Buckling analysis of high strength stainless steel stiffened and unstiffened slender hollow section columns

This paper investigates the buckling behaviour of cold-formed high strength stainless steel stiffened and unstiffened slender square and rectangular hollow section columns. The high strength duplex material is austenitic-ferritic stainless steel approximately equivalent to EN 1.4462 and UNS S31803. The columns were compressed between fixed ends at different column lengths. A nonlinear finite element model has been developed to investigate the behaviour of stiffened slender square and rectangular hollow section columns. The column strengths, load-shortening curves as well as failure modes were predicted for the stiffened and unstiffened slender hollow section columns. An extensive parametric study was conducted to study the effects of cross-section geometries on the strength and behaviour of the stiffened and unstiffened columns. The investigation has shown that the high strength stainless steel stiffened slender hollow section columns offer a considerable increase in the column strength over that of the unstiffened slender hollow section columns. The column strengths predicted from the parametric study were compared with the design strengths calculated using the American Specification, Australian/New Zealand Standard and European Code for cold-formed stainless steel structures. It is shown that the design strengths obtained using the three specifications are generally conservative for the cold-formed stainless steel unstiffened slender square and rectangular hollow section columns, but slightly unconservative for the stiffened slender square and rectangular hollow section columns.     

Experimental and numerical investigations of cold-formed stainless steel tubular sections subjected to concentrated bearing load

Experimental and numerical investigations of cold-formed stainless steel square and rectangular hollow sections subjected to concentrated bearing load are presented in this paper. A total of 124 data are presented that include 64 test results and 60 numerical results. The tests were performed on austenitic stainless steel type 304, high strength austenitic and duplex material. The measured web slenderness value of the tubular sections ranged from comparatively stocky webs of 6.2 to relatively more slender webs of 61.4. The tests were carried out under end and interior loading conditions. A non-linear finite element model is developed and verified against experimental results. Geometric and material non-linearities were included in the finite element model. The material nonlinearity of the flat and corner portions of the specimen sections were carefully incorporated in the model. It was shown that the finite element model closely predicted the web crippling strengths and failure modes of the tested specimens. Hence, the model was used for an extensive parametric study of cross-section geometries, and the web slenderness value ranged from 52.0 to 206.7. The test results and the web crippling strengths predicted from the finite element analysis were compared with the design strengths obtained using the American, Australian/New Zealand and European specifications for stainless steel structures. A unified web crippling equation with new coefficients for cold-formed stainless steel square and rectangular hollow sections subjected to concentrated bearing load is proposed. It is demonstrated that the proposed web crippling equation is safe and reliable using reliability analysis.     

Flexural behaviour of stainless steel oval hollow sections

Structural hollow sections are predominantly square, rectangular or circular in profile. While square and circular hollow sections are often the most effective in resisting axial loads, rectangular hollow sections, with greater stiffness about one principal axis than the other, are generally more suitable in bending. Oval or elliptical hollow sections (EHS) combine the aesthetic external profile of circular hollow sections with the suitability for resisting flexure of rectangular sections, whilst also retaining the inherent torsional stiffness offered by all tubular sections. This paper examines the structural response of recently introduced stainless steel oval hollow sections (OHS) in bending and presents design recommendations. In-plane bending tests in the three-point configuration about both the major and minor axes were conducted. All tested specimens were cold-formed from Grade 1.4401 stainless steel and had an aspect ratio of approximately 1.5. The full moment-rotation responses of the specimens were recorded and have been presented herein. The tests were replicated numerically by means of non-linear finite element (FE) analysis and parametric studies were performed to investigate the influence of key parameters, such as the aspect ratio and the cross-section slenderness, on the flexural response. Based on both the experimental and numerical results, structural design recommendations for stainless steel OHS in bending in accordance with Eurocode 3: Part 1.4 have been made.     

冷成型双相不锈钢截面材料特性

给出了6个不同截面冷成型双相不锈钢的特性,其中2个为圆形中空截面,4个为矩形中空截面。试样为冷轧双相不锈钢带。确定方形和矩形中空截面高强度冷成型双相不锈钢的材料特性。对每种型材的薄弱和转角处进行拉伸试验,由此测量每种型材的弹性模量、0.2%弹性极限、1.0%弹性极限、抗张强度、断裂延伸率和Ramberg-Osgood参数(n)。通过短柱试验获得冷轧状态全截面的材料特性。测量6种型材的初始局部几何缺陷,绘制每种型材含初始几何缺陷的横截面图。采用断面法测量150×50×2.5截面的残余应力,测量并绘制截面上薄膜屈曲残余应力分布图。此外,给出适用于短柱的有限元模型,并与试验结果进行对比。将不锈钢短柱的试验强度与美国规范、澳大利亚/新西兰规范和欧洲规范的设计强度进行对比。总体看来,三种规范的计算结果都较为保守,其中欧洲规范的计算结果最为保守。     

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.     

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。     

冷弯不锈钢管T型及X型节点设计

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。     

Comparative experimental study of hot-rolled and cold-formed rectangular hollow sections

Square and rectangular hollow sections are generally produced either by hot-rolling or cold-forming. Cross-sections of nominally similar geometries, but from the two different production routes may vary significantly in terms of their general material properties, geometric imperfections, residual stresses, corner geometry and material response and general structural behaviour and load-carrying capacity. In this paper, an experimental programme comprising tensile coupon tests on flat and corner material, measurements of geometric imperfections and residual stresses, stub column tests and simple and continuous beam tests is described. The results of the tests have been combined with other available test data on square and rectangular hollow sections and analysed. Enhancements in yield and ultimate strengths, beyond those quoted in the respective mill certificates, were observed in the corner regions of the cold-formed sections—these are caused by cold-working of the material during production, and predictive models have been proposed. Initial geometric imperfections were generally low in both the hot-rolled and cold-formed sections, with larger imperfections emerging towards the ends of the cold-formed members—these were attributed largely to the release of through thickness residual stresses, which were themselves quantified. The results of the stub column and simple bending tests were used to assess the current slenderness limits given in Eurocode 3, including the possible dependency on production route, whilst the results of the continuous beam tests were evaluated with reference to the assumptions typically made in plastic analysis and design. Current slenderness limits, assessed on the basis of bending tests, appear appropriate, though the Class 3 slenderness limit, assessed on the basis of compression tests, seems optimistic. Of the features investigated, strain hardening characteristics of the material were identified as being primarily responsible for the differences in structural behaviour between hot-rolled and cold-formed sections.     

Structural performance of cold-formed high strength stainless steel columns

This paper describes an accurate finite element model for the structural performance of cold-formed high strength stainless steel columns. The finite element analysis was conducted on duplex stainless steel columns having square and rectangular hollow sections. The columns were compressed between fixed ends at different column lengths. The effects of initial local and overall geometric imperfections have been taken into consideration in the finite element model. The material nonlinearity of the flat and corner portions of the high strength stainless steel sections were carefully incorporated in the model. The column strengths and failure modes as well as the load-shortening curves of the columns were obtained using the finite element model. Furthermore, the effect of residual stresses in the columns was studied. The nonlinear finite element model was verified against experimental results. An extensive parametric study was carried out using the verified finite element model to study the effects of cross-section geometries on the strength and behaviour of cold-formed high strength stainless steel columns. The column strengths predicted from the parametric study were compared with the design strengths calculated using the American Specification, Australian/New Zealand Standard and European Code for cold-formed stainless steel structures. The results of the parametric study showed that the design rules specified in the American, Australian/New Zealand and European specifications are generally conservative for cold-formed high strength stainless steel square and rectangular hollow section columns, but unconservative for some of the short columns.     

FRP strengthening of lean duplex stainless steel hollow sections subjected to web crippling

This paper presents the experimental and numerical investigations of lean duplex stainless steel hollow sections subjected to web crippling. The test specimens were strengthened with different fibre-reinforced polymer (FRP). The web crippling tests were conducted under end-two-flange, interior-two-flange, end-one-flange and interior-one-flange loading conditions. A series of web crippling tests was conducted. The investigation was focused on the effects of surface treatment, web slenderness, different adhesives and FRPs for the strengthening of lean duplex stainless steel hollow sections against web crippling. The lean duplex stainless steel type EN 1.4162 was used in the investigation. Two different surface treatments, three different adhesives and six different FRPs were investigated in this study. The tests were performed on five different sizes of square and rectangular hollow sections that covered a wide range of web slenderness ratio from 8.1 to 57.3. Three different failure modes were observed in the tests of the strengthened specimens, namely the adhesion, interlaminar failure of FRP plate and combination of adhesion and interlaminar failure of FRP plate. Finite element models have been developed and verified against the test results of the specimens subjected to two-flange loading conditions.     

Elastic buckling of elliptical tubes

Hot-rolled and cold-formed structural steel tubular members of elliptical cross-section have recently been introduced into the construction sector. However, there is currently limited knowledge of their structural behaviour and stability, and comprehensive design guidance is not yet available. This paper examines the elastic buckling response of elliptical hollow sections in compression, which has been shown to be intermediate between that of circular hollow sections and flat plates. The transition between these two boundaries is dependant upon both the aspect ratio and relative thickness of the section. Based on the results of numerical and analytical studies, formulae to accurately predict the elastic buckling stress of elliptical tubes have been proposed, and shortcomings of existing expressions have been highlighted. Length effects have also been investigated. The findings have been employed to derive slenderness parameters in a system of cross-section classification for elliptical hollow sections, and form the basis for the development of effective section properties for slender elliptical tubes.     

冷成型不锈钢管轴心受压柱试验研究

为研究冷成型不锈钢管轴心受压柱的稳定性能,进行了国产304牌号冷成型不锈钢方管、矩形管和圆管截面,共43根轴心受压柱试验。通过对不锈钢材料、轴压短柱试件和轴压长柱试件的试验研究,得到了试件的材料力学性能和极限荷载。分析了试件的长细比、宽厚比（径厚比）对其破坏模式及变形性能的影响。结果表明：试件的宽厚比（径厚比）对其破坏模式及变形性能有较大的影响。采用GB 50018-2002《冷弯薄壁型钢结构技术规范》、欧洲不锈钢结构设计规范、美国冷成型不锈钢结构设计规范中的计算方法以及Rasmussen提出的设计方法对试验试件进行了计算,并与试验数据对比结果表明,对于圆管试件,采用三本规范计算得到的承载力均高于试验值,偏于不安全,采用Rasmussen 提出方法的计算结果与试验值较为接近;对于方矩管试件,各种方法计算结果相近,除短柱试件试验结果高于计算结果外,其余试件试验值均与计算结果吻合较好;GB 50018-2002《冷弯薄壁型钢结构技术规范》中的计算方法不能直接用于计算不锈钢管轴心受压柱承载力。     

Testing and numerical modelling of lean duplex stainless steel hollow section columns

Stainless steels are employed in a wide range of structural applications. The austenitic grades, particularly EN 1.4301 and EN 1.4401, and their low-carbon variants EN 1.4307 and EN 1.4404, are the most commonly used within construction, and these typically contain around 8%–11% nickel. The nickel represents a large portion of the total material cost and thus high nickel prices and price volatility have a strong bearing on both the cost and price stability of stainless steel. While austenitic stainless steel remains the most favourable material choice in many applications, greater emphasis is now being placed on the development of alternative grades with lower nickel content. In this study, the material behaviour and compressive structural response of a lean duplex stainless steel (EN 1.4162), which contains approximately 1.5% nickel, are examined. A total of eight stub column tests and twelve long column tests on lean duplex stainless steel square (SHS) and rectangular hollow sections (RHS) are reported. Precise measurements of material and geometric properties of the test specimens were also made, including the assessment of local and global geometric imperfections. The experimental studies were supplemented by finite element analysis, and parametric studies were performed to generate results over a wider range of cross-sectional and member slenderness. Both the experimental and numerical results were used to assess the applicability of the Eurocode 3: Part 1-4 provisions regarding the Class 3 slenderness limit and effective width formula for internal elements in compression and the column buckling curve for hollow sections to lean duplex structural components. Comparisons between the structural performance of lean duplex stainless steel and that of other more commonly used stainless steel grades are also presented, showing lean duplex stainless steel to be an attractive choice for structural applications.     

Strength and stability criteria for thin-walled stainless steel circular hollow section members under bending

A series of tests consisting of various cross-section geometries were performed on structural stainless steel circular hollow sections (CHS) subjected to bending. The test program comprised a total of eight tests on CHS in two grades of stainless steel, namely 304 and Duplex 2205. For each grade four sections, each with a different slenderness, were tested, in order to cover a range of structural responses. Measurements of overall geometric imperfections and material properties were conducted. The test strengths are compared with the strengths predicted using the American, Australian and European specifications for cold-formed stainless steel structures. In the light of the test results and code recommendations, strength and cross-section classification criteria for stainless steel circular hollow section members in bending are examined.     

Ferritic stainless steel tubular members strengthened with high modulus CFRP plate subjected to web crippling

Web crippling failure of ferritic stainless steel tubular structural members could be found due to localised concentrated loads or reactions. This paper reports experimental and numerical investigation on strengthening of ferritic stainless steel tubular members using externally bonded high modulus carbon fibre-reinforced polymer (CFRP) plate. The CFRP plate strengthening is only applied to a small localise area subjected to concentrated load. A series of tests on CFRP strengthened ferritic stainless steel square and rectangular hollow sections subjected to web crippling was conducted. The web crippling tests were conducted under four loading conditions of end-two-flange (ETF), interior-two-flange (ITF), end-one-flange (EOF) and interior-one-flange (IOF). A total of 37 web crippling tests was conducted in this study. The investigation was mainly focused on the effects of web slenderness of ferritic stainless steel tubular sections on CFRP strengthening against web crippling. The tests were performed on five different sizes of square and rectangular hollow sections. The ferritic stainless steel type EN 1.4003 test specimens were used in this study. Tensile coupon tests were conducted to determine the material properties of the ferritic stainless steel specimens. Most of the strengthened specimens were failed by debonding of CFRP plate from the ferritic stainless steel tubes. Two different failure modes were observed in the tests of the strengthened specimens, namely the adhesion failure as well as the combination of adhesion and cohesion failure. Finite element models have been developed and verified against the test results. The failure loads, failure modes and the load-web deformation behaviour of the ferritic stainless steel sections are also presented.     

Experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns

This paper presents an experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns. The high strength stainless steel tubes had a yield stress and tensile strength up to 536 and 961 MPa, respectively. The behaviour of the columns was investigated using different concrete cylinder strengths varied from 40 to 80 MPa. A series of tests was performed to investigate the effects of the shape of the stainless steel tube, plate thickness and concrete strength on the behaviour and strength of concrete-filled high strength stainless steel tube columns. The high strength stainless steel tubes were cold-rolled into square and rectangular hollow sections. The depth-to-plate thickness ratio of the tube sections varied from 25.7 for compact sections to 55.8 for relatively slender sections. The columns had different lengths so the length-to-depth ratio generally remained at a constant value of 3. The concrete-filled high strength stainless steel tube specimens were subjected to uniform axial compression. The column strengths, load-axial strain relationships and failure modes of the columns were presented. The test strengths were compared with the design strengths calculated using the American specifications and Australian/New Zealand standards that consider the effect of local buckling using an effective width concept in the calculation of the stainless steel tube column strengths. Based on the test results, design recommendations were proposed for concrete-filled high strength stainless steel tube columns.     

考虑单侧翼缘受载腹板屈曲的不锈钢钢管设计

本文给出了冷成型不锈钢方钢管和矩形钢管在腹板屈曲时的设计公式。研究了两种单翼缘加载的情况,一种是端部单翼缘加载,另一种是内部单翼缘加载,此外还研究了内部加载的情况。采用屈服线理论预测了不锈钢管截面的腹板屈曲强度。屈服线理论模型是在试验中观察到的破坏模式的基础上发展起来的。在屈服线模型基础上采用不同的假定,给出了计算冷成型不锈钢方钢管和矩形钢管的腹板屈曲强度的三种设计方法。其中两种腹板屈曲设计方法是完全采用屈服线分析理论推导出来的,另外一种设计方法是综合理论分析和经验分析得到的。将试验得到的腹板屈曲强度和这三种设计方法得到的屈曲强度进行了对比。结果表明采用纯理论推导得到的设计方法计算得到的腹板屈曲设计强度偏于保守,而综合了理论分析和经验分析得到的设计方法其计算的腹板屈曲设计强度值比较合理,可以用于单翼缘受载时冷成型不锈钢管的设计。     

Experimental investigation on longitudinal residual stresses for cold-formed thick-walled square hollow sections

This paper presents the experimental study on cold-formed thick-walled square hollow sections with thickness greater than 6 mm. Square hollow sections are formed using two different forming processes of a “direct square” way and an “indirect way from circular to square”. Two test methods of the hole-drilling method and the X-ray diffraction method are used to measure the magnitudes and distributions of longitudinal residual stresses. The magnitudes and distributions of longitudinal residual stresses along the section perimeter as well as along the section thickness are obtained in this study. It is shown that the longitudinal residual stresses are in tension at outer surface and in compression at inner surface, and present nonlinear distributions, which seems like “sine” curve along the section thickness. Furthermore, the effects of forming process and cross-section geometry on the magnitudes and distributions of longitudinal residual stresses for cold-formed thick-walled square hollow sections are discussed. At last, two distribution patterns have been proposed for the square hollow sections formed using two different forming processes, respectively.     

厚壁矩形中空截面冷弯型钢纵向残余应力试验研究

对壁厚超过6mm的厚壁矩形中空截面冷弯型钢进行试验研究。矩形中空截面采用两种成型方法:直接法(直接形成矩形)和间接法(先形成圆形,再转换成矩形)。采用两种方法(钻孔法和X射线衍射法)计算纵向残余应力的大小和分布。研究了沿截面周长方向和厚度方向的纵向残余应力的大小和分布。结果显示,沿厚度方向的纵向残余应力在外表面为拉力,内表面为压力,表现出类似于正弦曲线的非线性特性。此外,讨论了厚壁矩形中空截面冷弯型钢的成型过程和截面几何尺寸对残余应力的大小和分布的影响。最后,针对厚壁矩形中空截面冷弯型钢两种不同成型过程,分别给出相应的残余应力分布情况。     

Resistance of stainless steel CHS columns based on cross-section deformation capacity

A conceptually new structural design approach has recently been proposed by the authors to predict the resistance of stainless steel members subjected to various types of loading with cross-sections formed from thin flat plates including angles, channels, lipped channels, I-sections and rectangular hollow sections (RHS). The proposed method does not follow the traditional cross-section classification approach, which primarily relies on the assumption of a bilinear, elastic-perfectly-plastic material model. Instead, deformation capacity of a cross-section is determined directly from the local buckling characteristics of the constituent plate elements. This is then used to obtain the corresponding local buckling stress utilising an appropriate material model. This basic concept is extended herein to predict compression resistance of stainless steel columns with circular hollow sections (CHS). Available test and finite element (FE) results have been used to develop the basic design equation to predict the compression resistance of cross-sections and to propose column curves to determine flexural buckling resistances. The predicted resistances have been compared to those obtained using the current Eurocode; the predictions are significantly more accurate and more consistent than those given by the existing Eurocode.