Cold-formed High Strength Steel Research Articles

High-Strength Cold-Formed Steel Stiffened Channel Section: Axial Compressive Strength and Initial Geometric Imperfections

This paper presents a summary of experimental findings from axial compression tests on columns featuring a cold-formed lipped channel section with intermediate stiffeners and return lips, roll-formed from high-strength low-allow steel with a nominal yield strength of 690 MPa (100 ksi). Additionally, the paper provides an analysis of the elastic stability of the studied section, a complete description of the initial geometric imperfections of the tested columns, results of tensile coupon tests, and comparison of the observed strengths of the columns with design predictions. The results provide important additional benchmarks for the wider adoption of high-strength cold-formed steel sections and indicate conditions where existing design methods may be reliably extended.

Numerical modelling and design of cold-formed steel battens subject to pull-out failures under bushfire conditions

Thin and high strength cold-formed steel (CFS) battens and claddings serve as non-combustible elements in roof and wall cladding systems, aligning with the recommendations of Australian bushfire standards. However, they are susceptible to significant damage from heat and strong winds experienced during bushfire events, particularly in the form of batten pull-out failures. Such failures may occur at the screw connections between cladding and battens, or battens and trusses/rafters. However, pull-out failures often occur in the thinner CFS battens, when the screw fastener pulls out of the batten’s top flange, leading to the loss of entire cladding and compromising the integrity of the building envelope. This study used finite element modelling of a range of CFS batten configurations to investigate their pull-out failures under combined wind action and bushfire conditions. Finite element models were developed to simulate the pull-out failures at elevated temperatures, validated using experimental results and used in a parametric study to investigate the effects of relevant parameters. Using the results, this study has proposed suitable design equations for predicting the pull-out capacities of CFS battens at elevated temperatures. Engineers can use them to design bushfire safe CFS cladding systems.

Design of cold-formed high strength steel irregular octagonal hollow section columns

This paper presents experimental numerical investigations on the structural behaviour of cold-formed high strength steel irregular octagonal hollow section (OctHS) columns with both non-slender and slender cross-sections. An experimental programme, including material tests, measurements of initial global geometric imperfection, and pin-ended column tests, was first conducted. The key findings from the experimental programme are presented and discussed. Following the validation against the experimental results, the proposed finite element modelling methodology was established to replicate the test observations, and then was adopted to generate a boarder range of numerical results through parametric studies. The collected experimental and numerical data were used to evaluate the applicability of current structural steel design methods on the column buckling strength for irregular OctHS columns. Assessment results demonstrate that the design method adopted in Chinese code can provide accurate prediction, whilst modified design method adopted in Eurocode 3, considering the effect of steel grade on the column strength, has been proposed and shown to greatly enhance the prediction accuracy with improved consistency. The corresponding assessments on the design approaches adopted in American and Australian codes were also discussed.

Behaviour and design of cold-formed high-strength steel built-up beams

The adoption of high-strength steel in the construction sector can provide potential advantages, such as supporting large-scale structures with small cross-sectional sizes leading to decreased self-weight and improved space availability. In this paper, detailed numerical investigations are presented to investigate the nonlinear behaviour of cold-formed high-strength steel (HSS) built-up beams subjected to in-plane flexure along with their bending moment capacities, deformed shapes, and moment-curvature curves. Finite element (FE) models incorporating the initial geometric imperfections of cold-formed sections and material nonlinearities were established and validated against the experiments presented in the literature by comparing the moment-curvature curves, deformed shape, and ultimate bending moment capacities. Following validation, the calibrated FE models were utilized to perform extensive parametric studies to generate further numerical data by varying three different parameters: cross-sectional yield strengths (S700, S900 and S1100), geometries (such that the local slenderness, λl values varied from 1.07 to 4.65) and cold-formed steel (CFS) sheet thicknesses (1.0, 1.5, 2.0, and 2.5 mm). The specimens considered in the present study were restrained to inhibit lateral-torsional buckling and demonstrated failure owing to local buckling. The applicability of the design principles for predicting bending capabilities was assessed using numerical data in accordance with direct strength method (DSM) of AISI codal provisions and continuous strength method (CSM). The obtained numerical results demonstrated that the existing standards lack precise design procedures for cold-formed HSS built-up members and additional research is still required to provide accurate design procedures. Therefore, an improved rational extension of DSM of AISI codal provisions and CSM is recommended to predict the ultimate bending moment resistance.

Fracture behaviour of thin-walled cold-formed steel at elevated temperatures

Cold-formed steel (CFS) is being increasingly used in structural applications due to its high strength-to-weight ratio, ease of construction and versatility. The performance of CFS structures in fire has received signification recent attention, but the fracture behaviour of thin-walled CFS at elevated temperatures, which is fundamental to the fire response of the key components, like connections has yet to be extensively studied; this is therefore the subject of the present paper. First, using experimental data on cold-formed grade S280GD+Z275 steel at elevated temperatures from the literature, damaged true stress-strain curves considering the post-necking behaviour are determined. Then, a fracture prediction approach, implemented in the finite element analysis software Abaqus and considering ductile damage and a damage evolution law is calibrated and validated against the experimental data. Finally, the applicability of the proposed approach to different types of CFS material, including high-strength CFS, is assessed. The results show that the proposed model can accurately predict the fracture behaviour of CFS at elevated temperatures.

Experimental and numerical investigations of high-strength cold-formed steel multi-limb built-up section columns

This paper investigates the buckling behaviour and load-carrying capacity of G550 high-strength cold-formed steel multi-limb built-up section columns under axial compression. Each built-up section consists of multiple lipped and unlipped channel sections connected by self-tapping screws. The C3U1 section is formed by three C-sections (i.e. lipped channel section) and one U-section (i.e. unlipped channel section), while the C2U2 section is formed by two C-sections and two U-sections. The experimental programme involved tensile coupon tests, measurements of initial geometrical imperfection, and column tests on ten C3U1 and ten C2U2 multi-limb built-up section columns. The numerical modelling programme was then performed, with the nonlinear finite element models created and validated against the experimental results. The applicability of the codified Effective Width Method and Direct Strength Method for predicting the strengths of G550 high-strength cold-formed steel multi-limb built-up section columns, as specified in the American Specification and Australian Standard, was then evaluated. The evaluation results showed that the codified Effective Width Method led to rather conservative and less accurate failure load predictions for G550 high-strength cold-formed steel multi-limb built-up section columns, while the codified Direct Strength Method provided accurate and consistent failure load predictions and thus applicable to the design of G550 high-strength cold-formed steel multi-limb built-up section columns. Concerning the lack of design guidelines specifically for multi-limb built-up sections, a modified Direct Strength Method was thus proposed as an alternative design method and shown to provide accurate failure load predictions.

Stability design of cold-formed high and ultra-high strength steel thin-walled box sections using effective stress-strain model

This paper proposes an effective stress-strain model for integrated analysis and design of cold-formed steel structures with thin-walled sections. The study focuses on square and rectangular hollow sections made from high and ultra-high strength steel. Initially, a shell-finite element model (SFEM) was developed and validated using experimental data, specifically for cold-formed members subjected to axial compression. Subsequently, a comprehensive parametric study is conducted to establish the stress-strain relationship model through nonlinear finite element analysis. The proposed model incorporates material nonlinearity, cold-forming effect, local plate imperfection, and residual stresses into a unified stress-strain curve, leading to advanced structural analysis and design of cold-formed structures using simple one-dimensional beam-column element. Subsequently, the proposed method is then implemented in the conventional finite beam-column element analysis, demonstrating consistent agreement with both experimental tests and sophisticated finite shell element results. Finally, the robustness and validation of the proposed method are established, and its application is exemplified through the design of a modular integrated construction (MiC) structure. This study highlights the versatility and reliability of the proposed approach for the analysis and design of cold-formed steel structures.

Nonlinear web crippling analysis and design of cold-formed high strength steel channel sections having different stiffened flanges

Web crippling analysis and design of cold-formed high strength steel channel sections having different stiffened flanges are presented in this paper. 3D finite element models were developed for the analysis of sections with unstiffened flanges, stiffened flanges with simple lips, stiffened flanges with inward return lips and outward return lips loaded under End-Two-Flange (ETF) and Interior-Two-Flange (ITF) loading conditions. The models were verified against tests recently reported by the authors on cold-formed high strength channel sections having different stiffened flanges. The web crippling strengths, load-displacement relationships and failure modes were predicted numerically and compared well against that measured experimentally. Extensive parametric studies were performed using the validated models on 280 channel sections having different web slenderness, ratios of bearing length to web thickness, cross-section geometries and shapes of flange lips. The web crippling numerical strengths were compared with the web crippling design strengths specified in North American Specification, Australian/New Zealand Standards and Eurocode as well as with other proposed design equations in the literature. In addition, a reliability analysis was performed to assess the reliability of the design rules. It is found that the design strengths were either unconservative or conservative, and generally unreliable for the cold-formed channels with unstiffened and stiffened flanges investigated. Therefore, a modification for the North American Specification design equation was proposed. The modified proposed design equation provided more accurate and reliable web crippling strengths compared with specified and available in the literature web crippling design strength predictions.

Improvement of CSM for high-strength S690 and S960 unlipped channel columns, beams and beam-columns

Existing design methods that are mainly based on cross-section classification usually predict conservative resistances for high strength steel (HSS) singly symmetric unlipped channel section members. This paper conducted numerical studies on the resistance of cold-formed S690 and S960 HSS channel section members under different loading types. Numerical simulations were firstly carried out to establish suitable finite element (FE) models, and then applied to parametric studies. The obtained numerical results were adopted to assess and modify the continuous strength method (CSM) for the design of cold-formed HSS unlipped channel section members under axial compression or bending loads. An improved beam-column design method of unlipped channel sections was proposed through providing a new linear design curve incorporating the modified CSM formulae, then to evaluate the newly method and the M - N interaction curves specified in existing standards, finally the reliabilities of proposed method were confirmed.

Testing, numerical modelling and design of G550 high strength cold-formed steel built-up section columns

This paper investigates the buckling behaviour and load-carrying capacity of G550 high strength cold-formed steel built-up section columns under axial compression through experiments and numerical simulations. Two types of built-up sectional profiles were formed, which were defined as built-up OI-section and built-up CB-section. Each built-up OI-section member is formed by connecting two cold-formed steel C-section members in a back-to-back manner using self-drilling screws, while each built-up CB-section member consists of a cold-formed steel C-section member and a cold-formed steel U-section member, which are connected in a face-to-face manner by self-drilling screws. The experimental programme included tensile coupon tests, initial geometric imperfection measurements and 20 pin-ended column compression tests. In the numerical modelling programme, finite element models were developed and validated against the experimental results, and then used for parametric analyses to generate a total of 250 numerical data with different cross-section dimensions and member lengths. Based on the experimental and numerical data, the accuracy of both the effective width method and the direct strength method for predicting the strengths of G550 high strength cold-formed steel built-up section columns, as set out in the American Specification, was evaluated. The evaluation results indicated that both the effective width method and direct strength method provided accurate and consistent failure load predictions for G550 high strength cold-formed steel built-up OI-section columns on average, but with some unsafe failure load predictions, while the predicted failure loads were inaccurate, scattered and conservative for G550 high strength cold-formed steel built-up CB-section columns. Moreover, the effective width method and direct strength method yielded a similar level of design consistency for G550 cold-formed steel built-up section columns, but the direct strength method resulted in more accurate and less conservative failure load predictions than the effective width method. The modifications to the codified DSM equations were proposed for G550 high strength cold-formed steel built-up section columns and shown to provide improved predictions of failure load over the design codes.

Testing and design of cold-formed high strength steel square hollow section columns

An experimental and numerical investigation into the flexural buckling behaviour of cold-formed (CF) high-strength steel (HSS) square hollow section (SHS) members is reported in this paper. A series of 12 flexural buckling tests were conducted on S700 and S900 CF SHS columns. Finite element (FE) models were developed to simulate the experimental observations, which were utilized in a parametric study encompassing a broader range of steel grades and specimen geometries. Subsequently, the current buckling curves in European, North American, and Australian codes was evaluated through reliability analyses. Meanwhile, the effective width method (EWM) and the modified generalized slenderness-based resistance method (GRSM) were compared for slender cross-sections. According to the results of reliability analyses, the modified buckling curves were proposed for CF HSS SHS columns.

Experimental investigation on the cold-forming effect of high strength cold-formed steel sections

Many researches were carried out on the cold-forming effect of cold-formed steel sections while research on that of high strength cold-formed steel sections was quite few. Thus, an experimental investigation on the material property and residual stress of high strength cold-formed steel sections was carried out and the effect of residual stress on the overall stability bearing capacity was studied. It was found that: (1) the increase of yield strength of high strength cold-formed steel was similar to that of Q235 and Q345 cold-formed steel; (2) the residual stress at corner parts was much higher than that at flat parts and the bending residual stress of high strength cold-formed steel was much lower than that of Q235 and Q345 cold-formed steel; (3) residual stress would lead to a decline of the overall stability bearing capacity of axially loaded high strength cold-formed C-shaped steel sections and the effect became lower with the increase of strength grade.

Tests, numerical simulations and design of G550 high strength cold-formed steel lipped channel section columns failing by interactive buckling

This paper presents the experimental and numerical investigations into the structural performance and strengths of G550 high strength cold-formed steel (CFS) lipped channel section columns failing by interactive buckling. A testing program was first conducted, comprising material testing, measurements of initial local, distortional and global geometric imperfections and ten pin-ended column tests. The interaction between different buckling modes was observed and discussed for all the examined specimens upon testing. A numerical modeling program was subsequently performed, where numerical models were created and verified with reference to the test results and afterwards utilized to conduct parametric analysis to produce more numerical data over an extensive spectrum of cross-section geometries and effective member lengths. The effective width method (EWM) codified in the European code and direct strength method (DSM) specified in American and Australian standards were evaluated, based on the combined set of numerical and test data, for their suitability to G550 high strength CFS lipped channel section columns susceptible to interactive buckling. The evaluation results indicated that (i) the EWM yielded scattered and conservative ultimate strengths for columns with small and intermediate slenderness ratios, but relatively accurate results for those of large slenderness ratios and (ii) the DSM led to more consistent and accurate strength predictions for G550 high strength CFS lipped channel section columns failing by interactive buckling, though a number of strength predictions were on the unsafe side.

Numerical Study on Residual Stresses and Plastic Strains in Cold-Formed High-Strength Steel Circular Hollow Sections.

This paper presents a numerical investigation on the residual stresses and co-existent equivalent plastic strains in cold-formed high-strength steel (CFHSS) circular hollow sections (CHS) by using an advanced finite element (FE)-based method. In this method, the entire manufacturing process of the CFHSS CHS was modeled numerically. The accuracy of the numerical predictions of equivalent plastic strains and residual stresses in the CFHSS CHS was verified by comparing the predictions with the existing test results of both the residual stress measurement and load-end shortening response of the stub column. By using the FE-based method, the effects of high-frequency electric resistance welding on the residual stresses and the stub column response were investigated. The through-thickness variations of both the equivalent plastic strains and residual stresses in CFHSS CHS, which are difficult to measure in the laboratory, were explored numerically. Finally, the effect of cold work (which is quantified by the equivalent plastic strains and residual stresses) on the stub column response of CFHSS CHS tubes was evaluated. It can be found that the equivalent plastic strains and longitudinal residual stresses are generally uniform around the cross-section of CFHSS CHS. The transverse and longitudinal residual stresses are generally uniform across each half-thickness, with the inner half-thickness under compression and the outer half-thickness under tension. The results also demonstrate that both the plastic strains and residual stresses may significantly affect the cross-section capacities of CFHSS CHS.

Experimental Investigation of Cold-Formed High Strength Steel K Joints

Experimental Investigation of Cold-Formed High Strength Steel K Joints

Web crippling behaviour of cold‐formed high‐strength steel unlipped channel beams

AbstractConstruction industries have increasingly sought to adopt Cold‐Formed Steel (CFS) sections as primary and secondary load‐carrying members. Also, the evolution of the CFS industry leads to fabrication of high strength CFS sections due to their added benefits such as higher strength‐weight ratio, most appropriate to employ in high‐rise and long‐span applications, and lesser carbon footprint. However, large width‐to‐thickness ratios of these thin‐walled beams make them vulnerable to local buckling failure, a major failure mode being web crippling when subjected to concentrated loads. The design standards predict the web crippling capacity of CFS sections according to the experimental studies conducted in previous years. Innovative concepts like the production of CFS using high‐strength materials should be examined undergoing web crippling. Therefore, the web crippling behaviour of the unlipped channel sections with material strength up to 1000 MPa under all four loading conditions: End‐Two‐Flange (ETF), Interior‐Two‐Flange (ITF), Interior‐One‐Flange (IOF) and End‐One‐Flange (EOF) was investigated in this study. Numerical simulations using Finite Element Analysis (FEA) software (ABAQUS) were conducted on 972 parametric studies following proper validation. New modified equations were proposed to predict the ultimate web crippling capacity of high strength unlipped channel sections and parametric analyses were carried out among various loading conditions.

Design of Cold-Formed High-Strength Steel Diamond Bird-Beak Tubular T-Joints and X-Joints

Numerical investigation and design of cold-formed high-strength steel (CFHSS) diamond bird-beak (DBB) T- and X-joints are presented in this paper. The 0.2% proof stress of braces and chords was 960 MPa. Tests of CFHSS DBB T- and X-joints undergoing compression loads were carried out by the authors. The test results were used to develop accurate finite element (FE) models in this study. A comprehensive FE parametric study was then performed using the verified FE models. The nominal strengths predicted from the literature and European code were compared to the joint failure strengths and ultimate capacities of 244 DBB T- and X-joints specimens, including 224 FE specimens investigated in this work. The failure of DBB T- and X-joints specimens at chord crown locations was identified as the dominant failure mode. It has been shown that the design provisions given in the literature and European code are unsuitable and uneconomical for the cold-formed S960 steel grade DBB T- and X-joints investigated in this study. Hence, accurate, less dispersed, and reliable design equations are proposed in this work, using two design approaches, to predict the joint failure strengths and ultimate capacities of the investigated DBB T- and X-joints.

Web crippling tests on cold-formed high strength steel channel sections having different stiffened flanges and stiffened web

This paper reports 59 tests on cold-formed high strength steel channel sections with different stiffened flanges and stiffened web. The test specimens were brake-pressed from high strength zinc-coated grades G450, G500 and G550 structural steel sheets. The test program consisted of 6 series of channel sections having different stiffened flanges, web slenderness, material strengths and loading conditions. The loading conditions were End-Two-Flange (ETF), and Interior-Two-Flange (ITF) loadings as specified in the North American Specification for cold-formed steel structures. The web crippling test strengths and load–displacement relationships of the channel section specimens were obtained from the tests. The channel sections having stiffened flanges as well as the channel sections having stiffened web enhanced the web crippling strengths of the specimens, especially for those specimens loaded under ETF loading condition. The web crippling test strengths were also compared with the design strengths calculated using the current North American Specification and European Code for cold-formed steel structures. In addition, reliability analysis was performed to assess the reliability of the design rules. Generally, it is found that the predictions obtained from the North American Specification are unconservative and unreliable for the cold-formed high strength steel channel section specimens, except for the specimens with unstiffened flanges under ITF loading condition, while the European Code was unreliable but conservative in predicting the web crippling strengths, except for the specimens with unstiffened flanges under ETF loading condition.

Behaviour and design of cold-formed high strength steel RHS T-joints undergoing compression loads at elevated temperatures

This study presents a comprehensive numerical program aiming to investigate the static resistances of cold-formed high strength steel (CFHSS) T-joints with square and rectangular hollow section (SHS and RHS) braces and chords at elevated temperatures. The included angle between brace and chord members was 90°. The static behaviour of simply supported SHS and RHS T-joints undergoing compression loads through brace members was investigated at four elevated temperatures, including 400°C, 500°C, 600°C and 1000°C. The mechanical properties at elevated temperatures given in the literature for cold-formed S900 steel grade tubular members were used in this study. The numerical investigation was performed using the finite element (FE) models developed and validated by Pandey et al. [1] and Pandey and Young [2] for cold-formed S960 steel grade T-joints at ambient temperature and post-fire conditions. In total, 756 FE T-joint specimens were analysed in this numerical study, including 189 FE T-joint specimens for each elevated temperature. The tubular T-joint specimens were failed by chord face failure, chord side wall failure and a combination of these two failure modes. The resistances of investigated T-joints at elevated temperatures were compared with the nominal resistances predicted from design rules given in European code and CIDECT using the mechanical properties at elevated temperatures. Overall, it is shown that the current design rules given in European code and CIDECT are uneconomical and unreliable. As a result, economical and reliable design rules are proposed in this study through two design approaches for predicting the resistances of cold-formed steel SHS and RHS 90° T-joints of S900 grade at elevated temperatures.

Cold-formed high strength steel CHS-to-RHS T- and X-joints: Performance and design after fire exposures

The post-fire structural performance of cold-formed high strength steel (CFHSS) T- and X-joints with circular hollow section (CHS) braces and square and rectangular hollow section (SHS and RHS) chords is numerically investigated in this study. The tubular members had the nominal 0.2% proof stress of 900 MPa. The CHS-to-RHS T- and X-joints were subjected to compression loads through brace members. The nominal values of peak fire temperatures (ψ) were 300°C, 550°C, 750°C and 900°C. Tests carried out by the authors investigating the post-fire static response of cold-formed S900 steel grade CHS-to-RHS T- and X-joints were formed the basis of the numerical investigation carried out in this study. The test results reported by the authors were used to develop accurate finite element (FE) models. The validated FE models were used to perform extensive numerical parametric studies comprising 768 FE specimens. The validity ranges of critical geometric parameters were extended beyond current limits mentioned in international codes and guides. The residual strengths of test and FE specimens were compared with the nominal resistances predicted from design equations given in Eurocode 3 and Comité International pour le Développement et l’ Etude de la Construction Tubulaire (CIDECT) Design Guide 3 using the measured post-fire residual material properties. Generally, design rules given in Eurocode 3 and CIDECT are shown to be quite conservative with very dispersed and unreliable predictions. As a result, accurate and reliable design rules are proposed in this study.