Behaviour of cold-formed singly symmetric columns

An experimental investigation into the behaviour of cold-formed plain and lipped channel columns compressed between fixed and pinned ends is presented in this paper. It is shown experimentally that local buckling does not induce overall bending of fixed-ended singly symmetric columns, as it does of pin-ended singly symmetric columns. Consequently, local buckling has a fundamentally different effect on the behaviour of pin-ended and fixed-ended singly symmetric columns. In order to show this fundamental different effect caused by local buckling, a series of tests was performed on plain and lipped channels brake-pressed from high strength structural steel sheets. Four different cross-section geometries were tested over a range of lengths which involved pure local buckling, distortional buckling as well as overall flexural buckling and flexural-torsional buckling. The different effects of local buckling on the behaviour of fixed-ended and pin-ended channels are investigated by comparing strengths, load–shortening and load–deflection curves, as well as longitudinal profiles of buckling deformations. The purpose of the paper is to demonstrate experimentally the different effects of local buckling on the behaviour and strengths of fixed-ended and pin-ended channels.     

The flexural behaviour of fixed-ended channel section columns

The paper presents a study of the behaviour of thin-walled channel sections compressed between fixed ends. The paper emphasises the differences between the behaviour of fixed-ended and pin-ended channel sections, arising mainly from the fact that the local buckling induces bending of pin-ended channel sections but not of fixed-ended channel sections.As a result of the different effects of local buckling, the strength of a fixed-ended channel section column exceeds that of a pin-ended column of the same effective length. The increase in strength is quantified for a particular channel section, and is studied through the transition from pinned to fixed-end support by analysing columns which are elastically restrained against rotations at the ends.The paper also investigates the imperfection sensitivity and post-ultimate behaviour of fixed-ended channel section columns. It is shown that fixed-ended columns are less sensitive to local imperfections and that they exhibit greater post-ultimate ductility than pin-ended columns.The study is confined to columns whose overall buckling mode is the flexural mode.     

直接强度法计算冷弯薄壁斜卷边槽钢轴压柱的承载力

通过计算得到了适合各种弯起角度的斜卷边槽形截面特性计算公式,方便了手算求解构件的屈曲应力。采用直接强度计算法对斜卷边槽钢轴压固支柱的稳定承载力及破坏模式进行了分析,并与已有的试验资料进行了对比。结果表明:直接强度法可以有效地预测斜卷边槽钢轴压固支构件的稳定承载力,从而说明了建立在简支试验结果基础上,经回归得到的直接强度法同样适用于固支柱稳定承载力的计算。     

用我国规范计算高强度冷弯薄壁型钢柱的适用性

将《冷弯薄壁型钢结构技术规范》(GB 50018-2002),用于计算比Q345钢强度更高的钢材制成的冷弯薄壁非卷边等边角钢和槽钢柱。对计算结果与试验、有限元分析结果及国外规范计算结果进行比较发现,对两端固支的槽钢和宽厚比大于25的等边角钢,计算偏于安全,对宽厚比小于25的等边角钢和两端铰支槽钢的安全性有待研究。提出采用多条柱子曲线以适应不同截面、不同壁厚、不同强度的高强度冷弯薄壁型钢柱。     

Bifurcation of singly symmetric columns

The paper derives the governing equations for the fundamental and bifurcated states of members with singly symmetric cross-sections that locally buckle in the fundamental state. The members are subject to pure compression and assumed to be geometrically perfect in the overall sense. It is shown using the fundamental state equations that fixed-ended columns exhibit overall bifurcation behaviour while pin-ended columns do not. The bifurcation equation is applied to plain channel sections and the results are compared with tests of fixed-ended columns. The variation of the bifurcation loads with the length is shown to be in good agreement with the tests. The results are shown to be sensitive to the magnitudes of local and overall geometric imperfections.     

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.     

Experimental investigation of built-up cold-formed steel section battened columns

This paper presents an experimental investigation on behaviour and design of built-up cold-formed steel section battened columns. The built-up columns were pin-ended and consisted of two cold-formed steel channels placed back-to-back at varied spacing of intersection. The two channels were connected using batten plates, with varying longitudinal spacing. The cold-formed steel channel sections were manufactured by brake-pressing flat strips having a plate thickness of 2 mm. The built-up cold-formed steel section battened columns had different slenderness and geometries but had the same nominal length of 2200 mm. The column strengths, load–axial shortening, load–lateral displacement and load–axial strain relationships were measured in the tests. In addition, the failure modes and deformed shapes at failure were observed in the tests and reported in this paper. Overall, the built-up column tests provided valuable experimental data regarding the column behaviour that compensated the lack of information on this form of construction as well as used to develop nonlinear 3-D finite element models. The column strengths measured experimentally were compared against design strengths calculated using the North American Specification, Australian/New Zealand Standard and European Code for cold-formed steel columns. Generally, it is shown that the specifications were unconservative for the built-up cold-formed steel section battened columns failing mainly by local buckling, while the specifications were conservative for the built-up columns failing mainly by elastic flexural buckling.     

Design of cold-formed steel oval hollow section columns

This paper presents the numerical simulation and design of cold-formed steel oval hollow section columns. An accurate finite element model was developed to simulate the fixed-ended column tests of oval hollow sections. The material non-linearities obtained from tensile coupon tests as well as the initial local and overall geometric imperfections were incorporated in the finite element model. Convergence study was performed to obtain the optimized mesh size. A parametric study consisted of 100 columns was conducted using the verified numerical model. The failure modes of material yielding, local buckling and flexural buckling as well as interaction of local and flexural buckling were found in this study. The experimental column strengths and numerical results predicted by the parametric study were compared with the design strengths calculated using the current North American, Australian/New Zealand and European specifications for cold-formed steel structures. In addition, the direct strength method, which was developed for cold-formed steel members for certain cross-sections but not cover oval hollow sections, was used in this study. The reliability of these design rules was evaluated using reliability analysis.     

椭圆环形截面钢柱的设计

对椭圆环形截面钢柱进行数值模拟和设计。建立准确的有限元模型,模拟两端固接的椭圆环形钢柱。对拉伸试验得出的材料非线性及初始局部(整体)几何缺陷都进行了考虑,通过收敛性研究,以获得最佳的单元网格尺寸。采用此数值模型,对100根柱试件进行参数化研究。对材料屈服、局部屈曲、弯曲屈曲及局部屈曲与弯曲屈曲同时发生的破坏模型进行了分析。将柱的承载力试验值和数值分析结果与基于北美规范、澳大利亚规范、新西兰规范和欧洲规范的计算值进行对比。另外,还采用了不适用于椭圆环形截面钢杆的直接强度法进行分析。对这些设计方法均进行了可靠度分析。     

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.     

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.     

Nonlinear analyses of thin-walled channel section columns

The paper presents a detailed comparison of nonlinear analyses of thin-walled channel section columns with tests. The columns are analysed as beam-columns having nonlinear constitutive relationships. The constitutive relationships are obtained firstly, by assuming elastic material behaviour and allowing local buckling of both flanges and web, and secondly, by assuming elastic-plastic material behaviour and confining local buckling deformations to the web. Based on the comparison, including theoretical and experimental load-shortening and load-deflection curves, it is concluded that the nonlinear theory generally closely agrees with the tests.The paper also investigates the applicability of combining an elastic nonlinear analysis with a spatial plastic mechanism analysis to describe the structural behaviour both before and after the ultimate load. The question of when this combination can be expected to accurately describe the column behaviour over the full loading range is discussed.A separate section compares theoretical ultimate loads with test strengths. The nonlinear analyses employed in the paper provide ultimate loads which agree with the test strengths to within 2% on average where primary local buckling occurs in the web of the channels, and 11% on average where primary local buckling occurs in the flanges of the channels.     

Design of high strength steel columns at elevated temperatures

The main objective of this paper is to study the behaviour and design of high strength steel columns at elevated temperatures using finite element analysis. In this study, equations predicting the yield strength and elastic modulus of high strength steel and mild steel at elevated temperatures are proposed. In addition, stress-strain curve model for high strength steel and mild steel materials at elevated temperatures is also proposed. The numerical analysis was performed on high strength steel columns over a range of column lengths for various temperatures. The nonlinear finite element model was verified against experimental results of columns at normal room and elevated temperatures. The effects of initial local and overall geometrical imperfections have been taken into consideration in the analysis. The material properties and stress-strain curves at elevated temperatures used in the finite element model were obtained from the proposed equations based on the material tests. Two series of box and I-section columns were studied using the finite element analysis to investigate the strength and behaviour of high strength steel columns at elevated temperatures. Both fixed-ended stub columns and pin-ended slender columns were considered. The column strengths predicted from the finite element analysis were compared with the design strengths predicted using the American, European and Australian specifications for hot-rolled steel columns at elevated temperatures by substituting the reduced material properties. In addition, the direct strength method, which was developed for the design of cold-formed steel columns at normal room temperature, was also used in this study to predict the high strength steel column strengths at elevated temperatures. The suitability of these design rules for high strength steel columns at elevated temperatures is assessed. Generally, it is shown that the American and European specifications as well as the direct strength method conservatively predicted the column strengths of high strength steel at elevated temperatures. The European Code predictions are slightly more conservative than the American Specification and the direct strength method predictions.     

Tests and numerical study of ultra-high strength steel columns with end restraints

High strength steels with the nominal yield strength more than 460 MPa have begun to be applied in the construction of many steel structures, but there are short of sound researches on the major axis buckling behavior of such steel welded I-section columns, especially for the ultra-high strength steels having the nominal yield strength more than 690 MPa. In this paper, the experimental research is described on the overall buckling behavior about the major axis of ultra-high strength steel compression I-section columns with end restraints. In this research 8 columns made from 2 kinds of ultra-high strength structural steels S690 and S960, with nominal yield strengths of 690 MPa and 960 MPa, respectively, were tested. Based on the test results, the finite element analysis (FEA) model was validated to analyze this behavior of ultra-high strength steel columns, and the buckling strength of pin-ended columns fabricated from such steels were calculated by the verified FEA model, which were compared with the design buckling strengths according to the Eurocode 3, the American specification for structural steel buildings ANSI/AISC 360–05, and the Chinese codes for steel structures design GB50017-2003 respectively. It shows that the major axis nondimensional buckling strengths of the ultra-high strength steel compression columns, whose buckling curve is type b according to Eurocode 3 and GB50017-2003, are much higher than that calculated according to the column curve b, even higher than the curve a₀ in Eurocode 3 and the curve a in GB50017-2003 on average, and they are also higher than the design values according to ANSI/AISC 360–05. It is therefore indicated that the buckling strength about the major axis of the ultra-high strength steel I-section columns is improved a lot compared with the ordinary strength steel columns on a non-dimensional basis, and the column curve a₀ and curve a can be adopted to design this behavior in Eurocode 3 and GB50017-2003, respectively. Besides, there is no obvious difference between the major axis nondimensional buckling strengths of the pin-ended I-section columns fabricated from these two kinds of ultra-high strength steels: S690 and S960. These research works will provide the test basis to complete the buckling design method and theory of the ultra-high strength steel columns, and also be helpful for the application of ultra-high strength steel structures.     

Design of cold-formed steel channels with stiffened webs subjected to bending

The objectives of this study are to investigate the structural behaviour and evaluate the appropriateness of the current direct strength method on the design of cold-formed steel stiffened cross-sections subjected to bending. The stiffeners were employed to the web of plain channel and lipped channel sections to improve the flexural strength of cold-formed steel sections that are prone to local buckling and distortional buckling. An experimental investigation of simply supported beams with different stiffened channel sections has been conducted. The moment capacities and observed failure modes at ultimate loads were reported. A nonlinear finite element model was developed and verified against the test results in terms of strengths, failure modes and moment–curvature curves. The calibrated model was then adopted for an extensive parametric study to investigate the moment capacities and buckling modes of cold-formed steel beams with various geometries of stiffened sections. The strengths and failure modes of specimens obtained from experimental and numerical results were compared with design strengths predicted using the direct strength method specified in the North American Specification for cold-formed steel structures. The comparison shows that the design strengths predicted by the current direct strength method (DSM) are conservative for both local buckling and distortional buckling in this study. Hence, the DSM is modified to cover the new stiffened channel sections investigated in this study. A reliability analysis was also performed to assess the current and modified DSM.     

Aluminum alloy tubular columns—Part I: Finite element modeling and test verification

A numerical investigation on fixed-ended aluminum alloy tubular columns of square and rectangular hollow sections is described in this paper. The fixed-ended column tests were conducted that included columns with both ends transversely welded to aluminum end plates using the tungsten inert gas welding method, and columns without welding of end plates. The specimens were extruded from aluminum alloy of 6061-T6 and 6063-T5. The failure modes included local buckling, flexural buckling, interaction of local and flexural buckling, as well as failure in the heat-affected zone (HAZ). An accurate finite element model (FEM) was developed. The initial local and overall geometric imperfections were incorporated in the model. The non-welded and welded material nonlinearities were considered in the analysis. The welded columns were modeled having different HAZ extension at the ends of the column of 25 and 30 mm. The nonlinear FEM was verified against experimental results. It is shown that the calibrated model provides accurate predictions of the experimental loads and failure modes of the tested columns. The load-shortening curves predicted by the finite element analysis are also compared with the test results.     

Tests and design approach for plain channels in local and coupled local-flexural buckling based on eurocode 3

Thin-walled plain channels are often subjected to coupled local and global flexural buckling. The objective of this paper is to verify and discuss the current design procedure of Eurocode 3 for plain channels in coupled instabilities. This paper deals with experimental investigations on plain channel stub columns subjected to local buckling only and long columns subjected to coupled local-flexural buckling. The test series consists of cold-formed and welded plain channels made of steel grade S355 and S460. Based on this experimental results modifications of the method of effective width (and thickness) as stated by Eurocode 3 Part 1-3 are discussed. Previously developed modified buckling coefficients, which take into account the rigidity of the connection of web and flange, are verified by comparative calculations. Additionally an approach for an approximation of effective stiffness for coupled instabilities is discussed as well.     

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.     

Post-buckling behaviour and DSM design of web-stiffened lipped channel columns with distortional and local mode interaction

This paper examines the design and load-carrying capacity of fixed-ended web-stiffened lipped channel columns eroded by mode interaction behaviour combined with distortional and local deformations. Initially, the paper presents the results of an experimental investigation of compressive tests on web-stiffened lipped channel columns fabricated from cold-formed mild steel with a thickness of 1.50 mm, which is aimed at determining their failure load-carrying capacity; the experimental investigation also aims to provide experimental evidence of the occurrence of such coupling phenomena concerning distortional and local modes, namely, local-distortional interaction and distortional-local interactive failures. Then, the paper examines the ultimate strength data of experimental columns, both reported in this paper and collected from the literature, and concludes that the current direct strength method (DSM) provides very unsafe predictions concerning such a detrimental interaction nature. Next, two DSM-based design approaches, namely, the nominal strength against local-distortional (NLD) and distortional-local (NDL) procedures, are presented and evaluated on the basis of all available experimental ultimate strength data. Finally, proposals and design considerations based on the DSM-shape for the thin-walled cold-formed steel sections, which fail in mixed modes of distortional and local buckling, are presented.     

腹板开孔复杂卷边槽钢双肢拼合构件轴压性能试验研究

通过12根腹板开孔复杂卷边槽钢和Σ形复杂卷边槽钢双肢拼合工字形简支轴压构件的轴压试验，研究了构件承载能力、失稳模式和拼合作用。采用有限元软件ANSYS对试验进行了模拟，验证了分析模型准确性。并通过有限元变参数分析研究了孔高、孔宽和孔间距对拼合构件承载力的影响。结果表明：复杂卷边槽钢截面双肢拼合开孔构件的腹板多波失稳现象明显，屈曲发生时两腹板间的相互支撑作用较强；Σ形复杂卷边槽钢截面双肢拼合开孔构件能有效地控制腹板局部屈曲的发生并显著提高短柱、中长柱的承载力；设置腹板加劲肋有助于提高孔洞周围板件变形的约束作用，同时也减弱了两单肢腹板间的相互支撑作用；相同条件下，Σ形复杂卷边槽钢截面双肢拼合开孔构件的轴压承载效率与复杂卷边槽钢截面双肢拼合开孔构件相比，短柱提高了32%，中长柱提高了10%，长柱提高了2%；非加劲截面构件在不同长度下，孔高为腹板高度1/2(69 mm)时构件的稳定承载力较孔高为25 mm时下降约7%；而孔宽、孔间距对上述两类截面构件稳定承载力影响不大；此外，采用直接强度法预测非加劲截面双肢拼合构件的承载力结果偏于保守，而对加劲截面双肢拼合构件则略显不安全。