising technique for predicting EDBS of cold-formed steel C sections.     

Numerical modelling of light gauge cold-formed steel compression members subjected to distortional buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing loss of properties and lives during fires. However, fire performance of light gauge cold-formed steel structures is not well understood despite its increased usage in buildings. Cold-formed steel compression members are susceptible to various buckling modes such as local and distortional buckling and their ultimate strength behaviour is governed by these buckling modes. Therefore a research project based on experimental and numerical studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. Lipped channel sections with and without additional lips were selected with three thicknesses of 0.6, 0.8, and 0.95 mm and both low and high strength steels (G250 and G550 steels). More than 150 compression tests were undertaken first at ambient and elevated temperatures. Finite element models of the tested compression members were then developed by including the degradation of mechanical properties with increasing temperatures. Comparison of finite element analysis and experimental results showed that the developed finite element models were capable of simulating the distortional buckling and strength behaviour at ambient and elevated temperatures up to 800 °C. The validated model was used to determine the effects of mechanical properties, geometric imperfections and residual stresses on the distortional buckling behaviour and strength of cold-formed steel columns. This paper presents the details of the numerical study and the results. It demonstrated the importance of using accurate mechanical properties at elevated temperatures in order to obtain reliable strength characteristics of cold-formed steel columns under fire conditions.     

中美规范关于卷边槽形受弯构件承载力比较分析

新近纳入北美规范NAS 2004的直接强度法对冷弯型钢构件的畸变屈曲要求单独验算,但《冷弯薄壁型钢结构技术规范》(GB 50018-2002)对此还无明确规定。在总结冷弯型钢构件畸变屈曲性能的基础上,对其承载力计算方法给予介绍,由简化模型计算得到的受弯构件的畸变屈曲弹性临界应力中,引入直接强度法计算“规范”(GB 50018-2002)附录中卷边槽形受弯构件的承载力。结果表明,附录中部分截面的受弯承载力由畸变屈曲控制。同时,NAS 2004与“规范”(GB 50018-2002)计算结果的比较表明,“规范”(GB 50018-2002)的计算规定虽安全,但太过保守。因此,提出将翼缘屈曲系数调高至3.0的建议。     

A study on flexural buckling strength F cr of inelastic buckling for compressive members

Since Euler’s classical theory, which he proposed in 1759, many column curve formulations have been proposed. This study investigates the flexural buckling strength (F _cr ) calculated using the allowable stress design specification and the load and resistance factor design (LRFD) specification of the American Institute of Steel Construction. It is noted that the exponential function of the column curve formulation using LRFD is difficult to use in practice. Therefore, a simple parabolic function is proposed for the inelastic buckling strength of a steel column loaded with uniaxial compression, and it is shown to be consistent with many design codes. The expressions for inelastic buckling strength formulation as defined previously for ASD are used here. To verify the proposed equation, 118 individual test results of steel columns are examined. The mean of the ratio of the column strength to the proposed flexural buckling strength is 1.089, indicating that the proposed strength curves are in good agreement with the test results.     

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。     

板件中间加劲的复杂卷边槽钢轴压构件弹性畸变屈曲应力的实用计算法

为了研究板件中间加劲的复杂卷边槽钢轴压构件畸变屈曲临界应力的简便计算方法,应用有限条分析软件CUFSM对冷弯薄壁板件中间加劲的复杂卷边槽钢以及腹板中间V型加劲的复杂卷边槽钢共90个轴压构件进行数值模拟,分析各参数对构件弹性畸变屈曲临界应力的影响。经拟合分析,得出针对板件中间加劲的复杂卷边槽钢、腹板中间V型加劲的复杂卷边槽钢轴压构件的弹性畸变屈曲临界应力的简化计算公式,并验证该公式的有效性。     

Local buckling of structural steel shapes

The objectives of this paper are to (1) provide analytical expressions for the elastic cross-section local buckling stresses, including element interaction, of hot-rolled steel structural shapes, and (2) compare these local buckling results to the assumptions inherent in the local slenderness limits of the US AISC structural steel specification. The cross-section local buckling stress is determined by finite strip analysis (FSA). Local stability of each cross-section in the AISC shapes database (excluding pipes) is considered in axial compression, as well as positive and negative bending about the major and minor geometric axes. Local buckling stresses are converted into plate buckling coefficients (k’s) and simplified expressions are provided for all observed k’s. The new k’s explicitly include elastic web-flange interaction amongst the elements comprising the cross-section. The k values from the FSA are compared to those inherently assumed in the AISC Specification, significant differences are observed.     

Buckling mode identification of thin-walled members by using cFSM base functions

The objective of this paper is to demonstrate an approximate method whereby eigen buckling modes from a shell finite element method (FEM) analysis of a thin-walled member can be quantified in terms of the fundamental buckling classes, namely, global, distortional, local, or other. The buckling classes are defined using the mechanical definitions employed in the constrained finite strip method (cFSM). The cFSM base vectors are used to approximate an arbitrary FEM buckling mode. The resulting identification and its associated error is investigated, including dependency on FEM discretization, the number of cFSM functions considered, boundary conditions, and loading. The long-term goal of the work is to provide a generalized method for identification of local, distortional, and global buckling modes for arbitrary thin-walled members modeled in general purpose finite element codes.