Cold-formed Circular Hollow Sections Research Articles

Comparative experimental analysis of local buckling in mild and high-strength steel (HSS) CHS subjected to various galvanization techniques

This article reports on an extensive experimental study on galvanized and ungalvanized cold-formed circular hollow sections (CFCHS). All samples were produced by cold-forming thermomechanically rolled steels (TM-steels) in S355, S550, S600, S700, and S960 with high-frequency induction welding (HFI). The test specimens were examined without galvanization, with a pre-galvanization and a post-galvanization. Hardness measurements and microstructural analysis were conducted on seven samples, while the mechanical behavior was examined through 82 tensile and 78 stub-column tests with corresponding imperfection measurements. Despite being classified as prone to local elastic buckling according to international standards, the S960 samples in this study did not exhibit such failure. This suggests that the classification by the codes was conservative. The effects of pre-galvanization on CHS have not been investigated so far, and current findings from literature regarding the impact of post-galvanization on load-bearing behavior suggest a severe capacity decrease for CFCHS in high steel grades. Contrary to previous findings, the current study reveals capacity-enhancing effects resulting from galvanization. Both galvanization types enhanced the stiffness and the cross-section capacity under compression. Galvanization induces changes in material properties, including yield and tensile strength, ductility, and the characteristics of the stress-strain curve. This study serves as a validation base for less conservative yet reliable approaches for the cross-section design of high-strength steel CHS and the utilization of beneficial effects due to galvanization.

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.

Prediction of the cross-sectional capacity of cold-formed CHS using numerical modelling and machine learning

The use of circular hollow sections (CHS) have seen a large increase in usage in recent years mainly because of the distinctive mechanical properties and unique aesthetic appearance. The focus of this paper is the behaviour of cold-rolled CHS beam-columns made from normal and high strength steel, aiming to propose a design formula for predicting the ultimate cross-sectional load carrying capacity, employing machine learning. A finite element model is developed and validated to conduct an extensive parametric study with a total of 3410 numerical models covering a wide range of the most influential parameters. The ANN model is then trained and validated using the data obtained from the developed numerical models as well as 13 test results compiled from various research available in the literature, and accordingly a new design formula is proposed. A comprehensive comparison with the design rules given in EC3 is presented to assess the performance of the ANN model. According to the results and analysis presented in this study, the proposed ANN-based design formula is shown to be an efficient and powerful design tool to predict the cross-sectional resistance of the CHS beam-columns with a high level of accuracy and the least computational costs.

Post‐fire Residual Strength and Ductility of Structural Steels from Hollow Sections

AbstractSteel structures are severely affected by the extreme temperatures reached during a fire. After this, if the structure has not collapsed, the remaining elements can be reused if they are not excessively distorted or the material is still fit for service. In the last case, residual properties of steel must be adequate and fulfil the requirements of the current standards. On this matter, it is hypothesized that residual behaviour of steel not only depends on the highest temperature reached during the fire episode, but also on the load it was simultaneously bearing.This work is focused on an experimental study on the post‐fire behaviour of structural steels. Specimens were cut from structural steel (S355) cold‐formed circular hollow sections (CHS) and subjected to a combination of tensile stress and high temperature. Afterwards, the specimens were cooled in air back to room temperature and, finally, load was increased until specimen failure. The obtained results allowed discussing on the residual yield strength, ultimate strength and stiffness of the steel, and a special focus was put on the residual ductility. The results of this work can provide a basis to the appraisal of steel structures after fire, supporting the further decision on its reinstatement or subsequent demolition.

Evaluation of Axial Compression Slenderness Limits of High and Ultra-High-Strength Steel Circular Hollow Sections

Despite significant advances in metallurgy and the potential to create high and ultra-high-strength steel, all international specifications for steel design provide little information about the limits of slenderness for high-strength steel sections (HSSs) and don’t provide anything about the design of ultra-high-strength steel sections (UHSSs). The current international steel codes such as AISC 360-16 and EC3 can be applied only to steel grades up to S690 and S460, respectively, according to their limitations. These approaches for normal-strength steel are used for HSSs and UHSSs without extensive studies to determine their accuracy in these cases. Therefore, it is one of the main objectives of this study. The behavior of high and ultra-high-strength steel circular hollow sections under axial compression load is studied in this research. Sixteen nonlinear finite element (FE) models were generated to replicate stub column tests that were experimentally tested by others in previous research. Hence, a parametric study was conducted using forty FE models developed to investigate the local buckling behavior under various slenderness ratios comprehensively. The developed models covered slenderness ratios ranging from 20 to 1226 and steel grades S460 and S1100 with yield stress equal to 460 MPa and 1152 MPa, respectively. The FE results were combined with 105 previously collected experimental results to assess the applicability of existing codified design methodologies in the Euro code and the North American codes of cold-formed circular hollow sections (CHSs). Based on the results of this study, new cross-section slenderness limits and new design equations for more efficient simple designs were presented for circular hollow sections of HSSs and UHSSs and compared with the results of experimental tests and FE models.

Experimental investigation into high strength S690 cold-formed circular hollow sections under compression

This paper presents an experimental investigation into the structural behaviour of both stocky and slender columns of high strength S690 cold-formed circular hollow sections (CFCHS) under compression. CFCHS are readily fabricated with cold-bending and welding on S690 steel plates, and these CFCHS are considered to behave similarly to those of hot-finished circular hollow sections. A total of 16 columns of S690 CFCHS were tested under compression, and these included eight stocky columns and eight slender columns with four different cross-section dimensions were tested. Tensile tests on typical curved coupons were also conducted to determine mechanical properties of these CFCHS while the sectioning method was employed to measure their residual stresses. All the stocky columns were found to have failed in material yielding in the sections while all the slender columns were found to have failed in overall buckling together with apparent plastic local buckling in the sections.The measured resistances of these columns of S690 CFCHS are then compared with those predicted resistances according to the current design rules given in EN1993–1. It is demonstrated that these design rules are effective to predict cross-section resistances of those stocky columns, and rather conservative to predict member resistances of those slender columns. The test results presented in the experimental investigation provide scientific data on their resistances for subsequent numerical investigations and design development for effective design rules.

Structural testing and numerical modelling of T-joints between cold-formed S690 circular hollow sections under brace in-plane bending

This paper presents a comprehensive investigation into the structural behaviour of T-joints between high strength S690 cold-formed circular hollow sections (CFCHS) under brace in-plane bending, and deformation characteristics of these T-joints under both monotonic and cyclic actions are examined experimentally and simulated numerically. These T-joints between S690 CFCHS were found to deform with a high level of resistances and ductility under both monotonic and cyclic actions.Through an integrated numerical modelling approach developed by the authors, advanced three-dimensional finite element models of CFCHS with solid elements were established. With a proper definition of weld collars at the brace/chord junctions of the T-joints between S690 CFCHS with different diameters and thicknesses, these models were readily adopted to perform a heat transfer analysis, a thermomechanical analysis and a structural analysis sequentially with compatible element types and meshes. Hence, the effects of the welding-induced residual stresses at the welded brace/chord junctions onto the structural behaviour of these T-joints were readily assessed. Consequently, these advanced models are demonstrated to be able to predict rationally deformation characteristics of these T-joints between S690 CFCHS under monotonic and cyclic actions of brace in-plane bending with a high degree of structural accuracy.

Flexural buckling of normal and high strength steel CHS columns

This paper presents an experimental and numerical investigation into the stability of normal and high strength steel circular hollow section (CHS) columns. Two cold-formed S700 CHS profiles – 139.7×4 and 139.7×5 (in mm), were studied in the experimental programme, and twelve column tests (six on each profile), together with accompanying material tests, were performed. The load-deformation histories and key results from the tests are reported. Following the physical testing, a numerical simulation campaign was conducted. The developed finite element (FE) models for CHS columns were initially validated against the test results. Parametric studies were then carried out, where 2000 additional buckling resistance data were numerically generated for hot-finished and cold-formed CHS columns, covering steel grades from S355 to S900. The obtained test and FE results, together with existing experimental data from the literature, were used to assess the current Eurocode 3 stability design rules. It was shown that the normalised performance of CHS columns is influenced by the yield strength, which is not fully captured by the EC3 design approach. The somewhat conservative Class 3 slenderness limit for compression further worsen the accuracy for those with slender cross-sections. Improvements to the EC3 design rules were proposed to address these shortcomings, including (a) modified Ayrton-Perry formulae enabling a continuous transition of buckling curves across the yield strength spectrum and (b) a new Class 3 limit for CHS in compression. The modified EC3 approach was assessed and shown to improve the accuracy and consistency of resistance predictions over the current EC3 approach, while meeting the Eurocode structural reliability requirements.

Experimental investigation of CHS T/Y‐joints fabricated from high‐strength steel

AbstractIn this study, an experimental program on welded hollow section joints fabricated from high‐strength steel is presented. The experimental program tested a total of six T or Y cold‐formed circular hollow section (CHS) joints under brace axial compression. One mild steel with a nominal yield stress of 355 MPa and two high‐strength steels with nominal yield stresses of 460 and 650 MPa were included. The test results and existing test database were used to evaluate the relevant design provisions for high‐strength steel joints. The material factor – used in the current standards to reduce the design resistance of high‐strength steel tubular joints – was found to be adequate for CHS T/Y‐joints with steel grades up to 700 MPa. The chord stress effect resulting from a particular test setup needs to be considered when evaluating the experimental joint strength. The experimental load‐indentation relationships were analysed to appraise the behaviour of high‐strength steel CHS T/Y‐joints from the perspectives of ductility and serviceability. The ductility of high‐strength steel T/Y‐joints is slightly lower than that of mild steel joints. T/Y‐joints show relatively lower ductility and serviceability performance compared to CHS X‐joint counterparts that comprise identical members. Local strain distributions in tested T/Y‐joints of different steel grades were analysed to identify the location and intensity of strain concentration. The possibility of fracture failure near the weld seam of the cold‐formed chord member is discussed.

Structural behaviour of T-joints between high strength S690 steel cold-formed circular hollow sections

This paper reports an experimental investigation into structural behaviour of T-joints between S690 cold-formed circular hollow sections (CFCHS). A total of twelve T-joints of both S355 and S690 CFCHS under i) brace axial compression, and ii) brace in-plane moments are tested to failure in order to examine their deformation characteristics, in particular, their joint resistances and failure modes. These tests are conducted with extensive instrumentation on both overall deformations of the T-joints and local deformations of their welded brace/chord junctions. Welding of all these T-joints between S690 CFCHS is carefully performed so that the heat input energy during welding varies narrowly between 1.2 and 1.5 kJ/mm. Standard tensile tests are also conducted on both flat and curved coupons extracted from the sections to provide mechanical properties for subsequent strength analysis.All the tests have been successfully conducted. For those T-joints between S690 CFCHS under brace axial compression, chord plastification is always found to be a critical failure mode while for those T-joints between S690 CFCHS under brace in-plane moments, both brace fracture and chord punching shear failure are found to be critical at the end of the tests.All the measured joint resistances of the T-joints between S690 CFCHS are found to be larger than those design resistances obtained with EN 1993-1-8 and Design Guide 1 of CIDECT. Consequently, this investigation provides structural insights and scientific data for possible improvements onto prediction capabilities of the design methods.

Test and design of stainless steel K-joints in cold-formed circular hollow sections

Stainless steel structures have obvious competitive advantages for buildings in the corrosive environment. In recent years, many studies have been conducted on the behaviors of stainless steel materials and members, but the behaviors of joint were rarely reported. This study carried out nine tests on stainless steel K-joints in cold-formed circular hollow sections. The material properties of circular hollow sections, the ultimate loads, the failure modes, and the load-deflection curves of joint were all reported. All the joints failed in the chord plastification. Finite element models were developed for K-joints, and were validated using the test data. Parametric studies were then conducted. Totally, 720 finite element models were built, and the effects of the geometric configuration, the chord preload, and the chord material properties on the joint capacity were explored. Based on the results of the parametric studies, the parameter Qu accounting for the influence of geometric configurations (i.e. β, γ, and g) and the parameter Qf accounting for the influence of chord preload were modified based on the corresponding formulae in the CIDECT design guide for low-carbon steel K-joints. To further improve the accuracy of prediction, a new parameter Qy400 was proposed to consider the effect of the chord material property variations. The predictions of the proposed were compared with test data collected in literature. It is concluded that the proposed design formulae have good performances in predicting the capacity of stainless steel K-joint in circular hollow section.

Cross-sectional behaviour of cold-formed high strength steel circular hollow sections

A comprehensive experimental and numerical study into the cross-sectional behaviour of structural steel circular hollow sections (CHS), with an emphasis on high strength steel, is presented in this paper. Six cold-formed high strength steel S700 CHS profiles – 168.3×4, 139.7×4, 139.7×5, 139.7×6, 139.7×8 and 139.7×10 (diameter × thickness, in mm), spanning from Class 1 to Class 4 in compression according to EN 1993-1-1, were experimentally examined. The test programme consisted of twelve tensile coupon tests, local geometric imperfection measurements, six stub column tests, six four-point bending tests, six three-point bending tests and fifteen short beam-column tests. In parallel with the experimental study, finite element (FE) models of CHS were established and validated against the obtained experimental results, and parametric studies were subsequently carried out using the developed models to expand the cross-sectional resistance data pool. Finally, the cross-section design provisions specified in the European code prEN 1993-1-1:2018 and the American Specification ANSI/AISC 360-16 were assessed using the freshly generated experimental and numerical results as well as the existing test data on hot-rolled and cold-formed CHS from the literature. The present study provides the basis for the development of improved cross-section design rules for normal and high strength steel CHS in future research.

Critical Buckling Strains in Thick Cold-Formed Circular-Hollow Sections under Cyclic Loading

AbstractContrary to the large dataset of test results exploring the monotonic bending response of steel tubes, the corresponding dataset of cyclic bending tests remains very small. Seven compact an...

Investigations into residual stresses in S690 cold-formed circular hollow sections due to transverse bending and longitudinal welding

This paper presents an experimental and numerical investigation into residual stresses of S690 cold-formed circular hollow sections (CFCHS) due to transverse bending and longitudinal welding. It is generally expected that adverse effects of residual stresses on both cross-section and member resistances in the S690 CFCHS are proportionally less pronounced, when compared with those in S355 CFCHS owing to increased yield strengths of the steels. Hence, there is a need to determine the distribution of residual stresses in the S690 CFCHS through a rational experimental and numerical investigation in order to provide accurate data for subsequent structural assessment on these sections.A total of four S690 CFCHS are fabricated with 6 mm thick plates with (i) transverse bending, and (ii) longitudinal welding. Surface temperature history at selected positions of these sections are measured with thermocouples during welding while surface residual stresses are measured with the sectioning method after welding. Owing to various practical constraints in measuring residual stresses of these sections accurately, a total of three coordinated finite element models are established in which their numerical results are integrated for rational analyses. The transverse bending process is simulated with two-dimensional models with plane-strain elements which undergo extensive plastic deformations to generate residual stresses after springback. The longitudinal welding process is simulated with two coupled three-dimensional models with solid elements to perform a sequentially-coupled thermomechanical analysis in the presence of those residual stresses due to transverse bending. Consequently, a rational distribution of the residual stresses due to both transverse bending and longitudinal welding in these sections are readily determined with these coordinated finite element models after careful calibration against measured data.

Material properties and residual stresses of cold-formed high-strength-steel circular hollow sections

Owing to the development of material processing technologies, high strength steel plates with yield strengths exceeding 460 MPa are commercially available at present. However, experimental investigations on material properties and residual stress distributions of cold-formed high strength steel circular hollow sections (CHSs) are rather limited. This paper therefore presents an experimental investigation to advance the knowledge in this area. In total, 11 steel circular hollow sections were manufactured from steel plates with the measured yield strength varying from 546.5 MPa to 973.3 MPa. A total of 58 tensile coupons taken from parent plates and hollow tubes were tested to examine the effect of cold-forming process on material properties within the cross-section. When compared with parent metals, strength enhancements were found in Q460 sections, while yield strengths remained nearly the same as parent metal in Q690 sections, and a slight strength reduction by around 1% was noticed in Q960 sections. Basic material parameters in existing material models to obtain stress-strain curves were thoroughly calibrated against the coupon test results. Results indicate that the use of the calibrated parameters can give excellent predictions in terms of stress-strain curves. Residual stress measurements on 2 cold-formed CHSs were performed, with 57 strips extracted and 684 readings taken. The maximum tensile membrane residual stress and maximum tensile bending residual stress on the external surface were observed to be 41% and 32% of the material yield strength. A multilinear predictive model for the distribution of membrane residual stresses in cold-formed high-strength-steel CHSs was subsequently proposed.

Behaviour and design of cold-formed CHS under static pure bending through finite element analysis

Abstract The current slenderness limits are significantly different in international design codes for cold-formed Circular Hollow Sections (CHS) under pure bending. This paper aims to use the Finite Element (FE) method to understand the behaviour of cold-formed CHS under pure bending and to propose new design rules. The model is calibrated by comparing its predicted load-deflection curves with previously published experimental data. In total, 21 specimens were modelled with diameter-to-thickness ratios ranging from 13 to 122. The current slenderness limits in the present international steel specifications were examined using the FE model and their suitability for cold-formed CHS is discussed. The effect of section slenderness on rotation capacity has been examined where the predicted variation of rotation capacity against section slenderness has been compared to the experimental results. A new equation for the amount of initial geometrical imperfection as a function of section slenderness has been developed and proposed for design purposes. The ovalisation deformation ratio and the critical strain at local buckling were determined and compared for compact, non-compact and slender sections. The progressive bending deformations of CHS at 10 critical steps have been presented and compared for the three cross sectional types, in particular at the maximum moment and bending rotation. In general, a good agreement has been obtained between the predicted strengths and ductilities using the current FE models and those of the experimental data of cold-formed CHS.

Design of cold-formed CHS braces for steel roof structures

Thin-walled cold-formed circular hollow sections (CHSs) are widely used as the primary and secondary structural members in the construction of roof structures often used for high rise buildings in the Middle East. The British steel design code BS 5950 is the main code used in the Middle East for the design of such structural elements. Existing experimental static axial tests performed by the second author on CHSs were used to assess BS 5950. This code was shown to over-estimate the axial capacity of compression members under static axial load in the middle member slenderness range of 0.35–0.75. This is because most of the braces in such range failed by the interaction of local buckling and overall flexural buckling. Newly derived design curve termed “Curve e” is proposed for design purposes. The newly derived curve is compared against other design codes such as the North American Steel Design code ANSI AISC 360-10, the European Steel Design Specification Eurocode 3, and the Australian Steel Design Code AS 4100. One case study for a newly constructed roof structure in the Middle East is presented. It was found that the existing curve “c” over-predicts the capacities of the most stressed secondary and primary braces by 37% and 15% respectively. Finite element models were constructed and found to provide good agreement against the experimental load-defection curves. Once validation is completed, additional FE models were created to expand the available database for strength of different CHS braces up to a member slenderness of 2.0. Newly derived design curve ‘‘e” within BS5950 platform was found to be a suitable lower bound for the experimental and numerical results. Additionally, a modified version for the AISC design model is suggested in this paper by reducing the strengths by 15%; applying a form factor of 0.85.

Compressive stress-strain model of cold-formed circular hollow section stub columns considering local buckling

A complete stress-strain model for cold-formed circular hollow section (CHS) stub columns under compression is proposed with emphasis placed on the modeling of post-local-buckling behavior. The proposed model comprises two mathematical expressions. One of the two equations is to define the ascending portion of the proposed stress-strain curve and depict the nonlinearity caused by residual stress induced during manufacturing process of cold-formed CHS, while the other is to define the descending portion and trace the post-local-buckling behavior. The proposed stress-strain model is a single parameter model. Only if the generalized outer diameter-to-thickness ratio is given, the compressive stress-strain relationship of a CHS can be completely determined. To calibrate the proposed model and verify its accuracy, test results of forty-eight CHS stub columns under compression are collected. The previous tests cover a wide range of structural factors such as outer diameter-to-thickness ratio and yield strength, particularly including CHS stub columns with yield strength of up to 1180MPa. Comparisons between the measured results and the calculated ones indicate that the proposed model can not only predict the local buckling strength as well as corresponding strain, but also trace the post-local-buckling behavior up to large strain with high accuracy.

Variable amplitude cyclic pure bending tests to determine fully ductile section slenderness limits for cold-formed CHS

This paper describes an experimental investigation of the cyclic inelastic flexural behaviour of cold-formed circular hollow section (CHS) beams. Controlled-rotation, symmetrical cyclic bending tests were performed using a variable amplitude loading history on different sizes of compact CHS with diameter-to-thickness ( D / t ) ratios ranging from 20 to 40. The CHS beams exhibited stable hysteresis behaviour up to local buckling and then showed considerable degradation in strength and ductility depending on the D / t ratio. Seismic capacity parameters are presented including strength, stiffness, hysteresis loops and modes of failure for each specimen. Peak moments obtained in the cyclic tests were compared with those obtained in monotonic and cyclic tests published previously and also with design moments predicted using a number of steel specifications. New section slenderness limits suitable for the design and construction of seismic resisting structural systems were determined. A comparison is made between these seismic slenderness limits and the limits available in the design codes. The effect of the number of cycles on ductility and energy absorption is examined.

Thin circular hollow section-to-plate T-joints: Stress concentration factors and fatigue failure under in-plane bending

Welded thin-walled ( t<4 mm) tube-to-plate T-joints made up of cold-formed circular hollow sections welded onto a plate to form a moment resistant connection are used in the road transport and agricultural industry to manufacture equipment and other structural systems. Fatigue design of these joints is not available in current standards. An understanding of the stress concentrations and failure in these connections is therefore necessary as a step towards understanding the fatigue behaviour of these connections. Stress concentration factors (SCFs) of welded thin-walled ( t<4 mm) circular hollow section (CHS)-to-plate T-joints are determined at different locations along the weld toes on the tubular brace. The distribution of SCFs along the weld toes shows that the highest SCF occurs at the weld toes in the circular brace at the 0° line. The ratio of the end of test fatigue life ( N4) to the through-thickness fatigue life ( N3) in the thin CHS-plate T-joints is found to fall within the range of N4/ N3 found in previous research of both thick and thin-walled joints. Surface crack growth monitoring is used to obtain an approximation of the length of surface crack at the point of occurrence of a through-thickness crack. The relationship between surface crack length and the occurrence of a through-thickness crack is important in that it can be used as a measure of the criticality of a surface crack during structural health monitoring of equipment or structures.