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.     

Design of cold-formed steel unequal angle compression members

Cold-formed steel unequal angles are non-symmetric sections. The design procedure of non-symmetric sections subjected to axial compression load could be quite difficult. The unequal angle columns may fail by different buckling modes, such as local, flexural and flexural–torsional buckling as well as interaction of these buckling modes. The purpose of this study is to investigate the behaviour and design of cold-formed steel unequal angle columns. A nonlinear finite element analysis was conducted to investigate the strength and behaviour of unequal angle columns. The measured initial local and overall geometric imperfections as well as the material properties of the angle specimens were included in the finite element model. The finite element analysis was performed on fixed-ended columns for different lengths ranged from stub to long columns. It is demonstrated that the finite element model closely predicted the experimental ultimate loads and the behaviour of cold-formed steel unequal angle columns. Hence, the model was used for an extensive parametric study of cross-section geometries. The column strengths obtained from the parametric study were compared with the design strengths calculated using the North American Specification for cold-formed steel structural members. It is shown that the current design rules are generally unconservative for short and intermediate column lengths for the unequal angles. Therefore, design rules of cold-formed steel unequal angle columns are proposed.     

Numerical study of built-up double-Z members in bending and compression

The use of the finite element method (FEM) for the design of composed, thin-walled, structural steel members is considered. The bolted double-Z frame member is an interesting and economical engineering solution, already used in practice [1]. However, the European recommendations for the design of steel structures do not consider built-up members from cold-formed steel profiles. Finite element analysis is used to capture the various buckling effects that shape the response of slender thin-walled members. From the finite element model, the importance of initial imperfections and stiffness of connections is identified. The experimentally validated model predictions show that a non-linear finite element analysis can predict the member behaviour, in terms of failure mode and ultimate load, yield line pattern, overall stiffness and local strain in the cold-formed profiles. To obtain a good prediction, overall and localised initial imperfections should be considered and included in the 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。     

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.     

螺栓连接的冷成型钢结构的结构性能

本文介绍了一系列螺栓连接的冷成型钢结构的结构性能的试验和理论研究。首先,研究了搭接剪切试验中冷成型钢条之间螺栓连接的基本变形特性,并采用了包含实体单元和接触单元的高等有限元建模作为对比。其次,介绍了带有螺栓抗弯连接的搭接Z型截面的结构性能,对搭接Z型截面的强度和刚度做了解析方法和数值方法的评估。最后,采用数值方法对双跨搭接Z型檩条的结构性能进行了研究,考察了跨越内部支座的搭接Z型截面对于沿檩条构件内力分布的影响。本文意在提供分析和设计方法,以便于结构工程师理解,使他们能够设计和建造出结构性能更好的冷成型钢结构房屋。     

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.     

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.     

Stub column tests of thin-walled complex section with intermediate stiffeners

A series of stub column tests on complex sections with intermediate stiffeners is presented in this paper. Initial geometric imperfections and material properties of the test specimens were measured. It is shown that the intermediate stiffeners could effectively enhance the local buckling stress of thin-walled sections. The test strengths are compared with the design strengths calculated using the direct strength method in the North American Specification and Australian/New Zealand Standard for cold-formed steel structures. It is shown that the direct strength method using finite strip method to obtain the buckling stresses is very conservative. Therefore, finite element method was used to predict the elastic buckling stresses. It is shown that the design strengths calculated using direct strength method based on the buckling stresses obtained from finite element analysis results generally agree with the test results well.     

腹板开矩形孔复杂卷边冷弯槽钢梁局部屈曲性能及直接强度法研究

为了研究腹板开孔复杂卷边冷弯槽钢梁的局部屈曲性能，以及探究北美冷弯型钢结构设计规范(AISI S100-2016)中腹板开孔冷弯槽钢梁局部屈曲直接强度法计算公式的可靠性，对孔高比(孔洞高度与腹板高度的比值)分别为0、0.2、0.4、0.6和0.8的10个腹板开矩形孔复杂卷边冷弯槽钢梁纯弯试件进行了静力试验研究。试验结果表明，开孔和不开孔试件均发生以局部屈曲为主的屈曲破坏模式，与不开孔试件相比，开孔试件的受弯承载力下降，且下降幅度随孔高比的增大而增大。利用ANSYS有限元程序对试验进行了模拟分析，分析结果与试验结果吻合良好；在此基础上，采用经试验验证的有限元模型，通过变换腹板高度、板厚和孔高比开展了有限元参数分析，并根据有限元参数分析结果对已有腹板开孔冷弯槽钢梁的弹性局部屈曲临界应力近似计算公式进行了修正。基于试验结果、有限元参数分析结果以及修正的弹性局部屈曲临界应力近似计算公式，对AISI S100-2016中开孔冷弯槽钢梁发生以局部屈曲为主破坏时的直接强度法计算公式进行了修正。     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

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.     

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.     

Bolted moment connections in drive-in and drive-through steel storage racks

The stability of steel storage racks, which are often unbraced, may depend solely on the pallet beam to upright connector and on the stiffness of the base plate to floor connection. This paper presents experimental results from cyclic tests performed on portal beam to upright bolted moment connections intended for cold-formed steel drive-in and drive-through storage racks. In storage racks, portal beams are typically connected to uprights by “tab connectors”, which are costly to manufacture and experience initial looseness. By simply bolting the portal beams to the uprights, bolted moment connections may represent a cost-effective alternative to “tab connectors”. A literature review shows that bolted moment connections between cold-formed steel members are economical and feasible. However, experimental results show a significant amount of looseness in the connection after an initial high moment-rotational stiffness. Being slender structures, storage racks are sensitive to the second-order P-Δ effect, and international racking specifications require the initial looseness of the tab connectors to be considered when analysing the stability of the rack in the down-aisle direction (sway motion). The non-linear cyclic behaviour of bolted moment connections is presented and explained herein. Based on finite element results, it is shown that, for drive-in and drive-through racks, the looseness in bolted moment connections can be ignored in ultimate limit states design. Finally, the paper concludes with proposing two methods, with different degree of complexity, for the design of drive-in and drive-through racks with bolted portal beam to upright bolted moment connections.     

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.     

新型冷弯箱形组合构件力学性能研究

基于箱形截面具有双轴对称、抗弯扭刚度大的特点,提出将冷弯∑形截面两两翼缘相对,并将其卷边焊接形成一种新型冷弯箱形组合截面——DS。应用非线性有限元方法分析新型截面构件在轴压、弯矩及压弯荷载作用时的诸如屈曲模式、承载力、刚度、延性及相关曲线等方面力学性能。同时,还对相同参数的新型截面构件与C形截面构件的单位承载力耗钢量进行比较。分析表明:新型截面构件在承受轴压力时具有高承载力及较高的截面模量,截面加劲充分而使子板件局部屈曲不易出现等力学性能优势。特别适宜承受轴压荷载,同时也适宜承受弯矩和压弯荷载的作用。轴压构件的单位承载力耗钢量一般仅为相同参数C形构件的50%左右,经济效益明显。新型箱形组合构件适于深入试验研究并合理应用于实际工程。     

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。     

Analysis and design of cold-formed steel channels subjected to combined bending and web crippling

The channel failures due to combined bending and web crippling may occur at the highly concentrated interior loading when there is no load stiffener in cold-formed thin-walled steel beams. This paper presents accurate finite element models to predict the behavior and ultimate strengths of cold-formed steel channels subjected to pure bending as well as combined bending and web crippling. Both geometric and material nonlinearities are considered in the finite element analysis. The nonlinear finite element models are verified against experimental results of cold-formed steel channels subjected to pure bending as well as combined bending and web crippling. The finite element analytical results show a good agreement with the experimental results in terms of the ultimate loads and moments, failure modes and web load-deformation curves thus validating the accuracy of the finite element models. The verified finite element models are then used for an extensive parametric study of different channel dimensions. The channel strengths predicted from the parametric study are compared with the design strengths calculated from the North American Specification for cold-formed steel structures. It is shown that the design rules in the North American Specification are generally conservative for channel sections with unstiffened flanges having the web slenderness ranged from 7.8 to 108.5 subjected to combined bending and web crippling. It is demonstrated that the nonlinear finite element analysis by using the verified finite element models against test results is an effective way to predict the ultimate strengths of cold-formed thin-walled steel members.     

钢结构屋顶承板的稳定性分析

采用有限元方法对钢结构屋顶承板进行承载力的稳定性分析。计算屋顶承板结构模型的总体刚度矩阵时考虑结构的几何效应,以载荷增量法逐渐对结构增加载荷,求出载荷与结构变形的关系,并由总体刚度矩阵来判定是否为奇异矩阵,进而计算出弹性屈曲载荷。将有限元计算结果与试验结果进行比较,通过分析发现有限元分析所得屈曲载荷值与在试验中获得的屈曲载荷值很相似,误差在9%以内。     

冷弯薄壁钢短柱在均匀高温下的性能

本篇章对常温及均匀高温条件下的冷成型薄壁短槽钢的轴向强度进行了初步研究。对常温及均匀高温下的一系列卷边的或非卷边的槽钢进行了试验研究。应用一系列的设计方法和商业化的有限元软件ABAQUS(1998)对试验进行了分析。本中涉及的设计方法包括：英国规范BS5950(1987)、欧洲规范Eurocode3Part1．3(CENl996)和美国规范AISI(1996)，在有限元分析中，考虑了几何非线性和材料非线性。高温下钢材的应力一应变曲线根据欧洲规范Eurocode3Part1．2(CENl995)和Qutinen(2001)采用。在某些试验中发现扭转屈曲，为了扩展针对这种破坏模式的设计方法，在这些规范中引用了Yong和Hancock(1992)考虑扭转屈曲的方法。对设计规范BS5950Part5(1987)、欧洲规范Eurocode3Part1．3(CENl996)和美国规范AISI(1996)中常温下薄壁柱的设计方法加以修改，来考虑钢材高温下的强度和刚度的变化。从试验结果、规范预期的结果和数值分析的比较可见，可很容易的通过上述修正当前规范的方法来分析薄壁型钢短柱高温下的性能。