Evaluation of the slenderness ratio in built-up cold-formed box sections

According to section D1.2 of AISI S100-2007 for compression members composed of two sections in contact whose buckling mode involves shear forces in the connectors, a reduction must be made, KL/r must be replaced by (KL/r)_m. This new modified slenderness ratio takes into account the connection weld spacing and the minimum radius of gyration of an individual shape in the built-up member. Under the provisions of section D1.2 a reduction in load capacity must be made for built-up welded box members, which are the subject of this study. An experimental investigation on 48 samples was addressed to determine the comparative behaviour under compression load of box sections composed of two C-section members in contact by seam welds with different weld spacings (ranging from 100 to 900 mm). The studs were tested simulating rigid and flexible end support conditions. The length of the samples was 900 mm with a cross-section of 100 mm×100 mm. The base material thickness was 1.5 mm (gauge 16) for 24 samples and 2.0 mm (gauge 14) for the rest. The testing done on the samples did not show a statistical reduction in the ultimate compression load capacity for these members except for a weld spacing of 900 mm and a flexible end support condition. The reduction considered in AISI S100-2007is not applicable to determine the ultimate load capacity for the rest of the members.     

Flexural behaviour and strength of cold-formed steel L-headers

Cold-formed steel headers are structural components used over wall openings in cold-formed steel residential and light commercial construction. Recently, there has been an increased interest in cold-formed L-headers among homebuilders primarily due to their ease of installation and low material cost. The findings from an extensive laboratory testing program, of full-scale single and double cold-formed steel L-headers are presented in this paper. The objective of the research was to investigate the flexural behaviour and strength of L-headers under both gravity and uplift loads. Based on the results improved ultimate strength design expressions and new deflection expressions for a wide range of L-header assemblies have been proposed.     

高强冷弯薄壁型钢抱合箱形截面受压构件承载力试验研究

由两个槽形截面构成的抱合箱形截面在超薄壁冷弯型钢结构中应用广泛,但关于其承载力的计算只是将单个构件的承载力简单地数学叠加,并没有相应公式来考虑单个槽形截面构件之间的相互加强。对40根高强冷弯薄壁型钢抱合箱形截面受压构件进行试验研究,考察其受力特性及破坏特征,包括轴压构件21个,绕弱轴偏心和绕强轴偏心构件共19个。试验研究结果表明:抱合箱形截面构件由于两个槽形截面试件的相互约束作用,实测承载力比按单根构件计算承载力叠加结果提高10%～20%左右。最后,在试验和理论分析的基础上,针对高强冷弯薄壁型钢抱合箱形截面受压构件极限承载力提出了一种建议计算方法,依照建议计算方法所得结果与试验结果吻合较好,且偏于安全,可供实际设计参考。     

Axial load capacity of cold-formed steel built-up stub columns

This paper aims to investigate the axial load capacity of innovative cold-formed steel (CFS) built-up stub columns. Four innovative CFS built up section is presented in this paper. Each section is composed of combination of more than two elements as follows: channels, channels with lip, Sigma section and/or plates. The elements of each section are assembled together by using self tapping screws. The concentric axial load capacity of each of the four sections was investigated numerically by using finite element (FE) model using ABAQUS program. The FE model was verified against previous test data. The FE model was used to study different parameters that affect the load capacities of the innovative CFS built-up stub columns, these parameters are: columns profile, steel thickness, steel grade and longitudinal spacing between screws (fasteners), cross sectional area. The axial load capacities obtained from FE models are compared with the perdition of the Effective width (EW) method (available in Eurocode, Egyptian code, American and Australian standards) and direct strength (DS) method (Available in American and Australian standards).     

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.     

Laser welded built-up cold-formed steel beams: Experimental investigations

The results of a research project aimed at designing and development a built-up cold-formed steel beam assembled by laser welding are described in this paper. The research activity was concerned with the evaluation of the applicability of laser welded connections to cold-formed members and with the assessment of the load bearing capacity of the assembled beams. With this aim, both lap-shear and U-tension tests were carried out on laser welds in order to assess the influence on connection strength of different parameters such as the gap between the steel sheets and the zinc coating. Finally, the load bearing capacity of laser welded built-up cold-formed members was investigated by four-point bending tests. Four full-scale prototypes were manufactured with different spacings of connections along the flanges in order to evaluate the effects of weld configuration on the load bearing capacity.     

冷弯厚壁型钢考虑冷弯效应的屈服强度计算方法研究

为研究冷弯效应对壁厚6.0 mm以上的冷弯厚壁型钢屈服强度的影响,对4种不同截面、不同厚度的冷弯厚壁型钢进行了截面不同部位的材性试验研究,同时对现有国内冷弯厚壁型钢的材性试验和短柱试验数据进行了汇总。在简要回顾国内外冷弯厚壁型钢考虑冷弯效应的屈服强度计算公式及其理论依据的基础上,将各国规范计算值与试验值进行了对比。结果表明：冷弯效应对冷弯厚壁型钢的屈服强度影响较大,其影响程度与板件的宽厚比关系明显;我国规范、北美、澳洲/新西兰规范公式,以及朱爱珠基于我国规范提出的修正公式计算结果偏于保守,而欧洲规范的计算结果略偏大;我国GB 50018-2002《冷弯薄壁型钢结构技术规范》中计算方法理论依据充分,且在计算结果偏于安全的同时变异系数较小,更适合于工程应用。     

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.     

双肢拼合冷弯薄壁型钢工字形截面梁受弯性能研究

对6个单肢冷弯薄壁型钢C形截面梁和18个双肢拼合冷弯薄壁型钢工字形截面梁进行了受弯性能试验研究 ,考察梁跨高比、翼缘宽厚比、截面高宽比、螺钉连接间距以及腹板开孔对双肢拼合工字形截面梁破坏模式和极 限受弯承载力的影响,验证双肢拼合截面梁受弯承载力具有“1×2≥2”的拼合效应,并采用ANSYS有限元软件进 行数值模拟与影响因素分析。结果表明：试件的破坏模式为翼缘及腹板局部屈曲和畸变屈曲的相关屈曲形式。改 变翼缘宽厚比和截面高宽比对双肢拼合冷弯薄壁型钢工字形截面梁的承载力影响最大,而改变螺钉连接间距 （300~600mm范围内）和梁跨高比对工字形梁的承载力影响较小。在实际工程设计中,建议腹板开孔采用圆形孔 洞形式,腹板开孔截面积比例取为35%~50%之间,同时腹板开孔间距应不小于400mm。在双肢拼合工字梁受弯承载 力折减强度法的基础上,提出了适用于腹板开孔双肢拼合冷弯薄壁型钢工字形截面梁受弯承载力计算的强度折减 修正法。     

Experimental investigation on laser welded connections for built-up cold-formed steel beams

A wide experimental investigation on laser welded connections based on both lap-shear and tension tests was performed at the University of Naples. The aim of the study was to assess the possibility of using laser welding in innovative built-up cold-formed steel beams. The experimental programme was designed in order to evaluate the effects of different parameters on the strength and ultimate displacement of the selected connections. In particular, the influence of sheet thickness, gap, loading direction, weld shapes and zinc coating were analyzed. The results of the experimental tests were compared with the predicted resistance values according to Eurocode 3, with the aim of validating for laser welding the mechanical models provided for spot welds.     

Minimum weight of cold-formed steel sections under compression

This paper presents a combined theoretical and experimental study on the minimum weight and the associated optimal geometric dimensions of an open-channel steel section with given length subjected to a prescribed axial compressive load. Sections both with and without lips are analyzed. The results obtained using a nonlinearly constrained optimization method are compared with those estimated from a simple-minded optimization procedure that assumes the simultaneous occurrence of all failure modes in a minimum weight structure. The types of failure mode considered include yielding, flexural buckling, torsional–flexural buckling, and local buckling. The failure criterion is based purely on compressive strength, with other possible design constraints (e.g. bending stiffness, minimum gauge and cost) ignored. The effects of end support conditions and restraint on torsional buckling are examined. The load capacity of a C-section calculated according to the 1998 British Standard Institution’s specifications on Structural Use of Steelwork in Building is used to check the validity of theoretical predictions. Finally, two new C-sections with lips were designed and manufactured based on the optimal results, and tested. Test results confirm the analytical predictions, with the optimal C-sections performing much better than the existing ones.     

Bending strength of hybrid cold-formed steel beams

For the purpose of determining the load-carrying capacity of cold-formed steel structural members, the effective width approach has been used. Since most studies were limited only to the structural members, which were assembled from the same material in a given section, this investigation was concentrated on a study of structural strength and behavior of hybrid cold-formed steel beams subjected dynamic loads. An investigation was also conducted to study the validity of effective design width formulas for the design of these specimens. The materials used in this study were 25 AK and 50 SK sheet steels. A total of 72 spot-welded closed-hat sections were tested under different strain rates. The results showed that the structural strengths including yield moment and ultimate moment of hybrid cold-formed steel beams increase with increasing strain rates. In the determination of the strength of hybrid sections, the effective cross-sectional area calculated on the basis of the dynamic yield stresses can be employed. A design procedure was also developed to compute the member strength of hybrid beams.     

The assessment of residual stresses in welded high strength steel box sections

Much work on the investigation of the magnitude and distribution of residual stresses in mild carbon steel sections have been made previously. However, limited efforts have been put on residual stress measurements of high strength steel sections. The differences of stress–strain curves and high-temperature material properties between the high strength steel and mild carbon steel demands a necessary study of the residual stresses in high strength steel welded sections. In the present study, three box columns fabricated from Q460 steel plates of 11 mm in thickness with different details were used for the examination. Both sectioning and hole-drilling methods are adopted for the measurement. The measured residual stress distributions of three different box sections are presented, and the corresponding simplified residual stress pattern is proposed. By comparing with the residual stress patterns for mild carbon steel, it is found that the box section fabricated from HSS plates has the lower compressive residual stress ratio. The differences in the measurement by using sectioning and hole-drilling methods are also compared.     

Corner properties of cold-formed steel sections at elevated temperatures

This paper presents the mechanical properties of the corner parts of cold-formed steel sections at elevated temperatures. Light-gauge structural members are cold-formed which results the mechanical properties of the corner parts being different from the flat parts. However, previous research has focused on the investigation of the corner parts of cold-formed steel sections at normal room temperature and the performance of the corner parts at elevated temperatures is unknown. An appropriate model for fire resistant design of steel structures necessitates a correct representation of mechanical properties of structural steel at elevated temperatures. Therefore, experimental investigation on corner coupon specimens at different temperatures ranged from approximately 20 to 1000 °C was conducted to study the behaviour of the corner parts of cold-formed steel sections at elevated temperatures. Two kinds of corner coupon specimens, namely the inner corner coupon specimens and outer corner coupon specimens having the steel grade of G500 (nominal 0.2% proof stress of 500 MPa) and nominal thickness of 1.9 mm were tested. The test results were compared with the flat coupon specimens taken from the same cold-formed steel sections as the corner coupon specimens. A unified equation to predict the yield strength (0.2% proof stress), elastic modulus, ultimate strength and ultimate strain of the corner parts of cold-formed steel sections at elevated temperatures is thus proposed in this paper. Generally, it is shown that the proposed equation adequately predicts the test results of the corner coupon specimens. Furthermore, stress–strain curves at different temperatures are plotted and a stress–strain model is also proposed for the corner parts of cold-formed steel sections.     

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.     

Effective Width Method for determining distortional buckling strength of cold-formed steel flexural C and Z sections

This paper proposes a design method, based on the Effective Width Method, for determining the nominal distortional buckling strength of typical cold-formed steel C and Z sections subjected to bending. The method can be integrated into the classic effective width design provisions specified in AISI S100, and it allows the conventional design approach to cover more comprehensive limit states. The proposed method is calibrated by the flexural distortional buckling strength predicted by the Direct Strength Method. Comparison with experimental results indicates that the proposed method yields reasonable predictions for the flexural distortional buckling strength of industrial standard C and Z sections. The method offers the same level of accuracy and reliability as the Direct Strength Method.     

Computational modelling of flange crushing in cold-formed steel sections

The computational modelling of the flange crushing phenomenon in cold-formed steel profiles is described in this paper, with particular emphasis to the development of shell finite element (SFE) models and performance of quasi-static analyses with an explicit integration scheme. Web crippling failure is widely recognised as the most relevant collapse mode of cold-formed steel members subjected to transverse concentrated loads. However, it has been experimentally and numerically observed that a somewhat different collapse mode may occur, due to the heavy stress concentrations stemming from the adoption of narrow bearing plates. This phenomenon, termed flange crushing, should not be confused with web crippling. Usually, the web crippling phenomenon is numerically investigated by means of non-linear static SFE models with an implicit integration scheme. In this study, SFE models are developed in ABAQUS code to study the flange crushing failure of a plain channel beam subjected to Internal Two Flange (ITF) loading conditions. These models are described in detail, as well as additional modelling concerns regarding quasi-static analyses and the explicit integration method. Different parameters are discussed in this article and the numerical results obtained are commented throughout. Such parameters include the (i) SFE type and mesh, (ii) load rate, mass scaling, adoption of smoothed displacement amplitude curves and control of inertial effects, (iii) contact and friction definitions, (iv) effects of forming cold-work and manufacturing process and (v) geometrical imperfections. Finally, the load–displacement response obtained with the quasi-static model and an equivalent non-linear static analysis are compared with the experimental test curves. It is concluded that very good results are achieved with the quasi-static approach, not only in terms of the ultimate load prediction, but also regarding the post-collapse load–deflection curve and the failure mechanism.     

Flexural performance of bolted built-up columns constructed of H-SA700 steel

The H-SA700 is a new high-strength structural steel that is more environmentally friendly and more suitable for mass production than conventional high-strength steel. A research program is underway to develop a new structural steel system that extends the benefits of H-SA700 steel to achieve sustainable and seismically resilient buildings. The envisioned system uses built-up columns that are fabricated from H-SA700 plates by high-strength bolts and uses these built-up columns in weld-free construction. This paper summarizes the first phase of the program, whose objective was to establish the flexural properties of the built-up columns. Three column specimens were fabricated and subjected to cyclic lateral loading. The tests demonstrated the very large elastic deformation capacity and stable inelastic behavior of H-SA700 columns. The flexural strength was not governed by fracture of the reduced section with bolt holes, but by inelastic buckling of the flanges. The strength was limited by the plastic strength of the reduced section. The test results were used to identify the key limit states and to develop a design methodology that addresses the unique behavior of the built-up columns. Finite element simulation suggested that bolt holes help distribute yielding over a wide area of the flanges, to supply some ductility and help avoid net section fracture of the flanges.     

Column tests of cold-formed steel non-symmetric lipped angle sections

The geometry of angle sections is simple, but the behaviour and design calculations of angle sections can be quite complicated. Furthermore, lipped angle sections with unequal flange widths form a non-symmetric section and the behaviour of the section is even more complicated than a singly-symmetric angle section with equal flange widths. A test program on cold-formed steel non-symmetric lipped angle columns is presented. The non-symmetric angle sections were brake-pressed from high strength structural steel sheets having nominal yield stresses of 450 and 550 MPa with plate thicknesses of 1.0, 1.5 and 1.9 mm. The material properties of the column specimens were obtained by tensile coupon tests. The behaviour and strengths of cold-formed steel non-symmetric lipped angle columns were investigated. The test strengths are compared with the design strengths calculated using the North American Specification for the design of cold-formed steel structural members. In addition, the current design rules in the North American Specification for cold-formed steel non-symmetric lipped angle columns are assessed using reliability analysis. It is shown that the design strengths are generally quite conservative.