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.     

An analysis of the structural behaviour of axially loaded full-scale cold-formed thin-walled steel structural panels tested under fire conditions

This paper presents a theoretical analysis to predict lateral deflections and failure times of six full-scale cold-formed thin-walled steel structural panels, tested under in-plane loads and exposed to fire attack on one side. The main objectives of this study are to investigate the effects of thermal bowing deflection and to check the relative merits of using either ENV 1993-1-2 or a modified version of ENV 1993-1-3 to perform design calculations for axially loaded steel studs under non-uniform temperature distributions. In general, the design of steel studs should also consider the effect of shift of neutral axes in both principal directions of the cross-section at elevated temperatures. However, such calculations can be rather time-consuming. Therefore, a secondary objective of this study is to assess how to effectively and accurately deal with this aspect in routine design calculations. It can be seen that thermal bowing deflections will have substantial effect on the fire resistance of steel structural panels exposed to fire on one side. However, for design calculations, it is not necessary to consider the effect of increasing thermal bowing deflections due to axial compression and reducing elastic modulus of steel at elevated temperatures. Both ENV 1993-1-2 and ENV 1993-1-3 may be used in design calculations of the ultimate load of this type of construction. It appears that ENV 1993-1-3 gives slightly better agreement with test results, but ENV 1993-1-2 is easier to implement because it does not require additional calculations of effective areas of thin-walled cross-sections at non-uniform elevated temperatures. The effect of shift of the minor axis is very small on the prediction of panel failure times and can be ignored to simplify routine design. Neutral axis shift of the major axis has some effect and may change the panel failure position from at the mid-height to the support. However, ignoring this neutral axis shift seems to give the best agreement to test results in term of panel failure location and panel failure times.     

An experimental study of loaded full-scale cold-formed thin-walled steel structural panels under fire conditions

This paper presents the results of eight tests on loaded full-scale cold-formed thin-walled steel structural panels, two tests at ambient temperature and six exposed to the standard fire condition on one side. The test panels used two types of lipped channels, 100×54×15×1.2 mm or 100×54×15×2 mm, each channel having two service holes, one near the top and one near the bottom. Three different load levels, being 0.2, 0.4 and 0.7 times the load carrying capacity of the same panel tested at ambient temperature, were applied during the six fire tests. At ambient temperature, failure was local buckling around the top service hole. Under fire condition, the main failure mode was overall flexural–torsional buckling about the major axis, with the lateral deformations of the test panels being mainly caused by thermal bowing due to temperature gradients. The interior insulation in some tests was burnt through and this had noticeable influence on temperature developments in the test steel channels. In two fire tests using the thinner channels, the test panels failed before 30 min that is considered to be the minimum standard fire rating of this type of construction.     

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.     

Inelastic behaviour and design of cold-formed channel sections in bending

The aim of this paper is to investigate the inelastic bending capacity of cold-formed channel sections, and provide design rules to account for such behaviour. An extensive experimental and analytical analysis of 42 cold-formed channel sections in three different geometric categories is conducted, including simple channel sections, channel sections with simple edge stiffeners and channel sections with complex edge stiffeners. The sections were cold-formed from G450 steel with nominal thickness of 1.6 mm, and varying theoretical buckling stresses ranging between elastic to seven times the yield stress. The results of the pure bending experimental investigations show that current international cold-formed steel specifications are conservative, for channel sections with low slenderness values. The experimental results are used to propose revisions to current international cold-formed steel specifications.     

Structural analysis and design of sandwich panels with cold-formed steel facings

Superior structural efficiency, ease of erection, mass-production capabilities and thermal-insulation qualities are making sandwich panels with flat or thin-walled cold-formed steel facings and rigid foamed insulating core increasingly popular as enclosures for system buildings. In this paper the structural behavior — including flexural stresses, deflections, vibration and thermal stresses — is presented, summarizing more than two decades of research. Methods used are analytical (boundary-value approaches), numerical (finite-strip, finite-layer, finite-prism approaches) and experimental (full-scale testing). Key equations are formulated, and results by different methods are compared. Design guidelines are also suggested.     

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.     

偏心受压冷弯薄壁槽钢的卷边角度优化设计

为了使得钢结构的性能与用钢量比达到最优,前人对槽型钢的截面尺寸优化进行了较为充分的研究。但是,涉及卷边角度的优化特别是偏心受压工况下的优化分析却很缺乏。以Yao-Teng偏心受压计算公式,结合遗传算法,以冷弯卷边槽钢柱偏心受压为例,将槽钢卷边角度与偏心距作为设计变量,寻找在不同偏心距受压情况下,达到最大畸变屈曲临界应力的卷边角度。基于有限条分析程序,对两端简支与两端固支情况下不同截面尺寸构件的畸变屈曲临界应力进行了计算分析,最终得出不同偏心距受压下统一的最优卷边角度。为了方便工程设计人员设计时参考,建议卷边角度统一取为100°。     

高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲性能研究

建立了考虑材料和几何双重非线性的550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件畸变屈曲性能分析的有限元模型,并通过对两种厚度高强冷弯薄壁型钢轴压构件畸变屈曲试验已有结果的分析比较验证了其有效性;采用该模型进一步分析了厚度、长度、初始缺陷模式及幅值等参数对畸变屈曲轴压构件承载力的影响,并对轴压构件畸变屈曲发生机理进行了探讨。结果表明：厚度、长度和初始缺陷模式是影响畸变屈曲轴压构件承载力的主要因素,且卷边面内屈曲是槽形截面轴压构件发生畸变屈曲的主要原因。通过理论计算与试验结果的对比分析,表明可以采用建议方法计算此类复杂截面轴压构件的畸变屈曲承载力。     

Observations on the design and modelling of some joined thin-walled structural sections

In a recent experimental and analytical study for the axial progressive collapse of some thin-walled structural sections, no consistent reliability could be obtained for the prediction of crush parameters for different geometries and materials with an analytical approach that relied on a yield hinge model. Square and spot-welded top-hat sections were compared. This situation occurs because the assumed equivalence between the top-hat and square sections according to the yield hinge model of the folding structures, does not appear valid for the actual structures. Some of the dependences between the actual structure and the model are discussed, particularly for the top-hat geometry. Observations on a beneficial positioning of the spot-welds in a top-hat section are reported, and common recommendations for an optimum weld pitch are critically examined. Modes 1 and 2 deformations are identified for the well-known quasi-inextensional, regular (asymmetric) progressive folding of thin-walled sections having a rectangular (core) cross-section, such as square and top-hat sections. The deformation modes are characterized by different proportions of inward and outward movements of the material during folding. Possible implications for the stability of collapse and for the analytical formulae are indicated.     

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.     

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.     

冷弯薄壁型钢四肢拼合箱形柱偏压受力性能试验研究与数值分析

对冷弯薄壁型钢四肢拼合箱形截面立柱进行轴压和偏压试验研究,得到各试件的荷载-位移曲线和极限承 载力,详细分析了试件的屈曲模式和破坏特征。建立了考虑材料、几何和接触非线性的有限元模型对试验试件进 行模拟分析,两者吻合较好,验证了有限元方法的正确性。进而采用数值方法分析了构件长细比、螺钉间距和位 置、偏心距和偏心方向对该类拼合立柱偏压受力性能的影响。结果表明：双向刀铰支座可以很好的实现铰接;螺 钉间距为300mm时,拼合柱各肢整体协同工作性能良好;轴压和绕弱轴偏压试件最终破坏模式均为绕弱轴整体弯 曲,绕强轴偏压时,试件破坏模式为弯扭失稳,但扭转不明显;拼合柱的偏压极限承载力和刚度随长细比和偏心 距的增大而降低;偏心距相同时,拼合柱绕强轴偏压的极限承载力和刚度比绕弱轴偏压略高。     

轴心受压冷弯薄壁型钢的承载力分析

介绍了冷弯薄壁型钢的优点及其屈曲后确定承载力采用有效宽度的方法,并结合具体的工程实例,比较了三种不同截面的惯性矩、回转半径和承载力;得出了在用钢量相同的情况下冷弯型钢具有更大承载力的结果,验证了冷弯型钢可以带来很好经济效益的结论,为工程应用提供了一定的依据。     

Ultimate load-carrying capacity of cold-formed thin-walled columns with built-up box and I section under axial compression

The use of cold-formed thin-walled steel structures has increased in recent years, and some built-up section members are motivated and also widely used for their excellent structural behaviors. In this paper, a series of axially-compressed tests on built-up box section members composed of two C-section by self-drilling screws at flanges are conducted. The differences of global, local and distortional buckling behaviors between members with built-up and single sections are investigated at first. Then the effects of installation error and fastener spacing on ultimate load-carrying capacity of built-up members are analyzed. A strength estimation method for built-up members under axial compression is proposed based on the experimental investigation in this paper, as well as some existing experiments, and corresponding numerical analysis studies. Finally, the predicted capacity obtained by using the proposed strength estimation method is compared with experimental results and the nominal axial strength determined according to the AISI provisions, by which the suitability and accuracy of the proposed strength estimation method have been established.     

Torsional behaviour of braced thin-walled open sections

A more rational and accurate analysis is presented for the torsion of braced thin-walled open section bars with transverse connections. The approach is based on Vlasov's thin-wall beam theory in conjunction with the continuous medium method. Shearing deformations in the middle surface of the thin wall are also taken into account. The analysis gives a generalized sectorial coordinate to estimate the realistic torsional stiffness of the thin-walled member, and provides a better physical interpretation of the relationship between the sectorial properties and the applied torque.     

夹芯墙板覆面冷弯薄壁型钢承重复合墙体受剪试验

为满足多层冷弯薄壁型钢房屋建筑的抗震及防火要求,同时兼顾施工便捷性,提出了夹心墙板覆面的新型冷弯薄壁型钢复合墙体,并完成了11片足尺模型水平加载试验。试验表明： 1） 复合墙体的受剪破坏主要由墙板周边的螺钉连接失效引起,即螺钉将墙板撕裂或螺钉剪断引起,墙板与自攻螺钉之间的连接力学性能成为影响复合墙体受剪性能的主要因素;增大墙板厚度或者采用玻镁板代替石膏板可提高复合墙体抗剪性能,而龙骨立柱的截面尺寸对复合墙体受剪性能影响不明显; 2） 同侧墙板层数的增加对复合墙体受剪承载力及刚度虽有明显提高,但未达到线性叠加程度;夹心墙板的使用有利于墙体蒙皮效应的发挥,相应的墙体受剪性能优于墙体同侧双层墙板覆面时的受剪性能; 3） 蒸压加气混凝土（ALC）板周边与自攻螺钉的连接区域在较低水平荷载作用下出现板材开裂现象,故不宜采取ALC板参与墙体受力的连接方式。研究给出了新型冷弯薄壁型钢复合墙体的受剪承载力及抗剪刚度设计指标,供工程设计参考。     

CFRP加固冷弯薄壁C型钢长构件的轴压承载力

为了研究CFRP加固冷弯薄壁C型钢长构件的承载能力,对腹板和翼缘均粘贴CFRP的试件进行了轴心受压加载试验。7根长度均为1 400mm的试件,其中1根为未加固的控制试件,其余6根封闭缠绕外贴50mm宽CFRP间距为50、100、150mm 3种情况,层数为1层和2层。试验结果表明,在轴心荷载作用下的破坏模式为整体弯扭失稳,与控制试件相比,加固后试件的稳定极限承载力均有不同程度的提高;当CFRP间距与腹板高度的比值小于1时,加固效果较理想,且2层CFRP的加固效果好于1层。最后,采用有限元对模型进行数值模拟,对比试验数据和数值模拟结果,二者吻合较好。     

高强冷弯薄壁型钢卷边槽形截面轴压构件试验研究及承载力分析

对63根屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件进行试验研究,分析了构件的屈曲模式和极限承载力,并将参考AISI规范、澳洲规范和北美规范及我国现行行业标准《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）计算的构件承载力与试验结果进行分析比较。在此基础上,对高强超薄壁型钢卷边槽形截面轴压构件的承载力合理计算模式进行研究。结果表明：高强超薄壁型钢卷边槽形截面轴压构件在宽厚比较大时会出现畸变屈曲模式;采用等效板件方法计算加劲板件有效宽度后,我国《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）适用于屈曲强度550MPa、厚度小于2.00mm的冷弯薄壁型钢卷边槽形截面构件承载力计算。     

Plastic mechanisms database for thin-walled cold-formed steel members in compression and bending

Short members of thin-walled cold-formed (TWCF) steel sections, in compression and bending, fail by forming local plastic mechanisms. Taking into account the localised buckling pattern, the collapse of slender members, due to the interaction between local and overall buckling modes, is always characterised by local plastic mechanism failure mode. Based on these two observations, the ultimate strength in interactive buckling of these members can be regarded as an interaction between localised plastic mode and overall elastic one.The yield line mechanism method has been widely used to predict the sectional strength (e.g. local) of thin-walled cold-formed steel members that involve failure mode characterized by local collapse mechanisms. This method can be also used to study post-collapse behaviour and to evaluate the load-carrying capacity, ductility and energy absorption.This paper is based on previous studies and some latest investigations of authors, as well as the literature collected data. It represents an attempt to make an inventory, classify and range geometrical and analytical models for the local-plastic mechanisms aiming to characterize the ultimate capacity of some of the most used cold-formed steel sections in structural applications.