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The utilization of cold-formed thin-walled members as structural members has gained significant popularity due to their advantages in fabrication, cost-effectiveness, and transportation convenience. However, the reduced thickness of the used sections poses challenges such as global, local, and distortional member buckling, leading to a decrease in their axial strength. This study focuses on addressing these challenges by connecting the channels together using screws as an alternative to welding, considering the cost, time, and ease of implementation. Conducting finite element analysis on structural columns built-up from cold-formed double C steel channels and subjected to axial loads, this paper verifies the numerical models used against experimental tests known from the literature. A comparison of experimental results with nonlinear FEA and AISI & AS/NZ standards reveals commendable agreement, particularly in predicting the buckling behavior of the built-up I-shaped CFS columns. While the results of the finite element analysis show an overestimation of approximately 3.6% compared to the experimental tests, the AISI and AS/NZS standards demonstrate a conservatism of about 3.0%. Furthermore, the current study investigates the influence of screw spacing on axial strength of built-up cold-formed steel columns. The findings are derived from 175 finite element experiments, evaluating seven different cross-sectional profiles with twelve distinct screw spacings. These spacings correspond to the half-wavelength of local, distortional, and global buckling, divided by values ranging from one to four. The screw spacing determined by half the local buckling half-wavelength along the webs' centerline resulted in enhancements of 22%, 7%, 13%, and 11% in the critical elastic local, distortional, and global column buckling loads, as well as the nominal axial strength, respectively. These increases were even more pronounced for double-lane fasteners with the same spacing, yielding improvements of 25%, 46%, 17%, and 12%, respectively. For economic considerations, it is advisable to utilize single-lane fasteners with a half-wavelength equal to half the local buckling half-wavelength. [ABSTRACT FROM AUTHOR]

This paper concerns the Eurocode 3 Part 1-3 (EN 1993-1-3) methods for calculating the distortional buckling (bifurcation) load of cold-formed steel-lipped channels subjected to axial force, major and minor axis bending. More specifically, the paper presents the results of a parametric study that assesses the accuracy of the simplified method in EN 1993-1-3, which relies on direct/iterative hand calculations and an approximate mechanical model, through comparison with "exact" numerical results, obtained using semi-analytical linearized buckling analyses based on Generalized Beam Theory, which are also allowed by the code. Isoline error maps are presented for a wide range of geometric and material parameters, covering common commercial profiles and corresponding to a dataset of more than 24,000 cases. These maps make it possible to identify the parameter ranges leading to an acceptable error and, even though they strongly depend on the loading, general remarks concerning the expected error pertaining to the simplified method are drawn. [ABSTRACT FROM AUTHOR]

This paper concerns the Eurocode 3 Part 1-3 (EN 1993-1-3) methods for calculating the distortional buckling (bifurcation) load of cold-formed steel-lipped channels subjected to axial force, major and minor axis bending. More specifically, the paper presents the results of a parametric study that assesses the accuracy of the simplified method in EN 1993-1-3, which relies on direct/iterative hand calculations and an approximate mechanical model, through comparison with “exact” numerical results, obtained using semi-analytical linearized buckling analyses based on Generalized Beam Theory, which are also allowed by the code. Isoline error maps are presented for a wide range of geometric and material parameters, covering common commercial profiles and corresponding to a dataset of more than 24,000 cases. These maps make it possible to identify the parameter ranges leading to an acceptable error and, even though they strongly depend on the loading, general remarks concerning the expected error pertaining to the simplified method are drawn.

This paper presents an energy‐based approach to obtain the critical length and stress of local (L) and anti‐symmetric distortional (D2) modes of simply supported lipped channel columns. For each mode, deformed shapes are assumed and the Rayleigh Quotient Method is applied to obtain analytical expressions for the buckling stress. The shape functions adopted for local buckling ensure compatibility of rotation and bending moments at wall junctions and at the stiffener's free end. For the D2 mode, equilibrium of bending and twisting moments are considered leading to an analytical derivation of the mode's warping stress distribution. While for L mode it is not feasible to obtain a closed expression for the critical length (but a simple length testing procedure is sufficient), for D2 mode an expression dependent on geometrical properties is derived. The developed equations for L and D2 modes are validated against CUFSM's pure local modes and GBTul's pure D2 mode (mode 6 in GBTul convention) respectively. For sections with flange‐to‐web width ratio, bf/bw, ranging from 0.2 to 1.0 and lip‐to‐web width ratio, bs/bw, from 0.1 to 0.4 the average ratios obtained for critical stresses (σcr,reference/σcr,proposed) are 1.014±0.019 and 1.011 ± 0.014 for L and D2 modes respectively. [ABSTRACT FROM AUTHOR]

This study investigates the web crippling performance of roll-formed aluminium-lipped channels (ALCs) made of 5052-H36 aluminium alloy. The influence of web perforations on the crippling resistance of webs subjected to Interior-One-Flange (IOF) loading was examined. Laboratory tests were conducted on ALCs with and without circular openings at the mid-depth of the web. Finite element (FE) models were then developed and validated against the experimental results, ensuring their accuracy. To explore the influence of various parameters on the web crippling resistance, a parametric study was carried out. The parameters considered in the study include opening diameter, section depth, inside bent radius, bearing length, and aluminium grade. Using the data obtained from the parametric study, a comprehensive assessment of the available design guidelines for cold-formed steel and stainless steel was performed. New equations in the form of reduction factors were developed to accurately predict the reduction in the web crippling strength, showing their applicability to predict the reduction in the web crippling resistance due to web openings and statistically verifying their reliability. [ABSTRACT FROM AUTHOR]

Abstract This work deals with the structural behaviour, ultimate strength and design of fixed-ended cold-formed steel (CFS) lipped channel columns experiencing various levels of local-distortional-global buckling mode interaction (more or less close critical local, distortional and global loads). First, a comparison between experimental results, obtained from three tests carried out at The University of Hong Kong (UHK), and the corresponding A baqus shell numerical simulations are presented and discussed – the UHK test campaign is reported in Part I of this two-part paper. The comparison (i) involves equilibrium paths, deformed configurations, failure loads and collapse mechanisms, and (ii) provides enough evidence to ensure that the numerical model developed may be deemed validated. Then, this numerical model is employed to perform a parametric study, aimed at obtaining numerical failure load data concerning lipped channel columns experiencing different levels of local-distortional-global interaction – 368 fixed-ended columns, exhibiting different geometries (cross-section dimensions and lengths) and various yield stresses, thus covering a wide slenderness range. Finally, the present (Part II) paper also assesses the quality of the failure load estimates provided by various design approaches, based on the Direct Strength Method (DSM), for CFS columns affected by the triple coupling phenomenon under consideration. This assessment is based on the comparison with both (i) experimental failure loads, namely those reported in Part I and others collected from the literature, and (ii) numerical failure loads, obtained from A baqus shell finite element analyses (SFEA) and either reported in this work or gathered from previous publications by the authors. [ABSTRACT FROM AUTHOR]

• Investigated web crippling behaviour in perforated aluminium lipped channel sections. • Studied the influence of circular web holes on web crippling strength for ITF load case. • Developed non-linear quasi-static finite element models for accurate simulations. • Evaluated existing design guidelines for web crippling prediction. • Proposed new design rules based on experimental and numerical results. Roll-formed aluminium members fabricated using 5052-H36 aluminium alloy grade have been recently employed as structural members in construction. Their web crippling performance has not been fully investigated, particularly when holes are perforated in the web element. Therefore, this study is performed to study the effect of web perforations on the web crippling strength of aluminium lipped channels (ALC's) under the Interior-Two-Flange (ITF) loading condition. Laboratory tests were performed on ALC's with circular holes located at the mid-depth of the web. Finite element (FE) models were then developed and validated against the experiments. A parametric study was conducted to explore the effect of several influential parameters, including opening diameter, section depth, inside bent radius, bearing length, and aluminium grade, on the web crippling capacity. Based on the acquired data, a detailed assessment of the available design guidelines was undertaken, and reduction factor equations were proposed for the ITF loading condition. The proposed reduction factor can accurately predict the reduction in the web crippling capacity for ALC's under the ITF loading condition with fastened and unfastened flange restraint scenarios. [ABSTRACT FROM AUTHOR]

This work reports the results of a numerical investigation concerning the elastic post-buckling behaviour of fixed-ended thin-walled lipped channel and zed-section columns affected by distortional-global (D-G) interaction – “unexpected” features associated with the global buckling nature are unveiled in both cases. The columns analysed (i) exhibit cross-section dimensions and lengths ensuring the simultaneous occurrence of distortional and global critical buckling, and (ii) contain critical-mode initial geometrical imperfections (linear combinations of the critical distortional and global buckling mode shapes). For comparison and clarification purposes, the post-buckling behaviour of lipped channel columns buckling in an “isolated” distortional mode and containing “pure” distortional and global (flexural-torsional) initial geometrical imperfections are also analysed. The results presented and discussed are obtained through geometrically non-linear Generalised Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the column deformed configuration (expressed in GBT modal form), relevant displacement profiles and modal participation diagrams, making it possible to acquire in-depth insight on the mechanics underlying D-G interaction in columns. Finally, particular attention is paid to interpreting the differences exhibited by the various column post-buckling behaviours investigated. [ABSTRACT FROM AUTHOR]

This paper reports the results of a numerical investigation concerning the relevance and Direct Strength Method (DSM) prediction of the ultimate strength erosion caused by local-distortional-global (LDG) interaction in cold-formed steel fixed-ended lipped channel columns. The geometries of the columns analysed (cross-section dimensions and lengths) were carefully selected to ensure that the three competing critical buckling loads are not more than 20% apart, thus guaranteeing a fairly high level of LDG coupling, and ordered in all the various possible sequences. In order to cover a wide slenderness range, several yield stresses are considered, falling below, in-between and above the lowest and highest critical buckling stresses. After providing a brief description of the column selection procedure, which is based on buckling analyses performed with Generalised Beam Theory (GBT), the methodology adopted to identify the most detrimental initial geometrical imperfection shape (in the sense it minimises the column strength) is addressed – it employs Koiter's asymptotic method along with a Monte Carlo simulation. Then, columns containing those initial geometrical imperfections are compressed up to failure, by means of A baqus shell finite element analyses (SFEA), making it possible to acquire in-depth knowledge on the behaviour of lipped channel columns undergoing LDG interaction and gather considerable failure load data. Finally, the last part of the paper is devoted to the DSM prediction of those failure loads and uses the obtained “data bank” to assess whether the available design approaches are able to handle adequately the ultimate strength erosion caused by the triple interaction phenomenon under investigation – if this is not the case, new design curves must be developed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to report an ongoing shell finite element investigation on the distortional post-buckling behaviour, ultimate strength and DSM design of cold-formed steel single-span lipped channel beams under elevated temperatures due to fire conditions. The beam ultimate strengths are computed by means of a steady-state loading strategy that consists of applying an increasing major-axis uniform bending moment to a beam under a uniform and constant (elevated) temperature distribution, until failure is reached. The steel constitutive law at elevated temperatures is simulated by means of the stress–strain–temperature models prescribed in EC3-1.2 for cold-formed steel. The materially and geometrically non-linear response of the cold-formed lipped channel beams is determined through ANSYS shell finite element analyses that incorporate critical-mode (distortional) initial geometrical imperfections. Finally, since there are no specific rules to predict the bending strength of cold-formed steel beams failing in distortional modes at elevated temperatures, the above failure moments and temperatures are used to establish preliminary guidelines for the design of cold-formed steel lipped channel beams under fire conditions. The approach followed is based on the Direct Strength Method (DSM) and has been already employed by other researchers – the currently available design/strength equations/curves, developed for ambient temperature, are modified to account for the appropriate Young’s modulus and yield stress reductions due to the temperature increase. The results presented in the paper provide solid numerical evidence that the currently codified DSM distortional strength curve is not appropriate to predict beam failure moments at elevated temperatures. This is because it either (i) does not account for the material non-linearity due to the elevated temperature (low-to-moderate slenderness range) or (ii) is already inadequate to predict room temperature failure moments (unsafe estimates obtained in the high slenderness range). [ABSTRACT FROM AUTHOR]

This paper presents a numerical (shell finite element) investigation aimed at assessing the performance of the current Direct Strength Method (DSM) provisions against distortional failure to estimate the ultimate strength of fixed-ended cold-formed steel lipped channel and rack-section columns (i) subjected to various uniform temperature distributions caused by fire conditions and (ii) exhibiting different room-temperature yield stresses, covering a wide distortional slenderness range. In particular, the work addresses how does the temperature-dependence of the steel material behaviour, which is felt through both the (reduced) Young’s modulus and nominal yield stress values, influences the quality (accuracy and safety) of the column ultimate strength predictions provided by the DSM distortional strength curve. Six different temperature-dependent steel constitutive laws are considered, namely (i) two models prescribed in part 1.2 of Eurocode 3 (EC3), for cold-formed and hot-rolled steel, and (ii) four experimentally-based analytical expressions recently reported in the literature. The DSM column ultimate strength estimates are compared with the numerical failure loads obtained through geometrically and physically non-linear Ansys shell finite element analyses incorporating critical-mode initial imperfections with small amplitudes. [ABSTRACT FROM AUTHOR]

This paper reports the results of an investigation on the structural behaviour and Direct Strength Method (DSM) design of cold-formed steel columns affected by local–distortional coupling interaction, aimed at extending findings unveiled earlier for lipped channels to other cross-section shapes, namely, hat, zed and rack-sections. Following a brief presentation of the most relevant aspects concerning the post-buckling behaviour and strength of columns with those cross-section shapes and identical local and distortional critical buckling stresses, the paper addresses the assembly of a significant column ultimate strength data bank, concerning fixed-ended hat, zed and rack-section columns undergoing strong local–distortional interaction and exhibiting several geometries (cross-section dimensions and lengths) and yield stresses. Then, these ultimate strength data are used to assess the performance of the existing DSM approaches to design columns against local–distortional interactive failures. It is shown that a novel DSM design approach, recently developed and validated in the context of cold-formed steel fixed-ended lipped channel columns affected by local–distortional interaction, can also be successfully applied to hat, zed and rack-section columns under the same circumstances ( i.e. , exhibiting similar interactive failures). [ABSTRACT FROM AUTHOR]

Abstract: Cold-formed lipped channels are extensively used in commercial steel buildings. Current design provisions provided by the American Iron Steel Institute (AISI), and Canadian Standard Association (CSA-S136-07), ignore the geometric interactions between the channel components. The development of the design equations is based upon treating the web and the flange in isolation. Furthermore, the influence of the lip size on the local stability of the web and the flange is not accounted for. The paper presents a cost-effective procedure that can be utilized in the North American steel industry for efficient design of cold-formed lipped channels. An efficient modelling strategy that stimulates the “actual” boundary conditions between the channel components is presented. The influence of the lip and flange sizes on the buckling and post-buckling strength of the web and the flange is highlighted. It is shown that the web buckling stress is largely affected by the sizes of the channel components and is not a constant value as treated by the North American cold-formed steel codes. A noticeable increase in the post-buckling stiffness of the web and the flange can be attained by accounting for the geometric interaction. Graphs are presented showing the design space of various channel sections that can be utilized in practice to achieve economical design. Comparisons with the existing AISI and CSA-S136-07 provisions are also made. It is shown that the present procedure yields substantial material savings. The paper provides useful guidelines to the cold-formed steel fabricators to determine the optimum section sizes that maximizes the buckling strength. [Copyright &y& Elsevier]

This paper describes a test campaign concerning the behaviour and strength of cold-formed steel (CFS) lipped channel (LC) beams experiencing local-distortional (L-D) interaction made of G450-G500 high-strength steel grades. This investigation involves the performance of 20 tests on simply supported beams arranged in a "back-to-back" configuration, subjected to four-point major-axis bending and laterally restrained at the loading points. All tested specimens failed in the expected L-D interactive modes and exhibited critical distortional-to-local buckling moment ratios ranging between 1.09 and 1.46 (i.e. , prone to "true L-D interaction"). The experimental results obtained and reported consist of beam (i) moment-displacement equilibrium paths, (ii) photos evidencing the evolution of the beam deformed configurations along those equilibrium paths (including the failure modes) and (iii) failure moments - it is found that these results are in good agreement with recently performed numerical simulations. Finally, the experimental failure moments obtained are compared with their estimates provided by the (i) currently codified Direct Strength Method (DSM) strength curves associated with local and distortional failures, and (ii) other available DSM-based design approaches developed to handle L-D interactive failures. This comparison provides solid evidence that the CFS specifications must include a DSM-based design approach able to handle beam L-D interactive failures - the current L and D design curves clearly overestimate all the experimental failure moments. Unlabelled Image • 4-point bending tests on simply supported beams undergoing local-distortional (L-D) interaction. • Substantial experimental failure moment data involving lipped channel beams (topic lacking research). • Clear experimental evidence of true L-D interaction in CFS lipped channel beams under uniform bending. • Equilibrium paths and photos showing failure modes and relevant deformed configurations along those paths. • Performance assessment of current and available Direct Strength Method (DSM) design approaches. [ABSTRACT FROM AUTHOR]