Slenderness limits for cold-formed channel sections in bending by experimental methods

Inelastic design methods allow for larger application of loads on sections than elastic design methods, due to the redistribution of yield stress through the depth of the section. Sections that can reach the full plastic capacity and maintain it for sufficient rotation are considered applicable for plastic mechanism design, resulting in more economical structural solutions. Cold-formed steel channel sections are used extensively in portal frame structures in agricultural and light industrial/commercial applications, structures well suited to plastic design, however may currently only be designed elastically. To address this limitation in design standards, experimental and numerical analyses on the inelastic bending capacity of cold-formed channel sections are performed, and design rules to account for such behaviour are developed. Design rules are prepared using the hot-rolled steel specification methodology of classifying a section as compact, non-compact or slender (according to the Australian Standards) and Classes 1, 2, 3 and 4 (according to the European Standards). Proposals for the Australian standard are shown to provide accurate and reliable capacity predictions for cold-formed steel channel sections whose bending capacity exceeds the elastic limit.     

Inelastic behaviour and design of slender I-sections in minor axis bending

Slender steel sections in bending are generally designed by taking the maximum moment as the yield moment. The assumption for the ultimate condition is thus the point at which first yield is reached in the section. Certain types of slender sections, however, have shown significant post-elastic behaviour in attainment of the ultimate moment. Experiments on I-sections in minor axis bending have shown this to be the case, where significant plastic stress distributions are attained in the tension flanges after the compression flanges have locally buckled. Current international steel specifications are unduly conservative when estimating the bending strength of these sections as the yield moment. This paper quantifies this conservatism and presents inelastic design methods whereby the post-elastic strength may be captured. Design equations are proposed for Australian, American and European hot-rolled and cold-formed steel specifications.     

The design of perforated cold-formed steel sections subject to axial load and bending

The uprights in a typical pallet rack are typically singly-symmetrical cold-formed sections subject to axial load together with bending about both axes. They usually contain arrays of holes in order to enable beams to be clipped into position at heights that are not pre-determined prior to manufacture. Their slenderness is such that their behaviour may be influenced by the three generic forms of buckling, namely local, distortional and global (lateral torsional). In practice, these members have generally been designed on the basis of expensive test programmes. This paper addresses the problem of how they might be designed analytically. The basis of the investigation is a comprehensive set of test results on upright sections in compression which embraces both stub column tests, in which the load position was varied along the axis of symmetry, and longer columns. The test results were analysed using both finite elements and a version of “Generalized Beam Theory” (GBT) which incorporated systematic imperfections. Consideration was also given to the design procedures proposed by the “Federation Europeene de la Manutention” (FEM) and recent research into the influence of perforations on the performance of cold formed steel sections. It is shown that GBT can be modified to take account of perforations so that the lower bound results give a sufficiently accurate column design curve, which takes account of local, distortional and global buckling, thus making extensive testing unnecessary.     

Global optimization of cold-formed steel channel sections

Cold-formed steel sections have an important advantage which is the great flexibility of cross-sectional profiles and sizes available to structural steel designers. However, this flexibility makes the selection of the most economical section difficult for a particular situation. This paper presents a global optimization method for designing the cross-section of channel beams subjected to uniformly distributed transverse loading. The optimization of the cross-section is performed using the trust-region method (TRM) based on the failure modes of yielding strength, deflection limitation, local buckling, distortional buckling and lateral–torsional buckling. Numerical examples include the comparisons of the optimized sections obtained based on the applications of BS 5950-5 standard and the recently developed ENV-1993-1-3.     

Flange/web distortional buckling of cold-formed steel sections in bending

Recent experimental tests of cold-formed steel C- and Z-sections in bending have revealed unconservative results in the prediction of the bending moment resistance, using the current North American Design Standards. The failure mode of these tests was identified as flange/web distortional buckling. This mode of failure initially involves a rotation of the lip/flange component about the flange/web corner, which typically occurs for short half-wavelength distortional buckling. Near ultimate failure, an apparent lateral movement of the flange/web corner, which includes transverse bending of the web, is experienced. Various analytical methods that predict the moment resistance of sections which experience short half-wavelength distortional buckling were investigated and compared with the applicable test data. The modified Lau and Hancock 2 Model, with S136-94 Standard calculated effective section modulus, is recommended for use as the North American predictor model for the flange/web distortional buckling moment resistance of cold-formed steel sections in bending.     

Structural behaviour and design of lightweight structural panels using perforated cold-formed thin-walled sections under compression

Cold-formed thin-walled steel sections are widely used as primary loadbearing members in lightweight panels that form walls in residential and other low rise structures. In cold regions, the webs of the steel sections are often perforated to reduce the cold bridging effect in order to increase thermal comfort and reduce energy waste. Perforating the web of a steel section will reduce its loadbearing capacity. This paper presents the results of an experimental and numerical study to investigate the compression behaviour of lightweight structural panels using perforated sections. The primary objective of the tests is to provide experimental data to validate the numerical simulations, which were carried out using the commercial finite element analysis software ABAQUS. The validated FE analysis was used to develop a simple design calculation method to convert a section with perforated web to a section with solid web. In the equivalent solid web, the thickness of the solid web would have the same elastic local buckling strength as the original perforated web with the gross thickness while the thickness of the unperforated flanges remains unchanged. By converting a thin-walled section with perforated web to a solid section with an effective web thickness, the conventional design methods for thin-walled structures can be applied.     

The design of bolted joints in cold-formed steel sections

This paper gives background information on the behaviour of bolted joints and the parameters that affect strength and flexibility. Design expressions for the bearing strength of bolted joints and for the joint movement under load are also given.

Moment connections are considered and design expressions for moment capacity and moment/rotation relationships for various bolt groups under practical conditions are given.

Computer analysis of cold-formed steel assemblies is outlined and two worked examples of manual analysis, incorporating the above design expressions, are given. It is shown how economical design may be achieved by selecting the correct semi-rigid joint in such assemblies.     

Prediction of the strength of bolted cold-formed channel sections in tension

This study is concentrated on the investigation of the shear lag effect on bolted cold-formed steel tension members. Channel sections with different dimensions tested by using bolted connections were discussed in this study. The comparisons were made between the test results and predictions computed based on several specifications. In order to study the stress distribution at the various locations of the cross-section of specimen, the finite-element software ANSYS was also utilized in this research. Based on the experimental results, it was found that the tension strengths of test specimens predicted by the AISC-Code [Load and resistance factor design specification for structural steel buildings, Chicago, IL, 1999], which takes into account the shear lag effect, provide good correlation with the test results for most specimens. The predictions according to AISI-Code [2001 Edition of the specification for the design of cold-formed steel structural members. Washington DC, 2001] and AS/NZS 4600 Code [Cold-formed steel structures, AS/NZS 4600:1996, Australia, 1996] seem to be overestimated as comparing to the test results. It is also noted that there is a quite discrepancy between the test results and the values predicted by both British Standard [British Standard: structural use of steelwork in building—part 5, Code of practice for design of cold-formed thin gauge sections, London, 1998] and Holcomb Recommendation [Tensile and bearing capacities of bolted connections, Second Summary Report, Civil Engineering Study 95-1. University of Missouri-Rolla, 1995]. The equation proposed by this study provides good agreement with test results.     

Inelastic behaviour of composite members under combined bending and axial loading

This paper presents an account of the results of a series of tests on partially-encased composite steel/concrete beam-columns. The experimental inelastic behaviour of members is examined under idealised conditions representing extreme lateral loading in combination with co-existing axial gravity loads. Members with three different cross-sectional sizes, utilising Grade S460 steel, were employed in the tests. The specimens were tested under major- or minor-axis bending in conjunction with a constant level of axial loading. The experimental arrangement and test rig constructed for this purpose are described together with the material properties and details of the specimens. The main experimental results from tests carried out on ten composite models are presented and discussed. In addition to providing essential data for validating future analytical and design studies, the experimental results and observations enable a direct assessment of several important factors. Particular emphasis is placed on key parameters related to yield and ultimate capacity as well as on ductility and residual strength considerations.     

Analysis and design of lapped connections between cold-formed steel Z sections

This paper presents an analysis and design method for lapped connections between cold-formed steel Z sections after careful calibration against test data obtained from a total of 26 one point-load tests on lapped connections. Based on the experimental observations on the lapped connection tests where combined bending and shear is always critical in the cross-sections at the end of laps, an analysis method is proposed to evaluate all the internal forces within the lapped connections. Once the co-existing moments and shear forces in the lapped connections are evaluated, the critical sections are readily checked against combined bending and shear using codified design rules. Moreover, design expressions are also proposed for the evaluation of effective flexural rigidities of lapped connections with various bolt configurations against practical lap length to section depth ratios. Consequently, the structural behaviour of lapped sections between cold-formed steel Z sections in terms of strength and stiffness is quantified rationally for general design. The research project aims to provide understanding to the structural performance of lapped connections between cold-formed steel Z sections, and hence, to develop a set of rational design rules for multi-span purlin systems with overlaps in modern roof construction.     

Effective shaping of cold-formed thin-walled channel beams with double-box flanges in pure bending

The paper is devoted to cold-formed thin-walled channel beams with double-box flanges. Geometric properties of the C-section are described in terms of dimensionless parameters. The warping function and the warping inertia moment are analytically determined. The optimization criterion and the dimensionless objective functions are defined as a quality measure. The space of feasible solutions is constrained by the strength, global, local buckling, and geometric conditions. Analytical solutions of the problems of global and local buckling for thin-walled beams are presented. Results of the numerical calculations of the optimal shaping problem are presented in tables and figures.     

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。     

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.     

Equivalent thickness of cold-formed thin-walled channel sections with perforated webs under compression

Cold-formed thin-walled channel sections with perforated webs (thermal studs) are widely used in external wall panels in cold regions to reduce the cold bridging effect. However, no design method appears to be available for this type of structure. A possible method is to convert the perforated web of a thermal stud into a solid one with a reduced thickness (which is referred to as the equivalent thickness) and then adopt an existing design method for solid sections (e.g. EN 1993-1-3). This paper presents the development of a method to calculate the equivalent web thickness. The equivalent thickness calculation equation is based on regression analysis of a large number of finite element simulation results of elastic local buckling strength of perforated plates under compression, considering the effects of a number of different design variables such as plate depth, thickness, perforation patterns and dimensions of the plate. The FE simulations were carried out using a general FE software. This study suggests that the equivalent thickness is mainly related to the plate width to thickness ratio, the total width of perforation at the critical section and the width of the perforation zone (total plate width between the first and last perforation). A regression equation has been proposed to relate the equivalent thickness to these parameters. To demonstrate the validity of the proposed equivalent thickness method, the compression strengths of a large range of perforated columns have been simulated by using either the original perforated sections or the equivalent solid section; and a comparison of the simulation results shows good agreement between the two sets of results.     

不同截面形式高强冷弯薄壁槽钢构件受弯承载力试验研究

对36个屈服强度为550 MPa的高强冷弯薄壁槽钢受弯试件进行静力试验研究,考虑了加劲形式和卷边形式对试件受弯性能的影响,其中加劲形式分为无加劲、翼缘中间V形加劲和翼缘及腹板中间V形加劲3种,卷边形式分为直卷边、斜卷边和复杂卷边3种。试验结果表明：加劲形式和卷边形式是影响试件受弯承载力和屈曲模式的重要因素;与无加劲形式相比,采用板件中间V形加劲有效减小了板件宽厚比,试件受弯承载力提高了30%~70%;同种加劲形式下,短（直、斜）卷边试件受弯承载力提高幅度最大,复杂卷边试件提高幅度次之,长（直、斜）卷边试件提高幅度最小;试验过程中试件发生了局部屈曲、畸变屈曲与局部和畸变相关屈曲。对试验进行了有限元模拟,模拟结果与试验结果吻合较好。     

Theoretical shape optimization of cold-formed thin-walled channel beams with drop flanges in pure bending

The paper is devoted to cold-formed thin-walled channel beams with open or closed profile of drop flanges. Geometric properties of two C-sections are described with consideration of warping functions and warping inertia moments. Optimization criterion and the dimensionless objective function as a quality measure are defined. Constraints of feasible solutions are strength, global and local buckling conditions and also geometric condition. Analytical solutions of the problems of global and local buckling for thin-walled beams are presented. Results of numerical investigation of optimization problem are compared and presented in tables and figures.     

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.     

Inelastic performance of cold-formed steel strap braced walls

The inelastic performance of sixteen 2.44 m×2.44 m cold-formed steel strap braced walls was evaluated experimentally. The performance was affected by the holddown detail, which in many cases did not allow the test specimens to reach or maintain a yield capacity and severely diminished the overall system ductility. “Test-based” R_d×R_o values of 3.65, 2.11 and 1.72 indicate the low ductility levels, which were not adequate to warrant the use of a seismic response modification coefficient of R=4.0 in design. Capacity design of the SFRS elements must account for the overstrength of the strap material.     

高强冷弯薄壁型钢卷边槽形截面构件设计可靠度分析

基于已有的承载力试验研究结果,对屈服强度550MPa高强冷弯薄壁型钢中常用的卷边槽形截面轴压构件和偏压构件的计算模式不定性进行了分析,并统计分析了高强冷弯薄壁型钢强度不定性、几何特性不定性。在此基础上,采用改进一次二阶矩方法,按现有规范的抗力分项系数要求,计算了高强冷弯薄壁型钢卷边槽形截面轴压构件和偏压构件不同可能荷载组合下的可靠指标。结果表明：对于宽厚比符合规范要求的屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件和偏压构件,按现有规范的抗力分项系数计算得到的可靠指标均能满足目标可靠指标的要求,证明了所采用的承载力计算方法的适用性;但对于宽厚比超出规范要求的轴压和偏压构件,计算得到的可靠指标不能满足目标可靠指标的要求。