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 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.     

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.     

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.     

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 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.     

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.     

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 high strength steel columns at elevated temperatures

The main objective of this paper is to study the behaviour and design of high strength steel columns at elevated temperatures using finite element analysis. In this study, equations predicting the yield strength and elastic modulus of high strength steel and mild steel at elevated temperatures are proposed. In addition, stress-strain curve model for high strength steel and mild steel materials at elevated temperatures is also proposed. The numerical analysis was performed on high strength steel columns over a range of column lengths for various temperatures. The nonlinear finite element model was verified against experimental results of columns at normal room and elevated temperatures. The effects of initial local and overall geometrical imperfections have been taken into consideration in the analysis. The material properties and stress-strain curves at elevated temperatures used in the finite element model were obtained from the proposed equations based on the material tests. Two series of box and I-section columns were studied using the finite element analysis to investigate the strength and behaviour of high strength steel columns at elevated temperatures. Both fixed-ended stub columns and pin-ended slender columns were considered. The column strengths predicted from the finite element analysis were compared with the design strengths predicted using the American, European and Australian specifications for hot-rolled steel columns at elevated temperatures by substituting the reduced material properties. In addition, the direct strength method, which was developed for the design of cold-formed steel columns at normal room temperature, was also used in this study to predict the high strength steel column strengths at elevated temperatures. The suitability of these design rules for high strength steel columns at elevated temperatures is assessed. Generally, it is shown that the American and European specifications as well as the direct strength method conservatively predicted the column strengths of high strength steel at elevated temperatures. The European Code predictions are slightly more conservative than the American Specification and the direct strength method predictions.     

Column tests of cold-formed steel non-symmetric lipped angle sections

The geometry of angle sections is simple, but the behaviour and design calculations of angle sections can be quite complicated. Furthermore, lipped angle sections with unequal flange widths form a non-symmetric section and the behaviour of the section is even more complicated than a singly-symmetric angle section with equal flange widths. A test program on cold-formed steel non-symmetric lipped angle columns is presented. The non-symmetric angle sections were brake-pressed from high strength structural steel sheets having nominal yield stresses of 450 and 550 MPa with plate thicknesses of 1.0, 1.5 and 1.9 mm. The material properties of the column specimens were obtained by tensile coupon tests. The behaviour and strengths of cold-formed steel non-symmetric lipped angle columns were investigated. The test strengths are compared with the design strengths calculated using the North American Specification for the design of cold-formed steel structural members. In addition, the current design rules in the North American Specification for cold-formed steel non-symmetric lipped angle columns are assessed using reliability analysis. It is shown that the design strengths are generally quite conservative.     

Design for openings in cold-formed steel channel stub columns

This paper is concerned with the ultimate load capacity of perforated cold-formed steel channel stub columns. A design equation has been developed to determine the ultimate load capacity of perforated channel short columns containing either single or multiple openings of square, circular and manufacturer's opening shape. The equation is based on extensive parametric studies carried out using finite element modelling on plain and lipped channel sections containing openings. A wide range of parameters such as plate slenderness, opening shapes and sizes have been considered in the study. Web plate slenderness and opening area ratio are the two main variables used to derive the design equations. The accuracy of the proposed design equation is established by comparison with a number of experimental and finite element results reported by other researchers.     

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.     

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.     

Nonlinear analysis of concrete-filled steel SHS and RHS columns

This paper presents an accurate nonlinear finite element model for the behaviour and design of axially loaded concrete-filled square hollow section (SHS) and rectangular hollow section (RHS) steel tube columns. The nonlinear material models for confined concrete and steel tubes were carefully modeled in the finite element analysis. The column strengths and load-axial shortening curves were evaluated. The results obtained from the finite element analysis were verified against experimental results. An extensive parametric study was conducted to investigate the effects of different concrete strengths and cross-section geometries on the strength and behaviour of concrete-filled SHS and RHS steel tube columns. The study was conducted over a wide range of concrete cube strengths ranged from 30 to 110 MPa. The overall depth of the steel tube-to-plate thickness ratio ranged from 10 to 40 covering compact SHS and RHS steel tube sections. The column strengths predicted from the finite element analysis were compared with the design strengths calculated using the American, Australian and European specifications. Based on the results obtained from the parametric study, it is found that the design strengths calculated using the American Specifications and Australian Standards are conservative, while the design strengths calculated using the European Code are accurate, except for the concrete-filled RHS compact steel tube columns having the overall depth of the steel tube-to-plate thickness ratio of 40.     

Behaviour of cold-formed singly symmetric columns

An experimental investigation into the behaviour of cold-formed plain and lipped channel columns compressed between fixed and pinned ends is presented in this paper. It is shown experimentally that local buckling does not induce overall bending of fixed-ended singly symmetric columns, as it does of pin-ended singly symmetric columns. Consequently, local buckling has a fundamentally different effect on the behaviour of pin-ended and fixed-ended singly symmetric columns. In order to show this fundamental different effect caused by local buckling, a series of tests was performed on plain and lipped channels brake-pressed from high strength structural steel sheets. Four different cross-section geometries were tested over a range of lengths which involved pure local buckling, distortional buckling as well as overall flexural buckling and flexural-torsional buckling. The different effects of local buckling on the behaviour of fixed-ended and pin-ended channels are investigated by comparing strengths, load–shortening and load–deflection curves, as well as longitudinal profiles of buckling deformations. The purpose of the paper is to demonstrate experimentally the different effects of local buckling on the behaviour and strengths of fixed-ended and pin-ended channels.     

Nonlinear behavior of concrete-filled stainless steel stiffened slender tube columns

This paper investigates the nonlinear behavior of concrete-filled high strength stainless steel stiffened slender square and rectangular hollow section columns. The stiffened slender tubes had overall depth-to-plate thickness (D/t) ratios ranging 60–160. The concrete strengths covered normal and high-strength concrete. The investigation focused on short axially loaded columns. A nonlinear finite element (FE) model has been developed to study the behavior of the concrete-filled stiffened tube columns. A parametric study was conducted to investigate the effects of cross-section geometry and concrete strength on the behavior and strength of the columns. The results of the concrete-filled stiffened tube columns were compared with the results of the companion concrete-filled unstiffened tube columns. It is shown that the concrete-filled stiffened slender tube columns offer a considerable increase in the column strength and ductility than the concrete-filled unstiffened slender tube columns. The column strengths obtained from the FE analysis were compared with the design strengths calculated using the American specifications and Australian/New Zealand standards. A design equation was proposed for concrete-filled stainless steel stiffened slender tube columns. It is shown that the proposed modified equation provides more accurate design strengths compared to the American and Australian/New Zealand predictions.     

Recent developments in the design of cold-formed steel members and structures

Cold-formed steel members and structures are extremely widespread in use at the present time. The design analysis of such structures is often complex, as their behaviour can be influenced by effects, which arise due to the slenderness of members, walls and cross-sections. Prime among these effects are the various types of buckling which can occur, and which may interact with each other to promote failure at loads substantially less than those, which would be obtained in the absence of these effects. The complications induced by such effects must be taken into account in design, if the potential benefits offered by the use of such members are to be realised, and in recent design specifications this has been realised. In this paper the main types of cold-formed steel members are described, the particular characteristics affecting their design are discussed, as are the ways in which design specifications deal with these characteristics.     

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。     

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.     

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

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