A theoretical investigation of the column behaviour of cold-formed square hollow sections

An experimental programme investigating the column behaviour of four sizes of square hollow section was undertaken at the University of Sydney using Australian produced cold-formed square hollow sections. Stub and pinended column tests were performed and detailed measurements of the yield stress and residual stress taken around the sections.

A large deflection elastic—plastic finite strip analysis including the measured distributions of yield stress and residual stress is used to investigate the behaviour of the stub and pin-ended columns. In particular, the influence of the measured through thickness residual stress components on the ultimate load and behaviour of the square hollow section columns is demonstrated. The analysis accounts for plate geometric imperfections, the variation of yield stress around a section, the stress—strain characteristics of the material forming the section and the highly complex patterns of residual stress produced by the cold-forming process. Comparison of the analytical results with the test results is provided.     

Tension buckling of plate having a hole

Generally, it is believed that buckling of plates never arises under tensile load. However, when a plate has a hole, compression stresses appear locally near the hole under a tensile load, and the compression stress may cause local buckling—so-called tension buckling—of the plate. In this paper, some results of numerical analysis on the tension buckling are presented, and basic behaviour on the tension buckling is discussed.     

Inelastic buckling analyses of beams, columns and plates using the spline finite strip method

A method of inelastic buckling analysis of thin-walled structural members and plates is described. The method is based on the spline finite strip method of structural analysis. The analysis takes into account the non-linear material stress-strain properties, strain hardening and residual stresses. The plastic theories used in the study are the flow theory of plasticity and the deformation theory of plasticity. The method of inelastic buckling analysis is applied to a variety of instability problems including plates, cold-formed columns, hot-rolled columns and welded tee section beams. The buckling modes and loads computed are compared with theoretical values and test results.     

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.     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

Ultimate strength of aluminium alloy outstands in compression: experiments and simplified analysis

An experimental investigation was undertaken to study the stability and ultimate strength of aluminium alloy outstands. In the tests, thin-walled cruciform aluminium extrusions were stressed into the post-buckling range in axial compression. The local buckling behaviour of the flanges of a cruciform section is the same as that of an outstand, i.e. a plate element which is free along one unloaded edge and simply supported along the other. Two tempers of alloy AA6082 with significantly different stress–strain curves were tested for five b/t ratios. The experimental ultimate strengths were compared with theoretical predictions, using the classical Stowell theory for plastic buckling in combination with the effective width concept, and with ultimate strength formulae recommended in the literature.     

薄壁开孔矩形钢管轴压下局部稳定分析

局部屈曲是薄壁矩形钢管的一种主要屈曲模式,分析时应考虑板组间的相关作用。开孔后,将导致应力重分布,进而改变构件的屈曲性能。应用ANSYS有限元软件对薄壁开孔矩形钢管构件轴压下的局部屈曲性能进行了分析研究,讨论了板件宽厚比、翼缘腹板宽度比、开孔率等参数对局部屈曲性能的影响。     

Effect of longitudinal stress gradient on the ultimate strength of thin plates

When thin-walled sections are subjected to a moment gradient, the plates that comprise the section are themselves subjected to a longitudinal stress gradient. This paper analyzes the effect of longitudinal stress gradient on the ultimate strength of thin plates. Two types of thin plates are investigated: (1) plates simply supported on all four edges; and (2) plates simply supported on three edges, and with one longitudinal edge free. These two cases illustrate the influence of longitudinal stress gradient on stiffened and unstiffened elements of cold-formed steel sections, respectively. Nonlinear finite element analysis (ABAQUS) was performed to determine the ultimate strength of thin plates under a longitudinal stress gradient. The results indicate that the longitudinal stress gradient increases the strength of both types of thin plates, but has significantly more influence on unstiffened elements than stiffened elements. The beneficial effect of longitudinal stress gradients can be accounted for in design by using a plate buckling coefficient modified to account for the longitudinal stress gradient, an example of the impact of this change on a common cold-formed steel channel is provided.     

Compression tests of welded section columns undergoing buckling interaction

This paper describes a series of compression tests performed on welded H-section and channel section columns fabricated from a mild steel plate of thickness 6.0 mm with nominal yield stress of 240 MPa. The ultimate strength and performance of the compression members undergoing nonlinear interaction between local and overall buckling were investigated experimentally and theoretically. The compression tests indicated that the interaction between local and overall buckling had a significant negative effect on the ultimate strength of the thin-walled welded steel section columns. The Direct Strength Method (DSM), which was newly developed and adopted as an alternative to the effective width method for the design of cold-formed steel sections recently by NAS (AISI, 2004), was calibrated by using the test results for application to welded steel sections. This paper confirms that the Direct Strength Method can properly predict the ultimate strength of welded section columns when local buckling and flexural buckling occur simultaneously or nearly simultaneously.     

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     

A finite element analysis model for the behaviour of cold-formed steel members

A finite element analysis model for the post-local buckling behaviour of cold-formed steel (CFS) members subjected to axial compression has been developed. The finite element model consists of a Total Lagrangian nonlinear 9-node “assumed strain” shell finite element, and experimental-based material properties models to represent the body of the CFS sections. Experimentally derived residual stress variations, and initial geometric imperfections have also been incorporated. A special loading technique and a displacement solution algorithm were employed to obtain a uniform displacement condition at the loading edges. Details of a test program involving 20 non-perforated, and perforated cold-formed stub-column steel sections have been presented in the second part of the paper. The comparison between the test results, and the finite element results was performed for axial and lateral displacement behaviour, buckling loads, ultimate loads, and axial stress distribution. The comparison forms the basis for the evaluation of the efficiency, and the accuracy of the finite element model, and it indicated that the finite element analysis model constructed herein gives accurate and consistent results for the behaviour of the cold-formed steel members subjected to axial compression.     

Elastic buckling of elliptical tubes

Hot-rolled and cold-formed structural steel tubular members of elliptical cross-section have recently been introduced into the construction sector. However, there is currently limited knowledge of their structural behaviour and stability, and comprehensive design guidance is not yet available. This paper examines the elastic buckling response of elliptical hollow sections in compression, which has been shown to be intermediate between that of circular hollow sections and flat plates. The transition between these two boundaries is dependant upon both the aspect ratio and relative thickness of the section. Based on the results of numerical and analytical studies, formulae to accurately predict the elastic buckling stress of elliptical tubes have been proposed, and shortcomings of existing expressions have been highlighted. Length effects have also been investigated. The findings have been employed to derive slenderness parameters in a system of cross-section classification for elliptical hollow sections, and form the basis for the development of effective section properties for slender elliptical tubes.     

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.     

Local and distortional buckling of cold-formed steel beams with edge-stiffened flanges

The economic use of cold-formed steel members means that buckling and the possible loss of effectiveness it produces are important features of design. The prediction of the true buckling behaviour of cold-formed steel beams accounting for all governing features such as geometrical imperfections, material nonlinearity, postbuckling etc. has been possible with the development of advanced numerical modelling. The FE models developed in previous research have been used in this paper to investigate the effect of edge stiffeners (lips) and their interaction with compression flanges on the postbuckling of laterally restrained cold-formed Z-section beams. Depending on the lip size-to-flange width ratio and angle of inclination of the edge stiffener, the cross-sectional bending resistance varied and transitions between local, distortional and combined local/distortional buckling were observed. The suitability of the design treatments available in Eurocode 3 (EC3) for local and distortional buckling of cold-formed Z-section beams was assessed. Overall, the EC3 predictions for cross-sectional bending resistances were unconservative. Some shortcomings were identified and some suggestions for improvements were made. This included improvements in plate buckling factors for edge-stiffened compression flanges.     

卷边加强冷弯型钢梁局部和畸变屈曲

设计时,应重点考虑冷弯型钢构件的屈曲特性及其导致的有效性损失,以保证结构的经济性。数值模型改进后,能够反映考虑几何缺陷、材料非线性特性、后屈曲性能等因素的冷弯型钢梁的真实屈曲特性。针对侧向约束下冷成型Z型钢梁,采用已有的有限元模型,研究钢梁卷边及其与受压翼缘的相互作用对后屈曲特性的影响。利用卷边翼缘宽度比以及卷边倾角,观测局部屈曲、畸变屈曲和局部/畸变屈曲相互作用下截面抗弯刚度的变化。评估了EC3中适用于冷成型Z型钢梁局部和畸变屈曲的设计方法的有效性。总体而言,采用EC3计算的截面抗弯刚度并不保守。指出其中的不足并提出改进建议,改善卷边受压翼缘的失稳系数。     

工字形截面压弯的局部稳定性

对压力和弯矩作用下工字形截面考虑板件间相互作用时的局部稳定性进行研究。在轴压下,得到精确的腹板弹性屈曲系数解析解;在压弯和弯曲作用下采用有限元方法求解;在轴压和弯曲单独作用情况下,拟合了精度很好的腹板屈曲系数计算公式;在压力和弯矩共同作用下则提出了压力和弯矩相关作用公式,拟合了相关作用公式中的指数。     

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。     

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.     

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.     

Local buckling strength of closed polygon folded section columns

The local buckling behavior of regular polygonal, short length steel columns, fabricated by welding two half sections made of folded steel plates, is described. The polygonal sections are composed of five different section profiles with four to eight sides and each profile having component plates with one to four varied width-to-thickness ratios. A total of 15 specimens are used in the compression test, sustaining uniform compression stress in the fixed end condition. Accurate measurements of welding and cold-forming residual stresses and geometric imperfections were taken prior to testing and are presented in this paper. The test strengths are compared with the current plate buckling code in Japan and with the ECCS recommendations for unstiffened circular cylinders. The empirical design formula based on the test data is also presented to predict the local buckling strength of the polygonal section columns.