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.     

Lateral distortional buckling tests of a new hollow flange channel beam

The LiteSteel beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. The LSBs are commonly used as flexural members in buildings. However, the LSB flexural members are subjected to lateral distortional buckling, which reduces their member moment capacities. Unlike the commonly observed lateral torsional buckling of steel beams, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist, and cross sectional change due to web distortion. An experimental study including more than 50 lateral buckling tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. It included the available 13 LSB sections with spans ranging from 1200 to 4000 mm. Lateral buckling tests based on a quarter point loading were conducted using a special test rig designed to simulate the required simply supported and loading conditions accurately. Experimental moment capacities were compared with the predictions from the design rules in the Australian cold-formed steel structures standard. The new design rules in the standard were able to predict the moment capacities more accurately than previous design rules. This paper presents the details of lateral distortional buckling tests, in particular the features of the lateral buckling test rig, the results and the comparisons. It also includes the results of detailed studies into the mechanical properties and residual stresses of LSBs.     

Experimental study of web crippling behaviour of hollow flange channel beams under two flange load cases

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel beam (LSB) subject to web crippling under End Two Flange (ETF) and Interior Two Flange (ITF) load cases. The LSB sections with two rectangular hollow flanges are made using a simultaneous cold-forming and electric resistance welding process. Due to the geometry of the LSB, and its unique residual stress characteristics and initial geometric imperfections, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending, predominant shear and combined actions. To date, however, no investigation has been conducted on the web crippling behaviour and strength of LSB sections. Hence an experimental study was conducted to investigate the web crippling behaviour and capacities of LSBs. Twenty-eight web crippling tests were conducted under ETF and ITF load cases, and the ultimate web crippling capacities were compared with the predictions from the design equations in AS/NZS 4600 and AISI S100. This comparison showed that AS/NZS 4600 and AISI S100 web crippling design equations are unconservative for LSB sections under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of LSBs based on experimental results. Suitable design rules were also developed under the direct strength method (DSM) format.     

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.     

冷弯槽钢受弯时长细比限值试验研究

非弹性设计方法与弹性设计方法相比,其截面的允许荷载值较大,这是由于屈服应力沿截面高度进行了重新分布。塑性设计方法使得截面的塑性能力和塑性铰的转动特性得到充分发挥,从而使结构设计更为经济合理。冷弯槽钢在农业和轻工/商业中广泛用于门式刚架结构,塑性设计方法对这类结构非常适用,然而目前仅采用弹性设计方法对其进行设计。为突破设计规范的限制,对冷弯槽钢的非弹性弯曲能力进行了试验研究和数值分析,以建立相应的设计准则。设计准则采用热轧钢分类方法,将截面分为紧凑型、非紧凑型及细长型(根据澳大利亚规范),或1,2,3,4级(根据欧洲规范)。澳大利亚规范所预测的超过弹性极限范围的冷弯槽钢弯曲能力精确可靠。     

Elastic lateral buckling of cantilever Litesteel Beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.     

Elastic shear buckling characteristics of LiteSteel beams

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam. The unique LSB section is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. To date, limited research has been undertaken on the shear buckling behaviour of LSBs with torsionally rigid, rectangular hollow flanges. For the shear design of LSB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the flange and web elements. Therefore finite element analyses were carried out to investigate the elastic shear buckling behaviour of LSB sections including the effect of true support conditions at the junction between their flange and web elements. An improved equation for the higher elastic shear buckling coefficient of LSBs was developed and included in the shear capacity equations of Australian cold-formed steel codes. Predicted ultimate shear capacity results were compared with available experimental results, both of which showed considerable improvement to the shear capacities of LSBs. A study on the shear flow distribution of LSBs was also undertaken prior to the elastic buckling analysis study. This paper presents the details of this investigation and the results including the shear flow distribution of LSBs.     

New design rules for the shear strength of LiteSteel beams

The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section produced using dual electric resistance welding and automated continuous roll-forming technologies. The innovative LSB sections have many beneficial characteristics and are commonly used as flexural members in building construction. However, limited research has been undertaken on the shear behaviour of LSBs. Therefore a detailed investigation, including both numerical and experimental studies, was undertaken to investigate the shear behaviour of LSBs. Finite element models of LSBs in shear were developed to simulate the nonlinear ultimate strength behaviour of LSBs, including their elastic buckling characteristics, and were validated by comparing their results with experimental test results. Validated finite element models were then used in a detailed parametric study into the shear behaviour of LSBs. The parametric study results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs. Significant improvements to web shear buckling occurred due to the presence of torsionally rigid rectangular hollow flanges, while considerable post-buckling strength was also observed. This paper therefore proposes improved shear strength design rules for LSBs within the current cold-formed steel code guidelines. It presents the details of the parametric study and the new shear strength equations. The new equations were also developed based on the direct strength method. The proposed shear strength equations have the potential to be used with other conventional cold-formed steel sections such as lipped channel sections.     

Lateral buckling strengths of cold-formed rectangular hollow sections

Code rules for designing steel beams against lateral buckling which are based on data for hot-rolled I-sections are unnecessarily conservative when used for cold formed rectangular hollow section beams.Cold-formed rectangular hollow section beams have different stress-strain curves, residual stresses, and crookedness and twist. The effects of residual stress on the inelastic buckling of I-section beams are not nearly as pronounced for hollow sections with two webs, while the strengthening effects of pre-buckling deflections are greater for hollow sections. Simplistic code rules for top flange loading are very conservative when applied to hollow sections.This paper reviews elastic lateral buckling behaviour and the strength rules used to design steel beams. It develops realistic models for cold-formed rectangular hollow beams which are analysed to predict the effects of moment distribution, load height and yield stress on their strengths. The results of the analyses are used to develop improved design rules which remove much of the conservatism of present design rules.     

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.     

Numerical modelling and design of LiteSteel Beams subject to lateral buckling

The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling.     

Member moment capacities of mono-symmetric LiteSteel Beam floor joists with web openings

Recently developed cold-formed LiteSteel Beam (LSB) sections have found increasing popularity in residential, industrial and commercial buildings due to their light weight and cost-effectiveness. Another beneficial characteristic is that they allow torsionally rigid rectangular flanges to be combined with economical fabrication processes. Currently, there is significant interest in the use of LSB sections as flexural members in floor joist systems. When used as floor joists, these sections require openings in the web to provide access for inspection and other services. At present, however, there is no design method available that provides accurate predictions of the moment capacities of LSBs with web openings. This paper presents the results of an investigation of the buckling and ultimate strength behaviour of LSB flexural members with web openings. A detailed fine element analysis (FEA)-based parametric study was conducted with the aim of developing appropriate design rules and making recommendations for the safe design of LSB floor joists. The results include the required moment capacity curves for LSB sections with a range of web opening combinations and spans and the development of appropriate design rules for the prediction of the ultimate moment capacities of LSBs with web openings.     

Plastic bending behaviour and section moment capacities of mono-symmetric LiteSteel beams with web openings

Recently developed cold-formed LiteSteel beam (LSB) sections have found increasing popularity in residential, industrial and commercial buildings due to their light weight and cost-effectiveness. Currently, there is significant interest in the use of LSB sections as flexural members in floor joist systems, although they can be used as flexural and compression members in a range of building systems. The plastic bending behaviour and section moment capacity of LSB sections with web holes can be assumed to differ from those without, but have yet to be investigated. Hence, no appropriate design rules for determining the section moment capacity of LSB sections with web holes are yet available. This paper presents the results of an investigation of the plastic bending behaviour and section moment capacity of LSB sections with circular web holes. LSB sections with varying circular hole diameters and degrees of spacing were considered. The paper also describes the simplified finite element (FE) modelling technique employed in this study, which incorporates all of the significant behavioural effects that influence the plastic bending behaviour and section moment capacity of these sections. The numerical and experimental test results and associated findings are also presented.     

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.     

侧向扭转屈曲时冷成型钢梁的特性及设计

建筑物中越来越多地使用冷成型钢梁作为楼板的辅助及受力构件,其在没有足够侧向约束时的性能和瞬时承载力将受到侧向扭转屈曲的影响。以往对侧向扭转屈曲的研究主要针对热成型卷边钢梁,因此需要对简单支撑下相同弯曲度冷成型卷边槽钢梁的特性进行数值模拟。采用业内广泛认可的有限元分析软件ABAQUS进行建模,对不同条件下冷成型钢梁微单元的侧向扭转屈曲性能和承载力进行分析和模拟。将瞬时承载力结果与冷成型钢结构规范中当前设计准则的预测结果进行比较并对其进行适当的修正。欧洲的设计规范较为保守,而澳大利亚、新西兰和北美的设计规范则较为宽泛。基于有限元分析结果,对规范中的瞬时承载力设计公式进行修正。阐述了参数分析的细节问题,修正了当前设计规范,提出了侧向扭转屈曲时冷成型卷边槽钢梁的新设计准则。     

Elastic, full plastic and lateral torsional buckling analysis of steel single-angle section beams subjected to biaxial bending

Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account.     

Experimental investigation into the structural behaviour of lapped connections between cold-formed steel Z sections

This paper presents an experimental investigation on the structural behaviour of lapped cold-formed steel Z sections. A total of 26 one point load tests on lapped connections between Z sections with various lap lengths and test spans were carried out, and both the strength and the deformation characteristics of these connections were examined in detail. Among all tests, section failure at the end of lap under combined bending and shear was always found to be critical in the connected Z sections. Moreover, the moment resistances of lapped connections with lap lengths equal to 1.2 times section depth were found to develop only 80% of the moment capacities of connected sections. For lapped connections with lap lengths equal to six times section depth, their moment resistances were found to be significantly increased to about 140% of the moment capacities of connected sections. Similar results in the flexural rigidities of the lapped connections were also found. Consequently, it is shown that the degree of structural continuity in lapped connections against bending depend on not only the load levels, the lap length to section depth ratios, but also the lap length to test span ratios. Hence, the widely adopted assumption of full strength and stiffness connections in lapped sections is not always correct. The research work 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. The analysis and design method will be fully presented in a complementary paper.     

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.     

厚壁冷弯方矩管和热轧H型钢轴压极限承载力的对比研究

运用ANSYS有限元软件,在综合考虑初始几何缺陷、残余应力、冷弯效应等因素的基础上,分析了厚壁冷弯方、矩钢管和热轧H型钢轴心压杆的极限承载力,并将它们的极限承载力计算结果进行对比,得出相关结论,为轻钢结构框架柱构件截面选型提供了参考.     

Analysis of bolted moment connections in cold-formed steel beam-column sub-frames

An extensive experimental investigation on bolted moment connections between cold-formed steel sections was carried out, and a total of 16 internal and external beam-column sub-frames with various connection configurations were tested under lateral loads. It is found that for those six beam-column sub-frames with large bolt pitches and thick gusset plates in the connections, flexural failure of connected sections is always critical. The moment resistances of the connections attain at least 85% of the moment capacities of the connected sections.This paper presents a theoretical investigation for predicting the structural behaviour of bolted moment connections between cold-formed steel sections. An analysis and design method for internal force distribution of the connections is presented, and hence a set of design rules for section failure of connected sections under combined bending and shear is proposed. Moreover, a non-linear finite element model of the beam-column sub-frames incorporating the effect of semi-rigid joints is also presented. On the basis of the measured moment joint rotation curves of the bolted moment connections, the overall lateral load-deflection curves of the sub-frames are predicted, and they are found to follow closely the curves obtained from tests. Furthermore, a semi-empirical formula for flexibility prediction of the bolted moment connections is also proposed after careful calibration against test data.It is demonstrated that the proposed rules are highly effective for predicting the structural performance of cold-formed steel frames with bolted moment connections. Hence, structural engineers are encouraged to design and build cold-formed steel structures with bolted moment connections to achieve practical and efficient construction.