Cold-formed Square Research Articles

Tension performance of joint made in cold-formed square tube with self-tapping screw connections

The tension behavior of cold-formed square tube (CFST) screw connections was investigated experimentally and numerically. Ten test specimens were fabricated from the square tubes connected by external steel plates and internal tube applying self-tapping screws such that the number of screws was varied. In addition, the mechanical properties of the single-screw connections were obtained through single shear tests. Experimental results revealed that an increase in the number of screws led to higher bearing capacity and stiffness in the specimens. Shear failure of the screws was observed as the primary failure mode. When the number of the screws was equal in both types of the specimens, those with the internal tube exhibited superior tensile behavior than the ones with external steel plates. Subsequently, finite element (FE) models of the test specimens were developed. Upon validation of the test results, an extensive parametric study was conducted to further examine the influence of the design parameters on the tensile behavior of the CFST screw connections. Variation of the arrangement of screws, wall thickness of steel plates and their strength had only a minor influence on the tension behavior, and steel strength had little influence on the tension behavior and the number, spacing, and diameter of the screws were the key parameters affecting the tension behavior of the CFST screw connections. Based on the test results and FE analyses, the existing calculation method was modified, and a formula for calculating the tensile bearing capacity of the CFST screw connections was obtained. Comparison with the results indicate that the formula was conservative and reliable for determining the tensile capacity of CFST screw connections.

Flexural performance of cold-formed square tube splice joints connected by self-tapping screws

Experimental studies and numerical simulations are performed to investigate flexural performance of cold-formed square tube (CFST) splice joints connected by self-tapping screws. Seven specimens were fabricated from the external steel plate and inner sleeve using self-tapping screws and underwent variations in screw quantity. Refined finite element models were developed and calibrated using a dataset of test results from cold-formed square tube splice joints. Subsequently, an extensive parametric study was undertaken to expand the CFST splice joints data pool, covering the CFST strength, thickness, screw diameter, spacing, as well as the number of rows and columns screws. Finally, a dependable design method for the flexural bearing capacity of CFST splice joints was derived from the experimental and finite element analysis results. The conclusions are as follows: (1) The flexural performance of inner sleeve specimens surpasses that of external steel plate specimens significantly. (2) Variations in steel strength and thickness minimally impacted the flexural bearing capacity of the specimens. Alterations in screw diameter, longitudinal spacing, rows and columns notably influenced the flexural performance of the specimens. (3) A comparison revealed that the proposed design method exhibited higher accuracy and safety in calculating the flexural bearing capacity of CFST splice joints.

Farklı Et Kalınlıklarına Sahip Soğuk Şekillendirilmiş Kare İçi Boş Kesitli Elemanlara Monte Edilen Kör Perçin Somunlarının (BRN'ler) Çekme Kapasitesi Üzerine Deneysel Çalışma

In this study, pull-out tests of blind rivet nuts (BRNs) mounted on cold-formed square hollow section (SHS) webs with 100×100 mm nominal cross-section dimensions and different wall thicknesses (2.0 to 5.0 mm) were performed, and the effect of different wall thicknesses and BRN thread sizes on the test results was experimentally investigated. M10 and M12 stainless steel BRNs were mounted on SHSs using a standard riveter tool, and the test elements were prepared for the experiment. Load–displacement curves and the final damage modes were obtained for each test specimen. The results show that the pull-out capacity depends on both the SHS wall thickness and rivet nut thread size. Although the pull-out capacity increased in both thread sizes with the increase in wall thickness parameters, the effect of thread size is negligible in the case of 2.5, 3.0, and 4.0 wall thickness. In addition, when a connection is created using a BRN, the design should consider the stripped thread strength in addition to the pull-out capacity.

Ultimate uniaxial compressive resistance of S600E cold-formed stainless steel square tubes

Sorbite stainless steel (S600E, SSS) is a promising alternative for conventional metals in diverse engineering applications due to its exceptional mechanical properties, superior corrosion resistance, weldability, and cost-effectiveness. Nonetheless, its understudied mechanical behavior hinders its widespread employment as a prospective structural element. To enrich the mechanical understanding of SSS, tensile coupons, uniaxial compressive stubs, and long columns with cold-formed square hollow sections (SHS) were examined, elucidating the stress-strain graphs, failure mechanisms, and uniaxial resistance. The yield stress of S600E reaches 700 and 870 MPa in the flat and corner regions. Furthermore, local buckling occurs in all stubs featuring symmetrical bulges at one end, with a mean ultimate compressive resistance of 670 MPa. Conversely, most long columns fail due to global buckling. To determine an appropriate capability estimation, the experimental and finite element model (FEM) data were compared with the theoretical outcomes of presently available methods. The continuous strength method (CSM) and most specifications provide conservative assessments of the load-carrying capacity of stubs, where CECS 410:2015 produces a relatively accurate evaluation, displaying a 1% error. Regarding long columns, the improved direct strength method (DSM) accurately predicts the uniaxial resistance with a 1% error. This study illuminates the mechanical behavior of S600E, providing critical insights that enable more efficient use of this promising material in engineering and construction applications.

Advanced numerical simulations on S690 cold-formed square hollow sections under compression

Based on a number of numerical investigations into welding simulations, highly non-linear welding-induced residual stresses within high strength S690 welded H-sections have been evaluated successfully, and surface residual stresses along their flange / web junctions have been carefully calibrated against measured data. This modelling technique has been extended to cover residual stresses of cold-formed circular hollow sections recently, and also of cold-formed square hollow sections as described in this paper. Hence, a full presentation on the proposed approach of integrated and coordinated numerical simulations on various mechanical, heat transfer and thermomechanical, and stresses analyses on these cold-formed square hollow sections is described. Subsequent structural analyses of these models on both stocky and slender columns of these cold-formed square hollow sections are then carried out. Structural adequacy of the proposed approach is thoroughly demonstrated through a systematic calibration against various measured data – both temperatures and residual stresses of these sections induced during fabrication, and load-deformation curves of these sections under compression. It should be noted that the proposed approach provides a scientific mechanism to determine directly residual stresses due to transverse bending and longitudinal welding as initial materials imperfections in these high strength S690 cold-formed square hollow sections. With an adoption of the lowest eigenmodes of these columns as their initial geometric imperfections after adjusted with measured or design values of the member out-of-straightness, both the effects of initial materials and of initial geometric imperfections onto the structural performance of these columns are readily quantified separately.

Experimental and computational study on local buckling of standard and improved cold-formed square hollow sections under static and dynamic loading

Because of aesthetics, economic advantages, easy composite member production and design, and a wide range of standard sizes, hollow sections are commonly utilized in various construction industry applications worldwide, including conventional and unique free-form structures. However, the sections must fulfill more restricted circumstances to avoid early local buckling. The behavior of cold-formed square hollow sections with different wall thicknesses under static and dynamic transverse impact loading was investigated experimentally and numerically in this study. A method that uses rivet nuts is proposed to improve the dominant local buckling behavior, which is observed in the experimental studies and causes a relatively low bending strength, for providing convenience in field applications. The effectiveness of the proposed method is demonstrated experimentally and numerically using finite-element analysis. In addition to conventional measurement techniques, motion analysis is performed using digital image correlation to measure the displacements during static and dynamic tests. With the proposed technique, the local buckling strength of the square hollow sections is increased by 64% under static loading and by approximately 40–85% under dynamic loading compared with standard square hollow sections, respectively. This is due to the internal stiffness plate, steel threaded rods, and rivet nut configuration connecting the flanges and webs of the square hollow section, which ensures load sharing between the section parts. Additionally, steel threaded rods prevent early buckling of the internal stiffness plate. In addition, parametric analysis results show that the thickness of the internal stiffness plate has a negligible effect on the local buckling strength, although the presence of an internal stiffness plate increased the strength. The numerical analysis results indicate that the local buckling behavior of both conventional and improved square hollow specimens can be predicted with acceptable errors in terms of their strength and damage modes using finite-element analysis models.

Experimental and numerical tests of cold-formed square and rectangular hollow columns

This paper summarizes the results of experimental tests and finite element simulations aimed at investigating the buckling response of cold-formed square and rectangular hollow columns. The material stress–strain curves of the tested columns have been derived from testing 83 coupons sampled from the flat and corner parts of the cross-sections, along with coupons containing the weld in both longitudinal and perpendicular directions. The experimental stress–strain parameters have been statistically processed to calibrate the parameters of Ramberg-Osgood and Giuffrè-Menegotto-Pinto material models. The cross-sectional geometry and geometric imperfections have been also measured for all tested profiles. The buckling resistance of 21 different pin-ended columns has been experimentally measured in order to examine the influence of the steel grade (both S275 and S355), the normalized slenderness and the shape of cross-section. Finite element simulations of the tested members have been carried out to investigate the influence of residual stresses and out-of-straightness imperfections on the buckling resistance of hollow profiles. The buckling resistance evaluated on the basis of current EN1993-1–1 and the measured properties of the members are in very good agreement with the tested buckling resistances, even though slightly underestimating the resistance of stocky columns. The partial safety factor for flexural buckling has been evaluated using the method given by Annex D of EN 1990 and the results show that the computed average partial safety factor of curve “c” of EN1993-1–1 for cold-formed square and rectangular hollow columns is 0.92.

Compression tests on stocky and slender columns of high strength S690 cold-formed square tubes

An experimental investigation into the structural behaviour of both stocky and slender columns of high strength S690 cold-formed square tubes (CFST) under compression is presented in this paper. A total of 8 stocky columns with two section types of four different cross-sectional dimensions were tested. Moreover, a total of 24 slender columns with two section types of six different cross-sectional dimensions were tested. Typical residual stresses of these two section types were also obtained. As expected, all of these columns of S690 CFST failed under compression similar to those stocky and slender columns of S355 CFST, namely, i) local plate buckling in stocky columns, and ii) overall axial buckling in slender columns. Hence, these tests may be regarded to be confirmatory tests to provide experimental evidence and test data on cross-section resistances of the stocky columns, and member resistances of the slender columns of these S690 CFST. In addition, the measured resistances of these columns were directly compared with those design resistances determined according to Structural Eurocode EN 1993-1-1 based on measured geometrical dimensions and mechanical properties. It is demonstrated that the measured resistances of these columns are significantly larger than those design values, and hence, these test data provide a scientific basis to enhance structural efficiency of the design rules.

Flexural behaviour of cold-formed steel square and rectangular hollow sections with moderate heat-treatment

This paper discusses the flexural behaviour of cold-formed square and rectangular hollow steel sections (SHSs and RHSs) with subsequent heat-treatment through experimental and numerical investigations. Firstly, an experimental programme comprising tensile coupon tests on flat and corner regions and three-point bending beam tests were conducted. A total of 12 specimens were tested under monotonic bending loads, covering a variety of section slenderness. Failure modes, moment-rotation curves and plastic hinge lengths have been evaluated highlighting the effect of the web-flange interaction on rotation capacity. Successively, experimental results were combined with numerical FE results to assess the corresponding moment and deformation capacities. Current cross-section classification limits given in Eurocode 3 and AISC 360–16 were assessed and new limits has been proposed.

Experimental study on elastic-plastic behavior of high-strength steel beam-to-column panel zone considering under-matching welding effect

This paper presents an experimental study on the elastic-plastic behavior of high-strength steel beam-to-column panel zones with the columns being formed by matching or under-matching welding conditions. Four column cross-sections, including built-up H-shape, built-up box-shape, cold-formed square, and cold-formed circular, are considered. The test involves eight beam-to-column joints subjected to cyclic loading with lateral displacements imposed at the beam ends. The failure modes, hysteretic curves, shear strengths, and shear strain distributions of panel zones are discussed. The test results indicated that all the specimens showed the linear elastic behaviors until the panel shear yield deformation angle and the panel zones exhibited stable hysteretic behavior even for large shear deformations. Regardless of welding conditions, the panel zones formed by built-up box-shape columns have the highest shear strength and initial stiffness among the four column types. The failure modes of specimens composed of built-up box-shape or cold-formed square columns were dependent on the welding conditions. In addition, the welding condition has negligible effect on the shear strength of panel zones formed by built-up H-shape or built-up box-shape columns; whereas, comparing to the matching welding, the under-matching welding resulted in a strength decreasing of about 8.96–12.67% for the panel zones formed by cold-formed square and cold-formed circular pipes.

Local buckling of cold-formed high-strength steel hollow section columns at elevated temperatures

A numerical investigation is conducted on the local buckling behavior of cold-formed square hollow section (SHS) and rectangular hollow section (RHS) columns made of normal and advanced high-strength steels at elevated temperatures. Shell finite element models validated against experimental results are used in a parametric numerical study to evaluate the local buckling strength at ambient and elevated temperatures of SHS and RHS columns fabricated with G450, dual-phase, and martensitic steels. The modeling uses recent experimental data on the elevated temperature behavior of advanced high-strength steels. The numerical results are compared with the design strengths calculated by the Direct Strength Method in AISI S100. Results show that the current method in AISI S100 consistently captures the trend but overestimates the ultimate capacity of G450 cold-formed columns both at ambient and elevated temperatures by about 10% for the SHS columns and 6% for the RHS columns. The current Direct Strength Method also yields higher estimates of capacity than the finite element models for advanced high-strength steel grades. Therefore, a modification to the method for local buckling capacity is proposed for these sections. The modified Direct Strength Method proposed herein can be used to evaluate the local buckling strength of cold-formed SHS and RHS columns made of normal and advanced high-strength steels at temperatures up to 700 °C.

Ultimate Behavior and Design of Cold-Formed Steel Square Hollow Section Members

Ultimate Behavior and Design of Cold-Formed Steel Square Hollow Section Members

Design of stainless steel gapped K-joints in cold-formed square hollow sections

Current research on the stainless steel structures mainly focus on material and member behaviors, rare on the design on joints. This study carried out tests and theoretical studies on stainless steel gapped K-joints in cold-formed square hollow sections (SHS). Six gapped K-joints were tested. Material properties, joint capacities and failure modes were reported in detail. Then, a yield line failure mechanism considering both the deformations of chord connecting face and chord sidewall was proposed, and the preliminary equation for joint capacity was derived. Afterwards, finite element models were developed and validated using the test data. Totally 560 finite element models were built and analyzed to calibrate the derived equation for the overall discrepancy, the effects of weld, and the yield strength of chord. Finally, test data on stainless steel gapped K-joint in SHS were collected in literature, and compared with the predictions of the design method in the CIDECT design guide and the proposed method. Results indicate that the proposed method has a better accuracy.

Analysis of Flexural Buckling Capacity of Stainless Steel Columns under Axial Compression

In order to provide a basis for the compilation of the bending buckling stability part of axially compressed columns in the technical code for stainless steel structures, the design methods and experimental research data of similar components are collected and compared. The results showed that there are some deficiencies in the current European code for the design of stainless steel structures and the American code for the design of cold‐formed stainless steel structures. According to the collected test data of square tube, rectangular tube, circular tube, elliptical tube, welded H‐shaped steel, and cold‐formed C‐shaped steel for 199 section columns and according to the influence of cold‐formed effect and residual stress on the stability of axial compression members, the members are divided into three categories: A, B, and C according to the section form, in which the columns with cold‐formed square, rectangular hollow section, and lipped C‐section were included in A, columns with circular and oval hollow section were sorted into B, columns with welded H‐section were separated into C, and the three categories of axial compression stability curves are expressed in the form of Perry formula. The comparison with the test data shows that the three kinds of curves can well estimate the stability bearing capacity of members, and the discreteness is small. The reliability of the proposed formula is analyzed, and the results show that its reliability index β meets the requirements of the GB 50068 standard.

Prediction of residual stresses in high-strength S690 cold-formed square hollow sections using integrated numerical simulations

In general, residual stresses are induced in structural members during various fabrication processes, such as welding, bending, press-braking, folding, flame cutting and punching. The presence of those residual stresses in cold-formed square hollow sections (CFSHS) primarily caused by i) transverse bending (or cold-forming), and ii) longitudinal welding, is widely considered to have modified both initial stress and strain conditions of these steel members significantly. Hence, these residual stresses are widely considered to have significant adverse effects onto the structural performance of these CFSHS under various actions.In order to examine and quantify both magnitudes and distributions of these residual stresses in S690 CFSHS, an investigation is undertaken to measure residual stresses due to transverse bending and longitudinal welding. Moreover, an approach of integrated numerical simulations is adopted in which a total of three co-ordinated finite element models are established together with various element types and block data transfers to generate compatible meshes for the following three analyses: i) two-dimensional plane-strain bending analyses with large plastic deformations and springback, ii) three-dimensional heat transfer analyses for transient temperature distributions under a heat source, and iii) three-dimensional thermomechanical analyses for welding-induced residual stresses.The predicted results of these three analyses have been carefully calibrated against various experimental data, such as surface temperatures during welding, and residual stresses and strains after welding. Good comparisons between the measured and the predicted data of these S690 CFSHS are demonstrated. The complete residual stress distributions within typical S690 CFSHS due to transverse bending and longitudinal welding are illustrated in three-dimensional plots while simplified residual stress patterns of these sections with specific values and parameters are also provided for subsequent advanced structural analyses and design.The proposed modelling technique for transverse bending and longitudinal welding with compatible meshes of two-dimensional and three-dimensional models with various element types and block data transfers is demonstrated to be highly effective. The technique is readily applicable to simulate residual stresses of all fabricated sections manufactured with transverse bending and longitudinal welding, and, thus, the simulated residual stresses can be employed in subsequent structural analyses of all fabricated members.

Experimental Study on Welded Joints of Dissimilar Strength Steels at the Corner Portion of Butt Welding between Cold-Formed Square Hollow Section Tube and Through-Diaphragm

Experimental Study on Welded Joints of Dissimilar Strength Steels at the Corner Portion of Butt Welding between Cold-Formed Square Hollow Section Tube and Through-Diaphragm

Behaviour of a Space Inverted Triangular Steel Truss

Behaviour of the inverted triangular truss, which is widely used as a bridge girder, was investigated analytically and experimentally. Cold-formed square hollow cross-sections of steel grade S355J2H with dimensions 80 mm × 4 mm, 90 mm × 4 mm and 40 mm × 4 mm were selected for the top and bottom chords and bracing elements of the truss with 12.56 m span, correspondingly. Five FEM models were developed using software Dlubal RFEM. The main specific feature of the models is the difference in modelling of joint behaviour considering plastic behaviour and stiffness of truss connections. It was shown that the FE model of the truss where the members were modelled by the truss type finite elements and the joints modelled by the shell type ones allows predicting behaviour of the truss with precision of up to 3.9%. It was shown that precision of the suggested FEM model grows 4.36 to 4.62 times in comparison with the traditional FEM models where the members were modelled by the truss finite elements with the pinned and rigid joints in case of plastic joint behaviour. Precision of the suggested FEM model is identical to that of the traditional FEM models regarding the case of elastic joint behaviour.

Flexural stiffness reduction for stainless steel SHS and RHS members prone to local buckling

In this paper, flexural stiffness reduction factor formulations, applicable to stainless steel members with compact cold-formed square and rectangular hollow section (SHS and RHS), are extended to account for local buckling effects and initial localized imperfection (ω). Local buckling effects and the influence of ω are accounted for by means of reducing the gross section resistance using a strength reduction factor ρ. ρ, determined by the Direct Analysis Method, depending on cross-section slenderness, is adopted. For in-plane stainless steel elements with non-compact and slender sections, results determined by the extended flexural stiffness reduction factor coupled with Geometrically Nonlinear Analysis (GNA) are verified against those determined by Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA). It is found that GNA with the extended flexural stiffness reduction factor (using beam element) generally achieves the accuracy of GMNIA (using shell element). Probabilistic studies based on 3D models with random ω are carried out to evaluate the effect of uncertainty in ω on the accuracy of GNA with the extended beam-column flexural stiffness reduction factor.

Geometrically non-linear analysis with stiffness reduction for the stability design of stainless steel structures: Application to members and planar frames

This paper focuses on the development of beam-column flexural stiffness reduction factor (τMN) applicable to the in-plane stability design of stainless steel beam-columns and frames with compact cold-formed square and rectangular hollow sections. The proposed τMN accounts for the deleterious influence of material non-linearity, residual stresses and member out-of-straightness. The use of a Geometrically Non-linear Analysis (GNA) with the proposed τMN eliminates the need for member buckling strength checks and thus, only cross-sectional strength checks are required. The proposed approach, aligned to AISC standards, is aimed at facilitating greater and more efficient use of stainless steel. Two types of τMN are proposed: analytical and approximate. The analytical τMN presumes knowing the maximum internal second order moment (Mr2) within a member. It is developed by means of extending the formulations for evaluating the elastic second order effects to the inelastic range. The accuracy of the analytical τMN is verified for beam-columns and sub-assemblages. Since in practical design Mr2 is not known in advance, an approximate expression of τMN, which is more likely to be used relative to the analytical τMN, is proposed by fitting variables to the analytically determined MN. The accuracy of the approximate τMN is verified for frames with different geometrical and loading configurations. Furthermore, the proposed approach is compared against the Direct Analysis Method (DM). Results show that, compared to the DM, GNA coupled with the approximate τMN provides improved estimations, since the proposed τMN can more accurately capture stiffness reduction resulted from material non-linearity and well capture additional second order effects due to material non-linearity.

Flexural performance of square concrete-filled steel tube beams stiffened with V-shaped grooves

The outward steel tube buckling failure of concrete-filled steel tube (CFST) beams is still considered to be a serious concern due to the typical bending loads. This research conducts experimental and numerical investigations on the flexural performance of slender square steel tubes filled with normal concrete. A total of 6 cold-formed square CFST specimens were tested under static bending loads. The cross-sections of 4 specimens were stiffened by single and double V-shaped grooves along the tube cross-sections, and 2 specimens were tested as control specimens (unstiffened square specimens). The results showed that adopting this stiffening concept in the slender square CFST beams led to restriction of the buckling failure of the outward steel tube (at the top flange). Due to the increase in the steel confinement factor of the stiffened square CFST beams, the bending moment capacity, flexural stiffness, and energy absorption capability were improved by 25.4%, 7.2%, and 31.4%, respectively, compared to those of the corresponding unstiffened specimens. Finite element models were also developed to further investigate the performance of the proposed CFST specimens by varying certain chosen parameters. The bending moment capacity and the flexural stiffness results obtained from the experimental and numerical investigations were validated with predicted values from different existing standards.