Cold-formed Steel Beam-columns Research Articles

More accurate design equations for cold-formed steel members subjected to combined axial compressive load and bending

Cold-formed steel (CFS) load-bearing members in multi-storey frame systems are subjected to combined actions sourced from gravity and lateral loads. However, limited information is available on the complex interaction behaviour of such elements affected by different buckling modes. This study aims to provide a better understanding of the behaviour and design of CFS sections under various combinations of compression and bending about both major- and minor-axes. Experimentally validated finite element (FE) models of CFS elements were developed in ABAQUS software, accounting for material nonlinearity and geometric imperfections. The validated models were then used to conduct a parametric study to assess the structural performance and failure modes of over 500 CFS elements with various lengths, thicknesses and cross-sectional dimensions under 19 different load eccentricities. It was demonstrated that the element and web slenderness ratios and the magnitude and direction of eccentricity are the key factors affecting the behaviour of the CFS beam–column elements. The accuracy of current design specifications, including American Iron and Steel Institute (AISI-S100), Australian/New Zealand Standard (AS/NZS-4600) and European standard (Eurocode-3) was then investigated. Subsequently, the results were used to propose a new design interaction equation as a function of element and web slenderness ratios. It was shown that the proposed equation could considerably improve the accuracy of the code strength predictions, especially in the case of medium to high slenderness elements. Finally, a reliability analysis was conducted within the framework of the AISI-S100 to ensure that the proposed design equation provides the required level of safety.

Experimental evaluation of DSM beam–column strength of cold-formed steel members under uniaxial eccentric compression

In this paper, the direct strength method (DSM) design of cold-formed steel (CFS) beam–column is evaluated using the results of controlled experiments. The experimental setup is devised to create a uniform moment along the member length about both the major and the minor axes of the member. A comparison of code provisions of AISI S100-2016 for CFS beam–column design against twenty-two experiments reveals a disagreement when the failure mode is due to an interaction of distortional–flexural torsional (D+FTB) buckling. The study proposes a modification to the linear interaction framework (LI) and nonlinear interaction (NLI) framework to include the distortional–global (D–G) interaction. These modifications have been demonstrated to result in strength predictions that are closer to the experimental evidence.

Buckling behaviour of cold-formed steel sigma and lipped channel beam–column members

To determine the load-bearing capacity of cold-formed steel (CFS) beam–column members, closed formed interaction formulas are generally used in most current design guidelines by linearly combining axial load and biaxial bending moment effects. However, this approach ignores the nonlinear interactions between these actions. To evaluate this issue, in this research the structural behaviour of eccentrically loaded beam–column CFS lipped and sigma channel profiles are investigated experimentally and analytically under simultaneous effects of axial loads and biaxial bending moments. Detailed Finite Element (FE) models are developed using ABAQUS software by considering geometric imperfections and actual material properties obtained from coupon tests, and validated against experimental data to estimate the strength and buckling behaviour of CFS beam–column elements. A total of 4480 FE analyses are then performed on 500 mm and 2000 mm long CFS members with different lipped and sigma channel sections subjected to a wide range of eccentricity values in various directions. The results of the analyses indicate that the failure modes are mainly dependent on the stress distribution of the cross-section generated by the combined actions. It is also demonstrated that regardless of the selected load combination, using sigma sections for the short beam–column members generally results in higher strength by up to 42% compared to those with lipped channel sections. It is shown that AISI and Eurocode underestimate the capacity of CFS beam–column members, on average, by around %50 and %25, respectively. However, the recently proposed extended Direct Strength Method (DSM) can generally provide more accurate strength predictions, especially in the case of short beam–column elements.

Capacity and design of cold-formed steel warping-restrained beam-column elements

In current design standards, cold-formed steel (CFS) beam-column elements are generally designed by considering fully warping free behaviour in their supports, which means the benefit of warping-restrained boundary conditions is neglected. In addition, while a non-linear relationship governs the interaction of axial compression and bending, simplified linear expressions are prescribed in design standards, which may lead to unreliable designs. This paper aims to investigate the efficiency of the well-known Direct Strength Method (DSM) as well as the methods proposed by previous researchers for CFS warping-restrained beam-column members. The results of experimentally validated warping-restraint Finite Element (FE) models, considering material nonlinearity and geometric imperfections, are used as a benchmark. A total of 270 CFS elements with various lengths, thicknesses and cross-sectional dimensions are considered under ten different load eccentricity levels. The results are then employed to investigate the effects of warping-restrained boundary conditions as well as code recommended interaction curves on the efficiency of the existing methods to estimate the strength of CFS beam-columns with warping restraint. The results indicate that the estimated capacity of CFS beam-columns is significantly affected (up to 55%) by the warping restraint effects and the errors associated with using the simple linear interaction curve, depending on the element length and thickness. While the influence of warping restraint is generally less than 6%, it is demonstrated that, on average, all existing design methods underestimate the capacity of CFS beam-columns by at least 20%, which highlights the need to develop more accurate design methods for practical design purposes.

Design of cold-formed steel SHS and RHS beam–columns considering the influence of steel grade

The structural behaviour and design of cold-formed steel square and rectangular hollow section (SHS and RHS) beam–columns, made of both normal and high strength steels, are investigated in the present study through a comprehensive numerical modelling programme. Refined finite element (FE) models were first established and calibrated against a collection of existing cold-formed steel member test results from the literature. Following this, an extensive parametric study was undertaken to expand the cold-formed steel beam–column data pool, covering a wider range of steel grades, cross-section geometries, member slendernesses and loading combinations. Results from the parametric study were then used to examine the accuracy of the current codified beam–column design methods, provided in the European Standards EN 1993-1-1 (2005) and EN 1993-1-12 (2007) as well as the American Specification AISC 360-16 (2016). The comparisons revealed that the codified design rules provide varying levels of accuracy in predicting the ultimate resistances of cold-formed steel beam–columns depending on the steel grade. An improved design approach, compatible with current codified design rules in EN 1993-1-1 (2005), is proposed that features (1) recently developed column buckling curves that reflect the increasing normalised column buckling resistance with increasing steel yield strength; (2) bending moment resistances calculated using the Continuous Strength Method (CSM) and (3) new interaction curves for cold-formed steel beam–columns, which are anchored to these more accurate end points. The newly proposed design approach is shown to yield more accurate and consistent resistance predictions over current design provisions for cold-formed steel SHS and RHS beam–columns made of different steel grades, and its reliability has also been statistically verified in accordance with EN 1990.

Structural Size Optimization of Single and Built-Up Cold-Formed Steel Beam-Column Members

AbstractThe use of cold-formed steel (CFS) elements in residential and industrial buildings is widely gaining popularity due to their ability to provide cost-effective and sustainable solutions. A ...

Constrained optimization of anti-symmetric cold-formed steel beam-column sections

Flexibility in the manufacturing of cold-formed steel (CFS) cross-sectional shapes provides a unique opportunity to improve the load-carrying capacity of these elements, leading to more efficient and economic structural systems. This paper presents a practical constrained optimization methodology for pin-ended anti-symmetric CFS beam-columns members with different lengths subjected to various combinations of axial compression and bending moment. The optimization process is carried out using a Genetic Algorithm (GA) with respect to buckling resistance of CFS elements determined according to the Direct Strength Method (DSM). In total, 132 CFS beam-columns with three different lengths (1000, 2000 and 3000 mm) and eleven different cross-sections are optimized under concentrically compressive loads with different levels of eccentricities varying from 0 to 30 mm. Each cross-section is formed using a certain number of fold-lines of steel plate, while the length and angle of the constituent elements of the cross-section are considered as the main design variables. To provide more practical beam-column elements, end-use constraints as well as a range of practical manufacturing and construction limitations are imposed on the selected cross-sections during the optimization process. A standard commercially available anti-symmetric Z section is taken as a starting point of optimization and used to assess the efficiency of the optimized sections. The results show that, for the given plate width and thickness, the adopted optimization process can significantly increase the strength of beam-column members on average 62%, 92%, and 188% for the short, medium and long length elements, respectively, compared to those with the standard section. It is also demonstrated that using more complex cross-sectional shapes does not necessarily provide higher strength for beam-column members. Finally, to verify the efficiency of the optimized sections, detailed nonlinear finite element models are developed using ABAQUS software. The developed models should prove useful for the efficient design of CFS beam-column elements in practice.

Experimental investigation on corroded cold-formed steel beam-columns under compression and major axis bending

This paper presents the results of the experimental and finite element study that was performed to analyze the buckling behavior of corroded cold-formed steel beam-columns. Six specimens with different corrosion degrees were tested under compression and major axis bending. The residual thickness distribution and the mechanical properties of the corroded specimens were analyzed. A nonlinear finite element model predicting the buckling behavior of corroded cold-formed steel beam-columns was proposed. Finally, the influence of the parameters on ultimate load and failure mode were discussed, and the parameters include the parts, locations and lengths of the corroded region. The results indicated that when the thickness loss ratio was below 0.467, the decrease of the corrosion reduction factor for the elastic modulus was small, and then accelerated obviously. The corrosion reduction factor for the yield strength decreased linearly as the thickness loss ratio increased. Local buckling of the web of the corroded specimens was easier to occur than the web of the non-corroded specimen. The corrosion reduction factor for the ultimate load mainly depended on the minimum thickness of the cross-section. The flange corrosion most significantly affected the bearing capacity of the cold-formed steel beam-columns with localized corrosion. The locations and length of the corroded region has a little effect on the ultimate load and failure mode of corroded cold-formed steel beam-columns.

Cold Formed Steel Beam-Column Joints with Latex Layer Wrapping

Columns are the primary element of a structure and are the first element to face the effect of lateral load during an earthquake. To resist such lateral seismic loading high strength and ductile steel frames with higher energy absorption capacity are generally preferred. The nominal ductile capacity of the steel can be boosted up with additional wrapping that could optimize the seismic performance significantly. The present work deals on the behaviour of cold-formed steel beam and cold formed steel column wrapped with latex layers for strengthening. The specimens were subjected to reversed quasi-static cyclic loading to partially simulate the seismic forces. Experimental results shows significant increase in strength capacity of beam-column with latex layer wrapping.

Shape optimization of cold-formed steel beam-columns with practical and manufacturing constraints

This study aims to present a practical method for optimization of symmetric cold-formed steel (CFS) beam-column members using Genetic Algorithm (GA). To eliminate impractical cross-section shapes from the optimization results, a range of manufacturing and construction constraints are incorporated into the optimization process. Axial forces are applied with different eccentricities (0 to 30 mm) to cover the full spectrum of beam-column actions from pure axial compression to pure bending. The effect of element length on the optimization results is investigated by using short, intermediate and long beam-column members. A total of 132 beam-columns with different cross section shape complexity (4 to 12 rollers/nodes and 1 to 3 lips) are optimized. The compression and bending moment strengths are obtained based on direct strength method (DSM) using CUFSM software by accounting for local, distortional and global buckling modes. The results show that using more complex shapes does not necessarily lead to better design solutions. Increasing the eccentricity generally leads to more spread optimum sections particularly when distortional buckling is the predominant mode in short and intermediate-length beam-columns. In cases where local and global buckling modes govern the design, however, less spread sections with higher turn angles generally provide higher strength capacities. With the variation of eccentricity, the ultimate strength of optimum beam-column sections normalized by the strength of a reference lipped-channel are in the range of 110–163%, 128–194% and 160–222% for short, medium and long members, respectively. The results of this study, should prove useful in more efficient design of CFS beam-column elements in practice.

Study of cold formed steel beam column joint to resist lateral load

Cold Formed Steel (CFS) is one of the materials that recently used in building structures. There are many advantages of CFS compared with other materials, such as lightweight, high tensile strength, and fast construction. Hollow Structural Sections (HSS) is the most commonly used as beam and column CFS sections. The purposes of this study are determining the behavior and capacity of CFS beam column joint under lateral load with manual calculation, numerical analysis and experimental. The test specimens used 1 mm thick, 4x4cm HSS for column and 2x4cm HSS for beam. Beam and column connected by two single angle plates placed above and below the beam sides. Both parallel and staggered fastener configurations used in this experiment. Four 4 mm diameter bolts used in this connection. Monotonic static loading applied on beam for modelling the lateral load. The experimental results show the behavior and the capacity of the beam column joint with parallel fastener configurations. The numerical results show that the staggered fastener configuration has better performance compared with the parallel fastener configuration. The CFS beam column joint are adequate to resist the lateral load and feasible to be apply as structural components in building structures.

Experimental investigation on the structural performance of a reinforced cold-formed steel beam–column joint

A reinforced beam–column joint specific to mid-rise cold-formed steel (CFS) dwellings was proposed and studied by six full-scale cyclic loading tests. Afterwards, a moment–rotation relationship prediction model and a numerical model of the joint were established. The results show that: (i) the joint has a certain bending moment transmission capacity; (ii) the joint’s moment–rotation curve has distinctive three-stage deformation characteristics, including elastic, nonlinear, and failure stages successively; the structural performance of the joint is better and more in line with the requirements of mid-rise CFS dwellings than conventional joint; (iii) the elastic buckling strength of beam flange can be taken as the elastic limit of the joint, and the ultimate bending moment of the joint is determined by elastic flexural capacity of beam section; (iv) the prediction model and the numerical model can be used to establish an overall model of mid-rise CFS dwelling with consideration of joints’ nonlinear behaviour.

In-plane behavior of cold-formed thin-walled beam-columns with lipped channel section

This paper is mainly concerned with the in-plane behavior of cold-formed steel beam-column with lipped channel section. The tested members are classified into three series by loading types, including: axial compression and major axis bending (X), axial compression and minor axis bending (lips in tension, Y1), and axial compression and minor axis bending (lips in compression, Y2). A numerical model is developed and verified by the experimental results. The elastic local buckling loads and second-order effects are discussed based on results of test, numerical analysis and design methods. Comparing with test results in this paper, numerical analysis overestimates the elastic local buckling loads and the actual second-order effect is more severe than the prediction by current design methods. Finally, the comparison between test strength and predicted strength obtained by AISI specification indicates that the interaction equation can provide conservative strength prediction for beam-column.

Experimental response of cold-formed steel Zee-section beam-columns

The structural strength and stability of cold-formed steel Zee-section beam-columns including 22 structural Zee-sections at a length of 305mm and 21 at a length of 1219mm were tested under several load combinations of biaxial bending moments and axial force. This testing on Zee-section beam-column specimens complements an earlier test series on lipped channel specimens and provides an exploration of the impact of the principal axis configuration and the differing location of shear center for Zee-sections as relative to their location in lipped channels. The short length specimens are intended to mobilize local buckling and avoid distortional and global buckling, while the long length specimens are intended to mobilize other buckling modes such as distortional and local-global buckling. The combined axial force and biaxial bending moments were applied via a special test rig designed to apply axial load with eccentricities. The results were used to evaluate the current AISI-S100-12 specification for beam-column strength prediction via both effective width and direct strength methods. Both methods employ a simple linear interaction equation for strength prediction of the members under combined actions. The experimental results showed a considerable prospective for improvement in the current specification approach by providing more optimized and realistic results in design considering the actual stress resulted from combined actions on the cross-section. Accordingly, the potentials for further improvements of the direct strength design method for cold-formed steel beam-columns are discussed.

Experimental response of cold-formed steel lipped channel beam-columns

In this paper, the structural strength and stability of cold-formed steel lipped channel beam-columns under bi-axial moments and axial force are experimentally investigated. The results are employed to evaluate the reliability of the current North American cold-formed steel design standard, AISI-S100-12, for predicting the strength of beam-columns, by both the effective width method (EWM) and the direct strength method (DSM). Fifty-five 600S137-54 (AISI-S200-12 nomenclature) lipped channel beam-column sections with three different lengths: 305mm (short), 610mm (intermediate), and 1219mm (long) are tested under combined bi-axial bending moments and axial force to characterize the failure modes and the member capacity. A loading rig specifically designed to apply eccentric axial load, in order to provide bi-axial bending and compression to the specimens, was developed and detailed herein. The experimental observations reveal that the failure modes are highly dependent on the stress distribution applied on the cross-section by the combined actions. The results show a considerable potential for improvement in current specification approaches which utilize a simple interaction equation, as this typically results in conservative strength predictions. The potential for further improvement of the current specification for predicting the strength of cold-formed steel beam-columns is discussed.

Hysteretic behaviors of cold-formed steel beam-columns with hollow rectangular section: Experimental and numerical simulations

This paper presents a comprehensive experimental and numerical investigation on the cyclic response of cold-formed steel columns with hollow rectangular sections. The present study examined the columns׳ post-buckling strength and rigidity degradation, deformation and failure modes, ductility, and energy dissipation capacity. The cold-formed steel members exhibited stable hysteretic performance up to the point of local buckling with considerable degradation in strength and ductility. The energy dissipation mechanisms from the in-plane plastic behavior and out-of-plane elastic buckling deformation were identified. The influence of the height-to-width ratio and axial-compression ratio on energy-dissipation and failure mode was also investigated.

Analysis of bolted moment connections in cold-formed steel beam–column sub-frames

An extensive experimental investigation on bolted moment connections between cold-formed steel sections was carried out, and a total of 16 internal and external beam–column sub-frames with various connection configurations were tested under lateral loads. It is found that for those six beam–column sub-frames with large bolt pitches and thick gusset plates in the connections, flexural failure of connected sections is always critical. The moment resistances of the connections attain at least 85% of the moment capacities of the connected sections. This paper presents a theoretical investigation for predicting the structural behaviour of bolted moment connections between cold-formed steel sections. An analysis and design method for internal force distribution of the connections is presented, and hence a set of design rules for section failure of connected sections under combined bending and shear is proposed. Moreover, a non-linear finite element model of the beam–column sub-frames incorporating the effect of semi-rigid joints is also presented. On the basis of the measured moment joint rotation curves of the bolted moment connections, the overall lateral load–deflection curves of the sub-frames are predicted, and they are found to follow closely the curves obtained from tests. Furthermore, a semi-empirical formula for flexibility prediction of the bolted moment connections is also proposed after careful calibration against test data. It is demonstrated that the proposed rules are highly effective for predicting the structural performance of cold-formed steel frames with bolted moment connections. Hence, structural engineers are encouraged to design and build cold-formed steel structures with bolted moment connections to achieve practical and efficient construction.

Torsional-flexural buckling of singly symmetric cold-formed steel beam columns

Torsional-flexural buckling of singly symmetric cold-formed steel beam columns