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.     

Torsion in thin-walled cold-formed steel beams

Thin-walled cold-formed steel members have wide applications in building structures. They can be used as individual structural framing members or as panels and decks. In general, cold-formed steel beams have open sections where centroid and shear center do not coincide. When a transverse load is applied away from the shear center it causes torque. Because of the open nature of the sections, torsion induces warping in the beam. This paper summarizes the research on the behavior of cold-formed steel beams subject to torsion and bending. The attention is focused on beams subject to torque, because of the effect of transverse loads not applied at the shear center. A simple geometric nonlinear analysis method, based on satisfying equilibrium in the deformed configuration, is examined and used to predict the behavior of the beams. Simple geometric analyses, finite element analyses and finite strip analyses are performed and compared with experimental results. The influence of typical support conditions is studied and they are found to produce partial warping restraint at the ends. This effect is accounted for by introducing hypothetical springs. The magnitude of the spring stiffness is assessed for commonly used connections. Other factors that affect the behavior of cold-formed steel members, such as local buckling, are also studied.     

Elastic buckling of cold-formed steel columns and beams with holes

Simplified methods for approximating the global, distortional, and local critical elastic buckling loads of cold-formed steel columns and beams with holes are developed and summarized. These methods provide engineering approximations appropriate for design, but are intended to be general enough to accommodate the range of hole shapes, locations, and spacings common in industry. The simplified methods are developed as a convenient alternative to shell finite element eigen-buckling analysis, which require laborious and subjective visual identification methods as well as commercial software not generally accessible to the engineering community. Global buckling of cold-formed steel beams and columns, including the influence of holes, is predicted with approximate “weighted average” cross-section properties formulated from classical energy-based stability solutions. Distortional and local buckling of a cold-formed steel member with holes are determined with the semi-analytical finite strip method, considering appropriate modifications to the element thickness and choice of buckling half-wavelength. The proposed methods are verified with shell finite element eigen-buckling studies. Unambiguous, simple methods for elastic buckling prediction of members with holes is central to the extension of the Direct Strength Method (DSM) for cold-formed steel member ultimate strength determination.     

方钢管高强混凝土短柱有限元分析

文章基于冷弯型方钢管高强混凝土短柱试件的轴心受压试验,采用ABAQUS通用有限元分析软件对试件的轴压工况进行数值计算。采用合理的材料本构方程、建模与网格划分方法,使有限元计算结果与试验结果吻合较好。分析了在荷载-应变典型曲线特征点时轴压短柱试件的核心混凝土横截面轴向应力分布和试件在各阶段的受力性能。得到如下结论:钢管的冷弯区域决定了核心混凝土横截面轴向应变的分布;轴压短柱达到极限承载力时,核心混凝土由于方钢管的约束作用,其抗压强度得到明显提高;文章采用的有限元模型在分析冷弯型方钢管高强混凝土轴压短柱时是可行的。     

Simulation of geometric imperfections in cold-formed steel members using spectral representation approach

In this paper, a summary of the available imperfection measurements for cold-formed steel members is presented. Three methods to simulate imperfection fields are introduced: the first is the classical approach employing a superposition of eigenmode imperfections, but scaled to match peaks in the measured physical measurements. The second is a method based on the multi-dimensional spectral representation method, in which imperfections are considered as a two-dimensional random field and simulations are performed taking a spectra-based approach. The third is a novel combination of modal approaches and spectral representation that directly considers the frequency content of the imperfection field, but employs a spectral representation method driven by the cross-sectional eigenmode shapes to generate the imperfection fields. The effect of these different approaches on the simulated strength and collapse behavior of members is investigated using material and geometric nonlinear finite element collapse modeling. The third imperfection generation method, termed the 1D Modal Spectra Method, provides an intriguing new tool in the simulation of thin-walled members.     

Simplified nonlinear finite element analysis of buildings with CFS shear wall panels

The use of panelized cold-formed steel framing as the primary structural system has become increasingly popular for low- and mid-rise residential and commercial construction. The primary load-resistant elements in such framing are the structural panels built with uniformly spaced cold-formed steel studs and covered with structural sheathing. By taking advantage of in-line-framing, the framing members can be designed manually by using load tables published by manufacturers or spreadsheets developed in-house. In the case where the overall behaviour of the structure is needed, a finite element analysis has to be carried out. Conducting a finite element analysis for such types of buildings can be time consuming due to the large number of elements involved in modeling the framing member and structural sheathing. In this paper we present a simplified approach for analyzing cold-formed steel buildings by using finite element methods. In the proposed method, a typical 1.2 m wide wall panel which is built with cold-formed steel studs and structural sheathing is modeled by a 16-node shell element having equivalent material properties. In addition, the nonlinear behaviour of shear wall panels is simulated by a stiffness degradation factor. Compared to the conventional finite element method, a lesser number of elements will be used in the proposed method for modeling a building structure. The accuracy and efficiency of the proposed method are demonstrated through the comparison of results of the proposed and the conventional method on single shear wall panels. In addition, an example of nonlinear analysis for a three-storey building is presented.     

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.     

Recent developments in the buckling and nonlinear analysis of thin-walled structural members

This paper describes recent work performed at the University of Sydney to develop buckling and nonlinear analyses of thin-walled structural members undergoing local, distortional and overall buckling. The analyses are based on the finite strip method of structural analysis and include elastic and inelastic buckling and the full nonlinear response with both post-local buckling and plasticity. Two variations of the finite strip method have been used, these being the semi-analytical and spline finite strip methods. A nonlinear beam-column analysis based on the influence coefficient method for including the local buckling behaviour in the overall member response is also described.

The analytical methods are compared with tests performed at the University of Sydney on cold-formed rectangular hollow sections, welded I-sections, welded channel sections and cold-formed channel sections. Spatial plastic collapse mechanismsdeveloped for the welded sections described above are also compared with the post-ultimate response of the test sections.     

卷边加强开孔的冷弯型钢受弯构件的性能、优化及设计

冷弯型钢(CFS)受弯构件的腹板常常开圆孔,用于通过管道、电缆、水管设施和安装横向支撑等。传统在冷弯型钢腹板上开孔的构件的翼缘是不带卷边的,最近研发出新型具有加劲卷边的C型截面冷弯薄壁型钢抗弯构件。然而,目前对于新型C型截面构件的研究尚不深入,有用的试验也有限。该文采用有限元分析方法分析加劲开孔的冷弯型钢薄板和典型C截面构件的稳定性。基于弹性屈曲分析方法得出孔洞的最佳剖面,并将其应用于标准C截面构件。采用屈曲后有限元分析方法确定构件的挠曲强度。结果表明加劲孔洞能够大大提高C截面CFS挠曲强度。计划提出新的设计准则以准确计算孔洞剖面最佳的新型C截面构件的挠曲强度。     

Cold-formed steel flexural member with edge stiffened holes: Behavior,optimization, and design

Circular holes are commonly found on the web of cold-formed steel (CFS) flexural members for piping, electric-wiring, plumbing, or installing lateral bracing, etc. Traditional holes on CFS members are flat bunched without edge lips. A new generation of CFS C-section flexural members with edge stiffened holes was recently developed by the industry. However, research on the new generation C-section members is underdeveloped and available test results are limited. This paper presents finite element analyses to study on the stability of cold-formed steel thin plates and typical C-section members when edge stiffened circular holes are placed on those plates or members. Based on the elastic buckling analyses, the optimized profiles of the holes are obtained and then applied to standard C-section flexural members. The post-buckling finite element analysis is utilized to determine the flexural strength of those members. The results indicate that the stiffened holes can significantly improve the flexural strength of CFS C-sections. New design provisions are proposed to accurately predict the flexural strength of the new generation C-section flexural members with the optimized hole profiles.     

冷弯型钢C形截面受弯构件平面内稳定性能研究

为了研究冷弯型钢受弯构件平面内的稳定性能,对直卷边和斜卷边的冷弯型钢C形截面受弯构件分别进行了试验研究和有限元参数分析。试验研究和有限元分析均包含构件纯弯和非纯弯两部分。研究结果表明,多数构件在非纯弯作用下的抗弯承载力高于纯弯作用下的,但也有部分以局部和畸变相关屈曲为主的构件在纯弯作用下的抗弯承载力略高。屈曲模式是影响构件抗弯承载力的重要因素,构件以畸变屈曲为主时,非纯弯作用下的抗弯承载力明显高于纯弯作用下的。     

Stress concentration factors of cold-formed stainless steel tubular X-joints

This paper describes experimental and numerical investigations on stress concentration factors (SCFs) of cold-formed stainless steel square and rectangular hollow section (SHS and RHS) tubular X-joints. Both high strength stainless steel (duplex and high strength austenitic) and normal strength stainless steel (AISI 304) specimens were investigated. The SCFs were experimentally determined under static loading by measuring the strains at typical hot spot locations using strip strain gauges. The corresponding finite element analysis was performed to simulate the non-uniform stress distribution along the brace and chord intersection region. Good agreement between the experimental and finite element analysis results was achieved. Therefore, an extensive parametric study was then carried out by using the verified finite element model to evaluate the effects of the SCFs of cold-formed stainless steel tubular X-joints. The SCFs at the hot spot locations obtained from the experimental investigation and parametric study were compared with those calculated using the design formulae given in the CIDECT for carbon steel tubular X-joints. It is shown from the comparison that the design rules for the SCFs specified in the CIDECT are generally quite unconservative for cold-formed stainless steel tubular X-joints. In this study, a unified design equation for the SCFs of cold-formed stainless steel tubular X-joints is proposed. The proposed design equation was based on the CIDECT design equation for carbon steel tubular X-joints. It is shown that the SCFs calculated from the proposed unified design equation are generally in agreement with the values predicted from finite element analysis.     

国际期刊导读

采用有限元方法,对冷弯不锈钢方管、矩形管支撑和弦杆中的T型、X型及预应力X型节点进行数值分析。考虑几何非线性和材料非线性,获得节点承载力、破坏模式及荷载-位移曲线。利用试验结果,对T型、X型矩形管、方管节点的非线性有限元模型进行修正,直到有限元结果和试验结果足够吻合。采用修正后的有限元模型对172个T型、X型节点进行参数分析,研究冷弯不锈钢管节点强度和性能的影响。将数值分析和试验中获得的节点承载力与按规范计算的设计承载力进行对比。对不锈钢管结构,采用澳大利亚规范、新西兰规范计算;对碳素钢管结构,采用国际管结构发展与研究委员会设计规范和欧洲设计规范计算。通过可靠性分析,分别评价本文提出的设计方法和现有规范的可靠度。结果表明：采用本文方法计算的设计承载力更准确、更可靠。     

冷弯薄壁背靠式组合受弯构件数值模型中栓钉模拟方法的研究

本文主要对栓钉连接的冷弯薄壁背靠式组合受弯构件进行了可靠的有限元建模,为新型组合构件的静、动力分析做准备。首先运用ANSYS有限元软件,采用壳单元Shell181,建立了构件的有限元计算模型,并通过算例比较给出了组合受弯构件栓钉的最优模拟方法一直接耦合法。其次,进行了11组不同栓钉间距构件的有限元分析计算,得到了栓钉间距对组合构件极限状态的影响规律,并给出经济合理的栓钉间距为200mm。最后将有限元模型试算结果与已有构件试验进行对比分析后,验证了模型的可靠性。     

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.     

Design of cold-formed stainless steel tubular T- and X-joints

This paper describes the numerical investigation of cold-formed stainless steel tubular T-joints, X-joints and X-joints with chord preload using finite element analysis. The stainless steel joints were fabricated from square hollow section (SHS) and rectangular hollow section (RHS) brace and chord members. The geometric and material nonlinearities of stainless steel tubular joints were carefully incorporated in the finite element models. The joint strengths, failure modes as well as load-deformation curves of stainless steel tubular joints were obtained from the numerical analysis. The nonlinear finite element models were calibrated against experimental results of cold-formed stainless steel SHS and RHS tubular T- and X-joints. Good agreement between the experimental and finite element analysis results was achieved. Therefore, an extensive parametric study of 172 T- and X-joints was then carried out using the verified finite element models to evaluate the effects of the strength and behaviour of cold-formed stainless steel tubular joints. The joint strengths obtained from the parametric study and tests were compared with the current design strengths calculated using the Australian/New Zealand Standard for stainless steel structures, CIDECT and Eurocode design rules for carbon steel tubular structures. Furthermore, design formulae of cold-formed stainless steel tubular T- and X-joints are proposed. A reliability analysis was performed to assess the reliability of the current and proposed design rules. It is shown that the design strengths calculated using the proposed equations are generally more accurate and reliable than those calculated using the current design rules.     

冷弯薄壁卷边槽钢轴心受压构件承载力计算的折减强度法

为了研究冷弯薄壁卷边槽钢轴心受压构件的极限承载力,对15根轴心受压的冷弯薄壁卷边槽钢进行了破坏性试验,并采用有限元分析方法对试件进行模拟分析,有限元计算结果与试验结果吻合良好,验证了有限元方法的有效性,然后对典型截面构件进行大量的有限元参数分析。研究结果表明：冷弯薄壁卷边槽钢轴心受压构件的极限承载力随着构件翼缘宽厚比、腹板高厚比、长细比以及钢材强度的增大而减小。通过参数分析得到了考虑局部屈曲、整体屈曲和畸变屈曲影响的构件屈服强度折减系数,提出了冷弯薄壁卷边槽钢轴心受压构件承载力计算的折减强度法及其相应计算公式,且通过试验验证了本文折减强度法计算卷边槽钢轴心受压构件极限承载力的适用性。     

Ultimate strength of bolted moment-connections between cold-formed steel members

The behaviour and design of bolted moment-connections between cold-formed steel members, formed by using brackets bolted to the webs of the section, is considered. The particular problem of the moment-capacity of such joints being lower than that of the cold-formed steel sections being connected because of web buckling, caused by the concentration of load transfer from the bolts, is addressed. In this paper, a combination of laboratory tests and finite element analyses is used to investigate this mode of failure. It is demonstrated that there is good agreement between the measured ultimate moment-capacity and that predicted by using the finite element method. A parametric study conducted using the finite element model shows that the moment-capacity of a practical size joint can be up to 20% lower than that of the cold-formed steel sections being connected. Web buckling so-caused must therefore be considered in the design of such connections.     

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。     

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.