Cold-formed Rectangular Hollow Sections Research Articles

Localized loading behavior of cold-formed stainless steel RHS under interior-one-flange load case at elevated temperatures

The localized loading behavior of cold-formed stainless steel (CFSS) rectangular hollow section (RHS) members at elevated temperatures is investigated in this paper. Fifteen localized loading tests conducted at various temperatures up to 800 °C were reported. The tests were carried out under the Interior-One-Flange (IOF) load case as specified in American Specification for the design of cold-formed stainless steel structural members. Tensile coupon tests were performed to obtain the material properties of the CFSS RHS at various temperatures. Detailed information on dimensions, temperature histories, failure modes, load-deformation curves, localized loading capacities of specimens at various temperatures were presented. In addition, a numerical investigation was supplemented, where a total of 192 finite element (FE) analyses were undertaken after validation of developed FE model against the elevated-temperature test results. The influence of various parameters on the localized loading capacities of CFSS RHS at different temperatures under IOF load case was revealed. The obtained results were utilized to assess the applicability of the localized loading design provision for CFSS RHS under IOF load case codified in the American Specification to elevated temperature conditions. Moreover, the results were also compared with predictions based on existing design rules in literatures for cold-formed RHS at elevated temperatures. Furthermore, reliability analyses were carried out to assess the reliability levels of the assessed design methods. It is shown that the existing design rules can generally provide conservative and reliable predictions of the localized loading capacities for the CFSS RHS under IOF load case at elevated temperatures.

Eurocode-compliant system safety factor for advanced design of hollow section Warren trusses

Eurocode allows for the design of structural systems by advanced analysis, i.e. by Geometrically and Materially Nonlinear Imperfection Analysis (GMNIA). In GMNIA, the entire structural system is designed by carrying out a nonlinear finite element analysis and by comparing the load proportionality factor obtained from the analysis to the predetermined system safety factor. This study determines the required Eurocode-compliant GMNIA system safety factor for the ultimate limit state design of Warren-type roof trusses. The system safety factor is determined based on system-level reliability studies conducted for 15 trusses. The investigated trusses are made of cold-formed rectangular hollow sections having a nominal yield strength of 700 MPa. The determined system safety factor is then applied for comparison calculations, in which three trusses are designed both by GMNIA and the conventional EN 1993-1-1 method. This comparison reveals a need for an accurate modelling method of hollow section connections in GMNIA. Furthermore, the comparison shows that GMNIA can offer reduced material consumption compared to the conventional method even in roof trusses, in which load redistribution capabilities are very limited. This reduction is achieved due to capability of GMNIA to accurately capture the buckling capacities of continuous top chords, whereas the conventional method must rely on conservative approximations of buckling lengths.

Equivalent material properties of the heat-affected zone in welded cold-formed rectangular hollow section connections

A welded connection consists of three main material zones, the base material (BM), the heat-affect zone (HAZ), and the weld metal (WM). The strength of HAZ depends on the BM grade and manufacturing process, electrode grade, and welding parameters. Under certain conditions, HAZ has the lowest material strength, especially for high-strength steel. Therefore, a semi-empirical methodology is proposed to establish a constitutive model of HAZ necessary for predicting the fracture position of welded connections. This methodology is based on an engineering approach to consider HAZ as an isotropic and homogeneous material, with no consideration of different volumetric fractions of microstructures within a HAZ. The equivalent material properties of HAZ in butt-welded hollow section connections were investigated experimentally and numerically. Hardness tests and microstructure investigations were conducted to determine the boundaries of material variations and the width of HAZ. The stress–strain relationship of HAZ was established and calibrated based on tensile coupon tests and finite element analyses. Using the calibrated HAZ stress–strain relationship, the effect of transverse constraint imposed by the adjacent and stronger material (BM and WM) on HAZ was evaluated in the welded connections. Finally, the new methodology of a semi-empirical constitutive model based on the Swift model was used to propose equivalent characteristics of HAZ as a function of the mechanical properties of BM for a specific welding procedure considered in the project.

Fracture simulation of welded RHS X-joints using GTN damage model

A welded rectangular hollow section (RHS) X-joint exposed to tension loading has three typical fracture-related failure modes: Punching shear failure (PSF), Brace failure (BF), and Chord side wall failure (CSWF). Prediction of these failure modes by finite element (FE) simulations requires modelling of the material damage. An appropriate damage model accurately predicts the behaviour of the fracture zone and provides the necessary information to improve design rules for welded high-strength steel (HSS) RHS X-joints based on parametric studies using validated model. In this paper, the parameters of the Gurson-Tvergaard-Needleman (GTN) damage model are calibrated for the base material (BM) and the heat-affected zone (HAZ) of butt-welded cold-formed RHS connections, no fracture appeared in the weld. A computational homogenisation analysis is carried out using representative volume element (RVE) models to calibrate the pressure-dependent yield surface parameters of the GTN damage model, considering the different combinations of the accumulated initial hardening strain and the void volume fraction (VVF) due to a varying stress triaxiality. The critical and final VVFs are calibrated against tensile coupon tests. Finally, the GTN damage models calibrated for BM and HAZ are used in the fracture simulation of nine welded cold-formed RHS X-joints in monotonic tension. The FE model successfully predicts the experimental load-displacement relationships and fractured zone, indicating the calibrated GTN models could effectively be used in parametric study of welded cold-formed RHS X-joints. Finally, possible improvements to the used FE model are outlined for future studies.

Effective material model for cold-formed rectangular hollow sections in beam element-based advanced analysis

This study develops and validates an effective material model for cold-formed rectangular hollow sections. Advanced design methods utilize non-linear finite element analysis in design. An accurate calculation model, which is usually beam element-based, is crucial such that the design outcome is safe but economical. Unfortunately, cold-formed sections have non-linear residual stress distribution over the material thickness, that cannot be explicitly modelled in general-purpose beam elements. Additionally, corner regions of cold-formed sections have higher material strength compared to flat regions. This beneficial feature is usually disregarded by assuming the flat region properties for the entire cross-section. This study develops an effective material model that replicates a stress-strain curve that would be obtained if the tensile test was made for the entire cross-section instead of a separate tensile coupon. Consequently, the effects of residual stresses and corner strength enhancements are included in the effective material model such that their consideration in beam element-based advanced design method is effortless. The effective material model is validated for the steel grade S700 against numerical shell element buckling tests and excellent modelling accuracy is achieved.

Probabilistic modelling of residual stresses in cold-formed rectangular hollow sections

This study revisits residual stress models of cold-formed rectangular hollow sections (CFRHS). Residual stresses of CFRHS have a complex distribution that varies along the cross-sectional perimeter and through the material thickness. The distribution depends on the manufacturing methods and steel grades, which constantly evolve. Existing residual stress models are based on old measurements and for normal strength steel specimens (nominal yield strength fy,nom ≤ 460 MPa). This study evaluates the suitability of these models for modern CFRHS made of normal- and high-strength (fy,nom > 460 MPa) steels. Evaluation is carried out as an extensive analysis for a data set, which is collected from the literature, and supplemented with new measurements made for grade S700 specimens. As a result of the evaluation, an updated residual stress model is proposed, which combines the best suitable features of the existing models with slight modifications. The proposed model is valid for CFRHS made of steel grades up to S960. The model can be used in the advanced analyses of CFRHS structures. Additionally, statistical information is provided for the residual stress components such that the model can be used in probabilistic modelling and reliability studies.

Fire resistance of stainless steel slender elliptical hollow section beam-columns

PurposeStainless steel has different advantages when compared to conventional carbon steel. The corrosion resistance and aesthetic appearance are the most known; however, its better behaviour under elevated temperatures can also be important in buildings design. In spite of the initial cost, stainless-steel application as a structural material has been increasing. Elliptical hollow sections integrate the architectural attributes of the circular hollow sections and the structural advantages of the rectangular hollow sections (RHSs). Hence, the application of stainless-steel material combined with elliptical hollow profiles stands as an interesting design option. The purpose of the paper is to better understand the resistance of stainless-steel-beam columns in case of fireDesign/methodology/approachThe research presents a numerical study on the behaviour of stainless-steel members with slender elliptical hollow section (EHS) subjected to axial compression and bending about the strong axis at elevated temperatures. A parametric numerical study is presented here considering with and without out-of-plane buckling different stainless-steel grades, cross-section and member slenderness, bending moment diagrams and elevated temperatures.FindingsThe tested design methodologies proved to be inadequate for the EHS members being in some situations too conservative.Originality/valueThe safety and accuracy of Eurocode 3 (EC3) design methodology and of a recent design proposal developed for I-sections and cold-formed RHSs are analysed applying material and geometric non-linear analysis considering imperfections with the finite element software SAFIR.

Stub column behaviour of heat-treated and galvanized RHS manufactured by different methods

A complementary study showed that hot-dip galvanizing can sometimes significantly change the residual stress properties of cold-formed rectangular hollow sections (RHS). Hot dipping the RHS specimens in a molten zinc bath maintained at 450 °C for 10 min provided a partial residual stress relief comparable to the onerous heat treatment specified in ASTM A1085 and CSA G40.20/G40.21. Hence, further research is needed to: (1) quantify the effects of galvanizing, and (2) determine the optimized heat treatment duration for a partial residual stress relief for improvement of column behaviour. In this study, the effects of galvanizing and heat treatments to different degrees on the stub column behaviour of cold-formed RHS has been investigated comprehensively for the first time, by means of 36 stub column tests. The RHS specimens were manufactured by two dominant cold-forming methods: (1) indirect-forming from circular to rectangular, and (2) direct-forming. The nominal yield stresses of the materials ranged from 350 to 690 MPa. The RHS stub column test matrix has 10 different width-to-thickness ratios and includes both nonslender and slender sections.

Effect of Uncertainty in Localized Imperfection on the Ultimate Compressive Strength of Cold-Formed Stainless Steel Hollow Sections

Stainless steel has excellent corrosion resistance properties, considerable long-term durability, and good mechanical strength. Hollow sections are a versatile and efficient form for construction applications. The use of cold-formed stainless steel rectangular hollow section (RHS) and square hollow section (SHS) in construction industry grasps the attention of designers conceiving long-term, cost-effective structures. For cold-formed RHS and SHS, localized imperfection (ω) resulting from rolling and fabrication process is inevitable. ω has inherent variability and has no definitive characterization. In this paper, statistical analysis of the maximum value of ω collected from available experimental data is conducted. A new approach utilizing Fourier series to generate the three-dimensional (3D) models of members with random ω is proposed. Probabilistic studies based on the proposed 3D models are then carried out to evaluate the effect of uncertainty in ω on the ultimate compressive strength of stainless steel columns with cold-formed RHS and SHS. A total of 21 columns that are prone to local buckling reduction are studied. The results show that uncertainty in ω has a considerable influence on the columns with relatively higher cross-sectional slenderness.

Finite element analysis and design for section moment capacities of hollow flange steel plate girders

This paper describes a numerical study on the section moment capacity of a doubly symmetric hollow flange steel plate girder (HFSPG) for use in long span applications. The HFSPG is manufactured by welding industrially available cold-formed rectangular hollow sections to a steel web plate. Suitable finite element models were developed first to simulate the section moment capacity tests conducted on the proposed HFSPGs using a four-point bending test arrangement. The experimental conditions in terms of boundary conditions, lateral restraints, mechanical properties, initial geometric imperfections and residual stresses were modelled carefully. The comparison of ultimate moment capacities, moment versus deflection plots and failure modes proved the validity of the developed finite element models to investigate the section moment capacities of HFSPGs. However, the slenderness of the tested HFSPGs was limited to the inelastic region. Hence the validated finite element models were used in a detailed parametric study to extend the results to a wider slenderness range. The parametric study results of the section moment capacities were compared with the predictions of the relevant Australian, American and European hot-rolled and cold-formed steel design standards and suitable recommendations were made in relation to their accuracy in predicting the capacities of compact, non-compact and slender HFSPGs. Finally this paper proposes a new Direct Strength Method based design for HFSPGs.

Effects of heat-treatment and hot-dip galvanizing on mechanical properties of RHS

Hot-dip galvanizing is widely used for corrosion protection of steel structures. However, there has been a plethora of recent reports on premature cracking in galvanized steel structures, which have resulted in some early decommissions or even hazardous collapses. This research focuses on cold-formed Rectangular Hollow Sections (RHS). A total of 108 tensile coupons were tested to investigate the effects of galvanizing as well as different pre-galvanizing treatments on the material properties around the cross sections of the specimens. For the first time, this paper reports a comprehensive measurement of residual stresses in different directions at the member ends which are directly relevant to the cracking issue. The results were also compared to the residual stresses far away from the member ends, which are relevant to structural stability research. In all, the research provides a better understanding of the characteristics and structural performance of galvanized RHS to facilitate its application. The recommendations can help engineers, fabricators and galvanizers mitigate the risk of cracking in RHS during galvanizing.

Section moment capacity tests of hollow flange steel plate girders

Hollow flange steel plate girder (HFSPG) is a new hollow flange I-section made using cold-formed rectangular hollow sections (RHS) as flanges and a steel plate as web. Due to the increased torsional rigidity and unique geometry, it can provide enhanced flexural capacities and thus are effective flexural members in long span applications. The production of proposed HFSPGs contains welding currently available RHS sections to a web plate, which allows engineers to form girders by varying dimensions, thicknesses and grades to suit their design requirements. As the first step of this study, the section moment capacities of fully laterally restrained HFSPGs were investigated. Despite earlier researches on the flexural capacities of hollow flange sections, HFSPGs have not been tested previously. Therefore, twelve section moment capacity tests were conducted to study the flexural performance and capacities of HFSPGs. The ratios of ultimate moment capacity per unit area of tested beams were compared with conventionally used hot-rolled I-sections with similar cross-sectional area, which proved the structural efficiency of HFSPGs over commonly used hot-rolled I-sections. The ultimate capacities of tested HFSPGs were then compared with capacity predictions provided by the Australian, American and European design standards (both hot-rolled and cold-formed). It was found that the current design standards under-estimate the section moment capacities of HFSPGs in general and the level of under-estimation varied depending on the section slenderness. Suitable recommendations are made regarding the appropriate use of these design standards for HFSPGs. This paper presents the details of this research and its findings.

Flexural Behavior of Concrete-Filled Double-Skin Tubes Subject to Blast Loading

AbstractLarge-scale tests on concrete-filled double-skin tubes, composed of pairs of concentric cold-formed rectangular hollow section members with the annulus between them filled with grout, are p...

Influence of elevated strain rate on the mechanical properties of hollow structural sections

As protective design engineering becomes more prevalent, cold-formed steel hollow structural sections are often desired design components. As such, it is necessary to understand the behavior of hollow structural sections subject to air-blast loading, including the material response under elevated strain rates. Dynamic tensile tests have hence been performed on subsize tensile coupons taken from the flats and corners of cold-formed rectangular hollow section members. Dynamic yield stresses were obtained at strain rates from 0.1 to 18 s−1, which encompasses and exceeds the range recorded during far-field blast arena testing. The dynamic increase factor was calculated for each data point and synthesized with previous cold-formed rectangular hollow section tests at even higher strain rates (100–1000 s−1). The data set was used to determine Cowper–Symonds and Johnson–Cook parameters. The resulting material models can now be used to determine the strength increase of cold-formed rectangular hollow sections subject to a wide range of impulsive, elevated strain rate loads.

Computation of Micro-Strains in Cold Formed Steels- FEA Approach

This paper describes the computations of micro-strains at inner corner of cold formed rectangular hollow sections (CFRHS) made up of structural steels using finite element analysis. In order to obtain the micro-strains, distortion test is simulated by modeling two-dimensional structural steel tubes in ANSYS software. Two dimensional linear static analyses are performed by defining elastic properties of steel. These simulations were performed for tubes with outer radius to thickness (<i>r_o/t</i>) ratios of 3. In real distortion tests, the direction of force at outer corner of the tube may vary in terms of angle. Therefore, this fact is taken into account while performing simulations. One more aspect is taken into consideration which is related to strain gauge placement during distortion testing. This problem is analyzed by modeling three-dimensional structural tubes and performing linear static analyses to investigate the variations in strains at inner bent section of the tube with different strain gauge locations.

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

This paper presents a comparative experimental study on the physical, chemical and mechanical properties of indirectly formed hot-formed, hot-finished and cold-formed structural steel rectangular hollow sections. Characteristic geometrical parameters and chemical compositions are examined to investigate the physical and chemical differences. Tensile test and charpy V-notch impact test are employed to evaluate the difference in strength, ductility and toughness. Further, the residual stress distributions in both transverse and longitudinal directions are measured using the sectioning method and hole-drilling technique. It is found out that although the geometrical parameters and chemical composition of the tested hollow sections are similar, the mechanical properties are significantly different, especially for strength, ductility and residual stress distribution. While the hot-finished and hot-formed sections are often treated equally in design, their mechanical properties and residual stresses distribution are actually different.

Buckling Analysis of Thin-Walled Steel Structural Systems Using Generalized Beam Theory (GBT)

This paper deals with the application of beam finite element models based on generalized beam theory (GBT) to analyze the buckling behavior of four thin-walled steel structural systems, namely (i) beams belonging to storage rack systems, (ii) pitched-roof industrial frames, (iii) portal frames built from cold-formed rectangular hollow section (RHS) profiles and (iv) roof-supporting trusses, exhibiting different support conditions and subjected to various loadings. In particular, taking advantage of the GBT unique and structurally clarifying modal features, it is possible to assess how different geometries and/or bracing arrangements affect (improve) the local, distortional and/or global buckling behavior of the above structural systems. The accuracy of the GBT-based buckling results is assessed through the comparison with values yielded by rigorous shell finite element analyzes carried out in the code ANSYS. In spite of the disparity between the numbers of degrees of freedom involved, which are orders of magnitude apart, there is a virtual coincidence between the critical loads and mode shapes provided by the GBT (beam) and ANSYS (shell) finite element analyzes.

Low‐temperature ductility and structural behaviour of cold‐formed hollow section structures – progress during the past two decades

AbstractCold‐formed hollow sections are a widely used tubular construction material. The applicability, weldability and reliability of cold‐formed rectangular hollow sections are sometimes questioned because of the consequences of cold forming and inhomogeneous cross‐sections. One of the main concerns is related to the cold‐formed corner areas and possible loss of toughness due to strain ageing in the vicinity of the welds. Conventional hot‐rolled C‐Mn steels are susceptible to strain ageing, and Eurocode 3 includes restrictions on welding in the cold‐formed corner area. Both steelmaking and hot rolling have undergone crucial developments and this has had an impact on cold‐formed hollow sections. Thermomechanically rolled fine‐grain steels became state of the art at the end of the 1990s. This study confirms that cold‐formed EN 10219 hollow sections made of suitable fine‐grain steels have a similar Charpy‐V toughness on the flat face and in the corner, and that even after ageing the transition temperature T40J in the corner area is at a very low level, typically below –50 °C. The load and deformation capacities of X‐ and K‐joints fulfil the requirements without any noticeable ageing effects. The advances in steelmaking and hot rolling enable the manufacturing of reliable and versatile cold‐formed EN 10219 hollow sections for welded structures with good low‐temperature ductility even in the cold‐formed corner area.

Charpy V-notch impact toughness of cold-formed rectangular hollow sections

The notch toughness of cold-formed rectangular hollow sections (RHS), at low temperatures or in dynamic loading applications, has been a concern in North America for some time. For the assessment of notch toughness of RHS, steel product standards normally require testing of Charpy V-notch (CVN) coupons taken longitudinally from one of the flat faces not containing the weld. This tends to lead to the most optimistic notch toughness result for the cross-section. Thus, serious consideration must be given to the notch toughness of the corner and weld seam regions when low temperature or dynamic loading is a design criterion. In this study, a total of 378 CVN coupons were tested and complete CVN toughness-temperature curves were generated for the flat face, corner and weld seam regions of six North American RHS, to study the effects of cold-forming, heat treatment, cross-sectional geometry and welding on the CVN toughness around the cross-section of RHS. In particular, the CVN toughness properties of RHS cold-formed by different methods (direct-forming versus continuous-forming) were directly compared for the first time.

High strain rate behaviour of cold-formed rectangular hollow sections

For blast- or impact-resistant design of steel structures, it is important to use realistic properties of steel under high strain rate. In particular, the substantial rise in yield stress under high strain rate may have important effects on the dynamic behaviour of a steel structure. The high strain rate properties of some steels have been studied in the past; mostly reinforcing bars, plates and hot-rolled sections. The goal of this research is to remedy the lack of knowledge on the high strain rate behaviour of cold-formed steel hollow sections. In this study, four cold-formed Rectangular Hollow Sections (RHS) manufactured by two different cold-forming methods (direct-forming and continuous-forming) have been examined. The dynamic properties of the RHS specimens were determined by performing a total of 166 compressive and tensile Split-Hopkinson Pressure Bar (SHPB) tests at strain rates ranging from 100 to 1000s−1 and their dynamic yield stresses were compared to their static yield stresses, to characterise the strength enhancement of cold-formed RHS under such loading rates.