Tests and behaviour of cold-formed stainless steel tubular X-joints

The paper presents a series of tests on cold-formed stainless steel tubular X-joints. The tubular X-joint specimens were tested without chord preload as well as with three different levels of preload applied to the chord members. The test specimens were fabricated from square and rectangular hollow sections as brace and chord members. A total of 32 tests was performed. High strength stainless steel (duplex and high strength austenitic) and normal strength stainless steel (AISI 304) specimens were tested. The test results were compared with the design strengths obtained using the CIDECT Guide and Eurocode for carbon steel structures. It is shown that the design strengths predicted by the current design specifications are very conservative for the test specimens calculated using the 0.1%, 0.2%, 0.5% and 1.0% proof stresses as the yield stresses. The 0.2% proof stress is comparatively more reasonable to predict the design strengths of stainless steel tubular X-joints for both ultimate limit state and serviceability limit state.     

Experimental investigation of cold-formed stainless steel tubular T-joints

This paper describes a test program on a wide range of cold-formed stainless steel welded tubular T-joints fabricated from square and rectangular hollow section brace and chord members. A total of 22 tests was performed. High strength stainless steel (duplex and high strength austenitic) and normal strength stainless steel (AISI 304) specimens were tested. The tests were performed by supporting the chord member of the specimen along its entire length with the pure concentrated force applied to the chord face by the brace member. The ratio of brace width to chord width (β) of the specimens varied from 0.5 to 1.0 so that failure modes of chord face failure and chord side wall failure were observed. The test results were compared with the design procedures in the Australian/New Zealand Standard for stainless steel structures, CIDECT and Eurocode design rules for carbon steel structures. It is shown that the design strengths predicted by the current design specifications are conservative for the test specimens calculated using the 0.1%, 0.2%, 0.5% and 1.0% proof stresses as the yield stresses. The 0.2% proof stress is comparatively more reasonable to predict the design strengths of stainless steel welded tubular T-joints for both ultimate limit state and serviceability limit state. In this study, it is shown that the ultimate limit state controls rather than the serviceability limit state for most of the test specimens.     

Tests of concrete-filled stainless steel tubular T-joints

This paper describes a test program on a wide range of concrete-filled cold-formed stainless steel tubular T-joints fabricated from square hollow section (SHS) and rectangular hollow section (RHS) brace and chord members. A total of 27 tests was performed. The chord member of the test specimen was filled with concrete along its full length. Both high strength stainless steel (duplex and high strength austenitic) and normal strength stainless steel (AISI 304) specimens filled with nominal concrete cylinder strength of 30 MPa were tested. The axial compression force was applied to the top end of the brace member, which was welded to the center of the chord member. Local buckling failure of brace member was the main failure mode observed during the tests. Hence, the axial compression force was then applied by means of a steel bearing plate to avoid failure of brace member. The failure modes of chord face failure and chord side wall failure as well as crushing of the concrete infill were observed. All the tests were performed by supporting the chord member of the specimen along its entire length to apply the pure concentrated force without any bending moment. The test results were also compared with design rules for carbon steel tubular structures, which is the only existing design guideline for concrete-filled tubular joints. It is shown that the design strengths predicted by the current design rules are quite conservative for the test specimens. It is also recommended that the contribution of stainless steel tubes should be included in the design rules since it has significant effects on the ultimate bearing capacity of concrete-filled stainless steel tubular T-joints.     

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。     

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.     

冷弯不锈钢管T形节点的试验研究

对冷弯不锈钢管T形节点进行试验研究,这些节点由方矩形中空截面的支撑和弦杆构成。对高强不锈钢（双相和高强度奥氏体）和普通强度不锈钢（AISI304）构件进行了测试,共进行了22个试验。试验方法：将支撑对弦杆正面所导致的全部集中力,沿试件长度施加到弦杆上。支撑和弦杆的宽度比值（β）范围为0.5～1.0,这样可以观察到弦杆正面和侧面的失效模式。将试验结果与采用澳大利亚/新西兰不锈钢结构设计标准、CIDECT和欧洲碳素钢结构设计规范的设计方法相对比。对比结果显示：采用0.1%,0.2%,0.5%和1.0%的弹性极限应力作为屈服应力,按照这些规范计算出来的设计强度略微保守。相对而言,0.2%的弹性极限应力比较适用于预测不锈钢管T形节点在使用和极限状态下的设计强度。     

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.     

Tests of cold-formed high strength stainless steel compression members

The paper describes a test program on cold-formed high strength stainless steel compression members. The duplex stainless steel having the yield stress and tensile strength up to 750 and 850 MPa, respectively, was investigated. The material properties of the test specimens were obtained from tensile coupon and stub column tests. The test specimens were cold-rolled into square and rectangular hollow sections. The specimens were compressed between fixed ends at different column lengths. The initial overall geometric imperfections of the column specimens were measured. The strength and behaviour of cold-formed high strength stainless steel columns were investigated. The test strengths were compared with the design strengths predicted using the American, Australian/New Zealand and European specifications for cold-formed stainless steel structures. Generally, it is shown that the design strengths predicted by the three specifications are conservative for the cold-formed high strength stainless steel columns. In addition, reliability analysis was performed to evaluate the current design rules.     

Experimental and numerical investigation of high strength stainless steel structures

The paper summarises research on high strength stainless steel tubular structures conducted at the University of Hong Kong, and the Hong Kong University of Science and Technology. Square and rectangular hollow sections were investigated. The test specimens were cold-rolled from high strength austenitic and duplex stainless steel sheets. The material properties of the test specimens were determined by tensile coupon tests at normal room and elevated temperatures. The initial geometric imperfection and residual stress of the specimens were measured. The experimental and numerical investigation focused on the design and behaviour of cold-formed high strength stainless steel structural members. The results were compared with design strengths calculated using the American, Australian/New Zealand and European specifications for cold-formed stainless steel structures.     

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.     

Structural performance of cold-formed lean duplex stainless steel columns

The structural performance of cold-formed lean duplex stainless steel columns was investigated. A wide range of finite element analysis on square and rectangular hollow sections and other available data, with a total number of 259 specimens, were considered. An accurate finite element model has been created to simulate the pin-ended cold-formed lean duplex stainless steel columns. Extensive parametric study was carried out using the validated finite element model. The column strengths predicted from the parametric study together with the available data are compared with the design strengths calculated from various existing design rules for cold-formed stainless steel structures. It is shown that the existing design rules, except for the ASCE Specification as well as the stub column and full area approach, are conservative. Modifications are proposed for the AS/NZS Standard, EC3 Code, and direct strength method. Reliability analysis was performed to assess the existing and modified design rules. It is also shown that the modified design rules are able to provide a more accurate and reliable predictions for lean duplex stainless steel columns. In this study, it is suggested that the modified design rules in the AS/NZS Standard and the modified direct strength method to be used in designing cold-formed lean duplex stainless steel columns.     

Research on cold-formed steel columns

The paper summarises research on cold-formed steel columns performed by the author. Cold-formed steel members are either cold-rolled or brake-pressed into structural shapes. As a result, cold-formed steel open sections are usually singly-point- or non-symmetric. The most common types of singly-symmetric sections are channel and angle. The research focused on cold-formed steel open sections, such as plain and lipped channels, channels with simple and complex edge stiffeners as well as plain and lipped angles, and unequal angles. In addition, cold-formed steel built-up closed sections with intermediate stiffeners were investigated. Both experimental and numerical investigations into the strength and behaviour of cold-formed steel columns were conducted. The column strengths obtained from these investigations were compared with the design strengths obtained using various international standards for cold-formed steel structures. Furthermore, the behaviour and design of cold-formed steel lipped channel columns at elevated temperatures were also investigated. The paper also summarises the design recommendations for cold-formed steel columns.     

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.     

Prediction of residual stresses and strains in cold-formed steel members

The objective of this paper is to provide an unambiguous mechanics-based prediction method for determination of initial residual stresses and effective plastic strains in cold-formed steel members. The method is founded on basic physical assumptions regarding plastic deformations and common industry practice in manufacturing. Sheet steel coiling and cross-section roll-forming are the manufacturing processes considered. The structural mechanics employed in the method are defined for each manufacturing stage and the end result is a series of closed-form algebraic equations for the prediction of residual stresses and strains. Prediction validity is evaluated with measured residual strains from existing experiments, and good agreement is shown. The primary motivation for the development of this method is to define the initial state of a cold-formed steel member for use in a subsequent nonlinear finite element analysis. The work also has impact on our present understanding of cold-work of forming effects in cold-formed steel members.     

Design of cold-formed steel channels with stiffened webs subjected to bending

The objectives of this study are to investigate the structural behaviour and evaluate the appropriateness of the current direct strength method on the design of cold-formed steel stiffened cross-sections subjected to bending. The stiffeners were employed to the web of plain channel and lipped channel sections to improve the flexural strength of cold-formed steel sections that are prone to local buckling and distortional buckling. An experimental investigation of simply supported beams with different stiffened channel sections has been conducted. The moment capacities and observed failure modes at ultimate loads were reported. A nonlinear finite element model was developed and verified against the test results in terms of strengths, failure modes and moment–curvature curves. The calibrated model was then adopted for an extensive parametric study to investigate the moment capacities and buckling modes of cold-formed steel beams with various geometries of stiffened sections. The strengths and failure modes of specimens obtained from experimental and numerical results were compared with design strengths predicted using the direct strength method specified in the North American Specification for cold-formed steel structures. The comparison shows that the design strengths predicted by the current direct strength method (DSM) are conservative for both local buckling and distortional buckling in this study. Hence, the DSM is modified to cover the new stiffened channel sections investigated in this study. A reliability analysis was also performed to assess the current and modified DSM.     

Strength of arc-welded T-joints between equal width cold-formed RHS

The paper describes laboratory tests of arc-welded T-joints between equal width rectangular hollow sections (called “matched box connections” in ANSI/AWS D1.1-2000 Structural Welding Code). The brace and chord members were cold-formed with a nominal yield stress of 350 MPa. The welds were laid using MMAW and GMAW processes without profiling the brace ends. The brace of each specimen was loaded in tension to failure with the chord supported continuously so as not to induce significant bending effects. The test results showed that the joint strength can be improved by using backing strips for the butt (or groove) welds, while backing rods (or filler rods) should not be used as they led to larger variation in joint strengths, and often, inferior strengths. The test strengths are compared with the design strengths obtained using the IIW Recommendations and Eurocode 3, Part 1.8. It is shown that for cold-formed tubes with a nominal yield stress of 350 MPa (or above), a design check on the strength of the butt (or groove) weld is required in addition to the checks on the strengths of the chord and brace members specified in the current design guidelines. An equation is proposed for calculating the strength of the weld.     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.     

Hysteretic behavior of multi-cell T- Shaped concrete-filled steel tubular columns

Several multi-cell improvement methods for solving existing problems of conventional T-shaped concrete-filled steel tubular (T-CFST) columns and for determining steel׳s optimal distributions for increasing the strength and ductility of the columns are presented. An experimental study with eight multi-cell T-shaped concrete-filled steel tubular (MT-CFST) columns and one conventional T-CFST column under low frequency cyclic loading was conducted. Effects of the multi-cell layout and the concrete strength on the hysteretic behavior of the specimens were investigated. Experimental results showed that the lateral load-displacement hysteretic curves of the columns were generally saturated with a slight pinching effect. Owing to the asymmetry of the T-shaped cross section, the hysteretic behavior of the composite columns is asymmetrical in different loading directions. The improved MT-CFST columns showed better seismic behavior due to high load bearing capacity, ductility and energy dissipation capacity. Furthermore, the non-linear finite element analysis was performed to simulate the hysteretic behavior of the specimens and the numerical results agreed well with the test results. In conclusion, with an increasing axial load ratio, the ultimate lateral load in the pushing direction gradually decreases and is reached earlier, whereas the ultimate lateral load in the pulling direction increases slightly under low axial ratio and decreases under high axial load ratio.     

Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method

A nonlinear finite element (FE) model is developed to simulate two series of flexural tests, previously conducted by the authors, on industry standard cold-formed steel C- and Z-section beams. The previous tests focused on laterally braced beams with compression flange details that lead predominately to local buckling failures, in the first test series, and distortional buckling failures, in the second test series. The objectives of this paper are to (i) validate the FE model developed for simulation of the testing, (ii) perform parametric studies outside the bounds of the original tests with a particular focus on variation in yield stress and influence of moment gradient on failures, and (iii) apply the study results to examine and extend the Direct Strength Method of design. The developed FE model shows good agreement with the test data in terms of ultimate bending strength. Extension of the tested sections to cover yield stresses from 228 to 506 MPa indicates that the Direct Strength Method is applicable over this full range of yield stresses. The FE model is also applied to analyze the effect of moment gradient on distortional buckling. It is found that the distortional buckling strength of beams is increased due to the presence of moment gradient. Further, it is proposed and verified that the moment gradient effect on distortional buckling failures can be conservatively accounted for in the Direct Strength Method by using an elastic buckling moment that accounts for the moment gradient. An empirical equation, appropriate for use in design, to predict the increase in the elastic distortional buckling moment due to moment gradient, is developed.