Recent research advances on the ECBL approach. Part II: interactive buckling of perforated sections

Perforated cold-formed steel sections are often used in civil engineering as structural members for residential buildings and storage racks construction. In the case of buildings the perforations are provided to permit piping and bridging, while for rack systems they allow for simple connections between members. The load bearing capacity of these sections are influenced not only by the local buckling, global buckling and interaction between these two, but also by the reduction of cross-sectional properties due to perforations. Because of the wide variety in the size and configuration of perforations, it is impossible to provide a practical design procedure to calculate the ultimate strength of such a type of sections. The main objective of this paper is to calibrate an effective design width formula for the perforated sections and, using the ECBL approach, to evaluate an equivalent α imperfection factor for European buckling curves, in order to adapt them for sections with different perforation patterns.     

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.     

Hysteretic behaviors of cold-formed steel beam-columns with hollow rectangular section: Experimental and numerical simulations

This paper presents a comprehensive experimental and numerical investigation on the cyclic response of cold-formed steel columns with hollow rectangular sections. The present study examined the columns׳ post-buckling strength and rigidity degradation, deformation and failure modes, ductility, and energy dissipation capacity. The cold-formed steel members exhibited stable hysteretic performance up to the point of local buckling with considerable degradation in strength and ductility. The energy dissipation mechanisms from the in-plane plastic behavior and out-of-plane elastic buckling deformation were identified. The influence of the height-to-width ratio and axial-compression ratio on energy-dissipation and failure mode was also investigated.     

Effect of imperfections on numerical simulation of instability behaviour of cold-formed steel members

The paper analyses the influence of imperfections on the behaviour of cold-formed steel members. Special attention is paid on the characterisation and codification of imperfections for non-linear FEM simulation. Based on the ECBL approach [2] and using an advanced non-linear inelastic analysis, the erosion of theoretical buckling strength, due to geometrical imperfections, in single and coupled instability modes is evaluated.     

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.     

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.     

A numerical imperfection sensitivity study of cold-formed thin-walled tubular steel columns at uniform elevated temperatures

A numerical study is carried out on cold-formed rectangular hollow section columns to evaluate the sensitivity of column failure strength to initial imperfections, stress–strain relationships and to assess the existing design methods. It is shown that the magnitude of initial local buckling imperfection has a significant effect on the ultimate strength of short columns where failure is predominantly local buckling. Its effect on long columns is relatively small. Similarly the magnitude of initial global imperfection has more influence on the ultimate strength of a long column, whose failure is governed by global buckling, than on short columns, where local buckling controls. The shape of the stress–strain relationship of cold-formed steel will have noticeable effect on the column failure load. Current design methods, for high temperatures in ENV1993-1-2 and for ambient temperature in ENV1993-1-3, can provide a valid basis of calculation but modification will be necessary, depending on the exact model of stress–strain relationship of cold-formed steel at elevated temperatures.     

受弯的冷弯卷边槽钢畸变屈曲强度和其相关屈曲承载力

受弯的冷弯薄壁卷边槽钢基本上有板件局部屈曲,截面畸变屈曲和构件弯扭屈曲三种屈曲模式,随后有它们之间的相关屈曲。由于畸变屈曲模式对缺陷的敏感度高,因此其屈曲后强度提高的幅度远低于局部屈曲模式。但是与局部屈曲模式相比,畸变屈曲模式抵抗破坏的能力却很强。可以用有限单元法计算受弯卷边槽钢截面的畸变屈曲强度。本文介绍了澳大利亚-新西兰标准AS/NZS4600-2005,用手算法计算受弯卷边槽钢截面的弹性畸变屈曲应力,並用直接强度法计算其相关的屈曲承载力。     

冷弯薄壁型钢卷边槽形截面构件畸变屈曲控制研究

基于部分加劲板件的畸变屈曲和局部屈曲的稳定系数比较,提出了冷弯薄壁型钢卷边槽形截面构件畸变屈曲发生于局部屈曲之后或畸变屈曲不发生的临界控制条件;给出了通过构件畸变屈曲计算长度控制畸变屈曲的临界条件;提出一种控制畸变屈曲的构造措施,即在卷边间加设缀板,并通过已有试验对其有效性进行验证,同时推导了卷边间缀板的刚度需求。结果表明：通过构件截面尺寸控制畸变屈曲不发生或发生在局部屈曲之后,可以不考虑构件畸变屈曲的影响,简化冷弯薄壁型钢卷边槽形截面构件承载力的计算;计算长度小于畸变屈曲半波长一半的构件不发生畸变屈曲;通过在卷边间加设缀板的构造措施能有效阻止部分加劲板件的转动,构件的畸变屈曲荷载和承载力都有很大的提高,缀板布置间距不同,构件承载力的提高幅度也不同,缀板间距越小,构件承载力提高幅度越大。算例分析表明,满足一定间距和刚度需求的缀板能够提高构件的畸变屈曲承载力或避免畸变屈曲的发生。     

Experiments on cold-formed steel columns with holes

The objective of this paper is to observe and quantify the relationship between elastic buckling and the tested response of cold-formed steel columns with holes. Compression tests were conducted on 24 short and intermediate length cold-formed steel columns with and without slotted web holes. For each specimen, a shell finite element eigenbuckling analysis was also conducted such that the influence of the boundary conditions and the hole on local, distortional, and global elastic buckling response could also be captured. Slotted web holes may modify the local and distortional elastic buckling half-wavelengths, and may also change the critical elastic buckling loads. Experimentally, slotted web holes are shown to have a minimal influence on the tested ultimate strength in the specimens considered, although post-peak ductility is decreased in some cases. Tangible connections are observed between elastic buckling and load–displacement response during the tests, including mode switching between local and distortional buckling. The columns are tested with friction-bearing boundary conditions where the columns ends are milled flat and parallel, and bear directly on steel platens. These boundary conditions, which greatly speed specimen preparation, are determined to be viable for evaluating the tested response of short and intermediate length columns, although the post-peak response of intermediate length specimens must be considered with care.     

Compression tests of high strength cold-formed steel channels with buckling interaction

This paper describes a series of compression tests conducted on cold-formed simple lipped channels and lipped channels with intermediate stiffeners in the flanges and web fabricated from high strength steel plate of thickness 0.6 and 0.8 mm with the nominal yield stress 560 MPa. A range of lengths of lipped channel sections were tested to failure with both ends of the column fixed with a special capping to prevent local failure of column ends and influence from the shift of centroid during testing. The high strength cold-formed steel channel sections of intermediate lengths generally displayed a significant interaction between local and distortional buckling. A noticeable interaction between local and overall buckling was also observed for the long columns. A significant post-buckling strength reserve was shown for those sections that showed interaction between local and distortional or overall buckling. Simple design strength formulas in the Direct Strength Method for the thin-walled cold-formed steel sections failing in the mixed mode of local and distortional buckling have been studied. The strengths predicted by the strength formulas proposed are compared with the test results for verification.     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

卷边加强冷弯型钢梁局部和畸变屈曲

设计时,应重点考虑冷弯型钢构件的屈曲特性及其导致的有效性损失,以保证结构的经济性。数值模型改进后,能够反映考虑几何缺陷、材料非线性特性、后屈曲性能等因素的冷弯型钢梁的真实屈曲特性。针对侧向约束下冷成型Z型钢梁,采用已有的有限元模型,研究钢梁卷边及其与受压翼缘的相互作用对后屈曲特性的影响。利用卷边翼缘宽度比以及卷边倾角,观测局部屈曲、畸变屈曲和局部/畸变屈曲相互作用下截面抗弯刚度的变化。评估了EC3中适用于冷成型Z型钢梁局部和畸变屈曲的设计方法的有效性。总体而言,采用EC3计算的截面抗弯刚度并不保守。指出其中的不足并提出改进建议,改善卷边受压翼缘的失稳系数。     

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements—the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.     

冷弯薄壁不锈钢受压构件变形屈曲的分析

介绍了目前国外有关冷弯薄壁不锈钢设计中受压构件强度的计算，重点阐述了变形屈曲的计算方法。对冷弯薄壁不锈钢槽钢和工字钢受压构件的变形屈曲进行分析，并做了部分试验，用于理论分析方法、有限元法和实际值之间的比较。     

Improved prediction of simultaneous local and overall buckling of stiffened panels

In this paper, improved expressions for elastic local plate buckling and overall panel buckling of uniaxially compressed T-stiffened panels are developed and validated with 55 ABAQUS eigenvalue buckling analyses of a wide range of typical panel geometries. These two expressions are equated to derive a new expression for the rigidity ratio (EI_x/Db)_CO that uniquely identifies “crossover” panels—those for which local and overall buckling stresses are the same. The new expression for (EI_x/Db)_CO is also validated using the 55 FE models. Earlier work by Chen (Ultimate strength analysis of stiffened panels using a beam-column method. PhD Dissertation, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2003) had produced a new step-by-step beam-column method for predicting stiffener-induced compressive collapse of stiffened panels. An alternative approach is to use orthotropic plate theory. As part of the validation of the new beam-column method, ABAQUS elasto-plastic Riks ultimate strength analyses were made for 107 stiffened panels—the 55 crossover panels and 52 others. The beam-column and orthotropic approaches were also used. A surprising result was that the orthotropic approach has a large error for crossover panels whereas the beam-column method does not. Some possible reasons for this are suggested.     

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。     

冷弯薄壁C型钢绕强轴偏心受压构件的极限承载力

冷弯薄壁型钢结构多采用有效截面法对构件承载力进行计算,该方法计算繁杂且未考虑构件的畸变屈曲性能。直接强度法采用全截面计算各类参数,能够考虑各种单独屈曲模式及其相关屈曲对构件稳定性能的影响,但目前该方法并不能应用于压弯构件。对冷弯薄壁C形钢绕强轴偏压构件的稳定性能进行参数分析,探讨了构件长度、偏心距、腹板高厚比、翼缘宽厚比和卷边高厚比等因素对构件承载力的影响规律。结合有限元分析结果,基于轴压构件和纯弯构件的直接强度法公式,提出了冷弯薄壁型钢绕强轴偏压构件的极限承载力计算方法。     

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.     

Application of direct strength method to axially loaded perforated cold-formed steel studs: Distortional and local buckling

A study to develop methods of analyzing perforated, axially loaded, cold-formed steel studs using the provisions of the Direct Strength Method [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004] was undertaken using the Finite Strip Method as the method for determining the elastic buckling stresses. Several different models were developed to represent the effect of the web perforations. The capacities predicted using the Direct Strength Method for the limit states of distortional and local buckling were compared to capacities calculated using the equations contained in the AISI Specification [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004]. The limit state of longwave buckling is considered in a companion paper [Sputo T, Tovar J. Application of direct strength method to axially loaded perforated cold-formed steel studs: Part 1. Longwave buckling. Thin Walled Struct, submitted for publication]. The validity of the results is discussed and recommendations are made for the use of the Direct Strength Method for these members.