Coupled instabilities with distortional buckling in cold-formed steel lipped channel columns

The paper addresses the elastic post-buckling behaviours of cold-formed steel lipped channel simply supported columns affected by mode interaction phenomena involving distortional buckling, namely local/distortional, distortional/global (flexural-torsional) and local/distortional/global mode interaction. The results presented were obtained by means of Abaqus shell finite element analyses adopting column discretisations into fine 4-node element meshes. In order to enable a thorough assessment of all possible mode interaction effects, the column lengths and cross-section dimensions were carefully selected to ensure similar local, distortional and/or global buckling loads. One analyses otherwise identical (elastic) columns having initial geometrical imperfections (i) with various configurations (combinations of the competing critical buckling mode shapes) and (ii) sharing the same overall amplitude.     

New method of inelastic buckling analysis for steel frames

In general, the concept of bifurcation stability cannot be used to evaluate the critical load of typical steel frames that have geometric imperfections and primary bending moment due to transverse loads. These cases require a plastic zone or plastic hinge analysis based on the concept of limit-load stability instead. However, such analyses require large computation times and complicated theories that are unsuitable for practical designs. The present paper proposes a new method of inelastic buckling analysis in order to determine the critical load of steel frames. This inelastic analysis is based on the concept of modified bifurcation stability using a tangent modulus approach and the column strength curve. Criteria for an iterative eigenvalue analysis are proposed in order to consider the primary bending moment as well as the axial force by using the interaction equation for beam-column members. The validity and applicability of the proposed inelastic buckling analysis were evaluated alongside elastic buckling analysis and refined plastic hinge analysis. Simple columns with geometric imperfections and a four-story plane frame were analyzed as benchmark problems. The results show that the proposed inelastic buckling analysis suitably evaluates the critical load and failure modes of steel frames, and can be a good alternative for the evaluation of critical load in the design of steel frames.     

GBT-based elastic–plastic post-buckling analysis of stainless steel thin-walled members

When compared with carbon steel, stainless steel exhibits a more pronounced non-linearity and no well-defined yield plateau, as well as appealing features such as aesthetics, higher corrosion resistance and lower life cycle cost. Due to its considerably high ductility/strength and cost, stainless steel structural solutions tend to be adopted mostly for slender/light structures, thus rendering the assessment of their structural behaviour rather complex, chiefly because of the high susceptibility to instability phenomena. The first objective of this paper is to present the main concepts and procedures involved in the development of a geometrically and materially non-linear Generalised Beam Theory (GBT) formulation and numerical implementation (code), intended to analyse the behaviour and collapse of thin-walled members made of materials with a highly non-linear stress–strain curve (e.g., stainless steel or aluminium). The second objective is to validate and illustrate the application of the proposed GBT formulation, by comparing its results (equilibrium paths, ultimate loads, deformed configurations, displacement profiles and stress distributions) with those provided by shell finite element analyses of two lean duplex square hollow section (SHS) columns previously investigated, both experimentally and numerically, by Theofanous and Gardner (Eng Struct 2009; 31(12): 3047–3058.). The stainless steel material behaviour is modelled as non-linear isotropic and the GBT analysis includes initial geometrical imperfections, but neglects corner strength enhancements and membrane residual stresses. It is shown that the GBT unique modal nature makes it possible to acquire in-depth knowledge concerning the mechanics of the column behaviour, by providing “structural x-rays” of the (elastic or elastic–plastic) equilibrium configurations: modal participation diagrams showing the quantitative contributions of the global, local, warping shear and transverse extension deformation modes - moreover, this feature makes it possible to exclude, from future similar GBT analyses, those deformation modes found to play a negligible role in the mechanics of the behaviour under scrutiny, thus further reducing the number of degrees of freedom involved in a GBT analysis, i.e., increasing its computational efficiency.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

冷弯薄壁卷边槽钢轴压构件畸变与局部相关屈曲试验研究

对卷边尺寸不同的两类腹板中间设置加劲卷边槽形截面,共18个冷弯薄壁型钢固支轴压试件进行畸变屈曲与局部屈曲相关作用的静力试验研究。得到试件的屈曲模式、相关屈曲行为、破坏模式以及极限荷载。试验结果表明：畸变屈曲与局部屈曲的耦合相关对试件的变形和极限荷载有不利作用;畸变屈曲与局部屈曲的耦合相关作用存有较大的屈曲后承载力;畸变屈曲与局部屈曲的耦合相关顺序,即畸变屈曲 局部屈曲耦合相关、局部屈曲 畸变屈曲耦合相关,对试件的变形、非线性平衡路径、破坏模式以及极限荷载的影响有所不同。采用ABAQUS有限元软件对试件进行模拟分析,计算结果与试验结果吻合良好。     

Local/distortional mode interaction in cold-formed steel lipped channel beams

This paper reports a numerical investigation concerning the post-buckling behaviour of cold-formed steel lipped channel beams, subjected to uniform major axis bending, affected by local/distortional mode interaction – the results presented and discussed were obtained through shell finite element analyses performed using the code Abaqus. One analyses simply supported beams (locally/globally pinned and free to warp end sections) (i) with cross-section dimensions ensuring coincident local and distortional critical buckling moments and (ii) having critical-mode initial geometrical imperfections with different shapes and the same overall amplitude – local buckling is triggered either by the compressed flange (most common case) or by the web. The results reported consist of (i) elastic and elastic–plastic post-buckling equilibrium paths, (ii) curves and figures showing how the beam deformed configuration evolves along those paths and, for the elastic–plastic beams, (iii) figures making it possible to visualise (iii₁) the location and growth of plastic strains and (iii₂) the nature of the failure mechanisms detected.     

Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners

This paper presents an experimental investigation and a finite element analysis on cold-formed channels with inclined simple edge stiffeners compressed between pinned ends. Compression tests of pin-ended channel columns with inclined simple edge stiffeners have not been performed till now. A total of 36 channel specimens including three different cross sections with different edge stiffener inclined angles and column lengths were tested. Detailed measurements of initial geometric imperfections and material properties of the specimens were also conducted before the above tests. Failure modes include local buckling, distortional buckling, flexural buckling and interaction among these buckling modes were observed in tests. The results indicate that inclined angle and loading position significantly affect the ultimate load-carrying capacity and failure mode of specimens. Moreover, a non-linear finite element model was developed and verified against tests. Geometric and material non-linearities were included in the model. Results from the finite element analysis agree well with experimentally ultimate loads and failure modes. However, it should be improved on prediction for certain displacement.     

Aluminum alloy tubular columns—Part I: Finite element modeling and test verification

A numerical investigation on fixed-ended aluminum alloy tubular columns of square and rectangular hollow sections is described in this paper. The fixed-ended column tests were conducted that included columns with both ends transversely welded to aluminum end plates using the tungsten inert gas welding method, and columns without welding of end plates. The specimens were extruded from aluminum alloy of 6061-T6 and 6063-T5. The failure modes included local buckling, flexural buckling, interaction of local and flexural buckling, as well as failure in the heat-affected zone (HAZ). An accurate finite element model (FEM) was developed. The initial local and overall geometric imperfections were incorporated in the model. The non-welded and welded material nonlinearities were considered in the analysis. The welded columns were modeled having different HAZ extension at the ends of the column of 25 and 30 mm. The nonlinear FEM was verified against experimental results. It is shown that the calibrated model provides accurate predictions of the experimental loads and failure modes of the tested columns. The load-shortening curves predicted by the finite element analysis are also compared with the test results.     

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.     

单轴对称截面轴心受压构件的弯扭屈曲设计问题

阐述单轴对称截面轴心受压构件弯曲屈曲和弯扭屈曲两种失稳形式,以及绕截面对称轴弯扭屈曲换算长细比的计算方法和应用实例。     

On the incorporation of equivalent member imperfections in the in-plane design of steel frames

This work deals with the incorporation of equivalent member imperfections in the global analysis of steel frames and, in particular, is intended to clarify the Eurocode 3 (EC3) provisions involved in such procedure. In fact, these provisions stem from the well-known “European column buckling curves”, which means that they are based on the behaviour of simply supported isolated members under uniform compression (columns). First, one addresses the geometrically non-linear behaviour of isolated columns displaying arbitrary support conditions and different initial geometrical configurations. Then, the results obtained are used to propose a systematic and rational method to evaluate the appropriate “equivalent initial imperfections” that need to be incorporated in the second-order global elastic analysis of a frame or isolated compressed member. This method (i) is fully consistent with the EC3 column buckling curves and (ii) adopts critical buckling mode shape initial imperfections with amplitudes determined by means of closed-form analytical expressions. In order to enable a better grasp of the concepts involved and also to illustrate the capabilities of the proposed methodology, several numerical examples are presented and discussed throughout the paper.     

毛竹压杆屈曲系数公式研究

为获得四川地区毛竹压杆更精确的屈曲系数公式，通过试验方法测定四川地区毛竹的顺纹抗压强度以及31根长细比分布较为均匀的竹压杆临界荷载，并对国内外现有的9个竹压杆屈曲系数公式进行研究。结果表明：此批毛竹顺纹抗压强度平均值约为51MPa；竹压杆的破坏是由于局部鼓曲变形和整体弯曲变形叠加，最终竹压杆管壁超过横纹抗拉强度极限值进而纵向开裂；现有竹压杆屈曲系数公式所得到的临界荷载计算值之间有所差异，与文中试验实测临界荷载值也有不同程度的差异。最后采用具有较好拟合优度的Ylinen方法，基于文中试验数据拟合提出适用于四川地区的毛竹压杆屈曲系数公式。     

Experimental investigation concerning lipped channel columns undergoing local–distortional–global buckling mode interaction

This work deals with the structural behaviour and ultimate strength of fixed-ended cold-formed steel lipped channel columns experiencing local–distortional–global buckling mode interaction, due to the closeness between the critical buckling stresses associated with these three buckling mode types. After briefly addressing the column specimen geometry selection and showing a few numerical elastic post-buckling results, the paper reports the results of an experimental investigation involving a set of 12 columns with several cross-section dimensions and yield stresses, which is aimed at (i) providing experimental evidence of the occurrence of the triple mode interaction under consideration and (ii) quantifying its effect on the column deformed configuration evolution and failure load erosion (drop). Various aspects concerning the test set-up and procedure are described in some detail before presenting and discussing the obtained column experimental results, which basically consist of (i) measured cross-section dimensions, lengths and initial displacements (geometrical imperfections), (ii) stress–strain curves and yield stresses determined from tensile coupon tests, (iii) recorded non-linear equilibrium paths (applied load vs. various relevant displacements) and ultimate strength values, and (iv) observed deformed configurations and collapse mechanisms.     

Loss-of-stability induced progressive collapse modes in 3D steel moment frames

This paper deals with the progressive collapse analysis of a tall steel frame following the removal of a corner column according to the alternate load path approach. Several analysis techniques are considered (eigenvalue, material nonlinearities, material and geometric nonlinearities), as well as 2D and 3D modelling of the structural system. It is determined that the collapse mechanism is a loss-of-stability-induced one that can be identified by combining a 3D structural model with an analysis involving both material and geometric nonlinearities. The progressive collapse analysis reveals that after the initial removal of a corner column, its two adjacent columns fail from elastic flexural-torsional buckling at a load lower than the design load. The failure of these two columns is immediately followed by the failure of the next two adjacent columns from elastic flexural–torsional buckling. After the failure of these five columns, the entire structure collapses without the occurrence of any significant plastification. The main contribution is the identification of buckling-induced collapse mechanisms in steel frames involving sequential buckling of multiple columns. This is a type of failure mechanism that has not received appropriate attention because it practically never occurs in properly designed structures without the accidental loss of a column.     

Elastic local buckling of perforated webs of steel cellular beam-column elements

In this study, the finite element method is employed to determine the critical in-plane longitudinal load at which elastic local buckling of the web of cellular beam-column elements occurs. To simplify the simulation of the problem, the interaction between the flanges and perforated web is approximated by modelling the web only as a long plate having aspect ratio (L/h_w≥10) with multiple circular perforations. The utilized model incorporates restrained out-of-plane displacements along the four edges of the plate. Analyzed plates are subjected to linearly varying in-plane loads to simulate various combinations of axial and flexural stresses. The effect of different geometrical parameters on the elastic buckling load of perforated web plate is investigated. These geometrical parameters include the plate’s length and width, and the perforations’ diameter and spacing. Comprehensive finite element analyses are conducted to identify the behaviour of wide spectrum of perforated web plates at buckling under various combinations of axial compressive load and bending moment. Outcomes of the study are expected to enhance the understanding of the elastic local buckling of web plates of cellular beam-column elements.     

Behaviour,failure and DSM design of cold-formed steel beams: Influence of the load point of application

This work presents and discusses the results of an ongoing numerical investigation on the buckling, post-buckling, collapse and design of cold-formed steel beams subjected to non-uniform bending due to transverse loadings acting away from the shear centre (either at the top or bottom flange). These results consist of (i) elastic buckling loads and modes, obtained through analyses based on Generalised Beam Theory (GBT), and (ii) elastic–plastic equilibrium paths and collapse loads, yielded by Ansys geometrically and materially non-linear shell finite element analyses. The numerical ultimate strength values are compared with their estimates provided by the current Direct Strength Method (DSM) strength curves and, on the basis of this comparison, it is possible to assess the merits of the DSM approach to design beams subjected to transverse loadings acting away from the shear centre – moreover, novel features that may improve the performance of this approach are identified.     

Y形柱稳定性分析研究

Y形柱是机场航站楼屋盖支承体系中常采用的一种构件形式,作为主要承重构件,其稳定性决定了屋盖结构的整体承载能力。利用荷载-位移全过程跟踪技术,考虑几何非线性、材料非线性和初始几何缺陷,研究了在竖向和水平风、地震作用下薄壁Y形柱的稳定性。研究表明:竖向荷载作用下Y形柱以分叉段平面外屈曲为主要失稳模式;Y形柱对初始几何缺陷不敏感;水平风荷载对Y形柱稳定性不起控制作用;竖向和水平荷载作用下,发生面外失稳前柱子分叉处已经进入塑性变形,柱子强度问题先于整体失稳。     

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.     

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。     

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。