Cold-formed Steel Lipped Channel Beams Research Articles

Data driven models for capacity prediction of CFS lipped channel flexural members

Cold-Formed Steel (CFS) is considered as a sustainable material and CFS members are becoming popular nowadays as primary or secondary load carrying structural elements. The increasing use of CFS members is owing to their other advantages like high strength to weight ratio, versatility in cross sectional shapes and dimensions, easy fabrication and mass production, uniform quality, good energy efficiency, easiness to handle and transport etc. The behaviour of cold-formed members under flexure is complex as it involves the occurrence of various buckling modes (Local, distortional or lateral-torsional buckling) and the possible interaction between them. Although, the moment carrying capacity of CFS beams can be estimated using existing codes and design standards, the present study is an attempt to introduce an alternate rapid capacity assessment tool based on machine learning for the same. Available data on experiments conducted on CFS lipped channel beams are collected to model and analyse in ABAQUS for validating the finite element model. The validated FE model is used for developing the input-output data set for training the Machine Learning (ML) models by sampling the geometric and strength related input parameters of the CFS beam. Recently introduced machine learning regression models like Linear Regression, Lasso regression, K-Nearest Neighbors, Decision Tree, Random Forest, Adaptive Boosting, Extreme Gradient Boosting, Light Gradient Boosting, Categorical Boosting, Gradient Boosting Regressor, Support Vector Machine and Artificial Neural Network are used to predict the ultimate flexural capacity of CFS beams. The CatBoost model is emerged as the best performing algorithm for predicting the flexural capacity, with 98.5% accuracy for the test data set. A SHAP (SHapley Additive exPlanations) analysis is also conducted for the global and local interpretation of the prediction of the best performing machine learning model. SHAP results not only indicate the influence of input parameters on output prediction, but also the influence of input parameters on each other in predicting the output.

CFS lipped channel beams buckling in distortional modes at elevated temperatures: Behaviour, failure and DSM design

This work reports the findings of a comprehensive numerical investigation on the post-buckling behaviour, failure and Direct Strength Method (DSM) design of cold-formed steel (CFS) single-span simply supported lipped channel beams buckling in distortional modes at elevated temperatures (up to 800 °C) due to fire conditions. It extends the scope of a previous investigation carried out by Landesmann and Camotim [1], by analysing a substantially larger lipped channel beam set, exhibiting various cross-section dimensions and yield stresses, selected to cover wider distortional slenderness ranges. As done before, (i) the beams analysed display two end support conditions, (ii) the Eurocode 3 (part 1.2) model to describe the temperature-dependence of the CFS material properties is adopted and (iii) the results are obtained by means of Abaqus shell finite element GMNIA. After presenting and discussing the main features of the beam distortional post-buckling behaviour, extensive beam failure moment sets are gathered and used to develop and validate DSM-based design approaches. The methodology followed consists of modifying the most performant available DSM-based design curves (developed for beams at ambient temperature [2]), which naturally involves the temperature-dependant reduction factors of the CFS model. A merit assessment procedure shows that the modified DSM-based strength curves predict the lipped channel beam distortional failure moments with remarkable accuracy and reliability, thus constituting an excellent starting point to search for a DSM-based design approach capable of handling arbitrary CFS beams failing in distortional modes at elevated temperatures.

Experimental investigation on cold-formed steel lipped channel beams affected by local-distortional interaction under non-uniform bending

This paper reports an experimental investigation, carried out at The University of Hong Kong, on the behaviour of cold-formed steel lipped channel beams affected by local-distortional (L-D) interaction under non-uniform bending – to the authors’ best knowledge, these are the first tests specifically devoted to this topic. This investigation consists of 16 non-conventional four-point simply supported bending tests involving twin lipped channel beams arranged in a “back-to-back” configuration and laterally restrained at the loading points. The 32 lipped channel specimens were brake-pressed from high-strength zinc-coated G450 grade structural steel sheets. Tensile coupon tests were performed to obtain the specimen material properties and initial geometrical imperfections were measured prior to testing. The beam geometries were carefully selected to enable testing beams that are prone to “true L-D interaction” (close critical distortional-to-local buckling moments) when acted by trapezoidal bending moment diagrams with four distinct gradients – all the tested specimens exhibited the sought L-D interactive nature. The output of the experimental investigation consists of (i) applied moment vs. displacement equilibrium paths, (ii) photos showing beam deformed configurations along those paths (including the failure modes) and (iii) the failure moment data. Lastly, the experimental failure moments obtained are compared with their predictions provided by the (i) current local and distortional Direct Strength Method (DSM) strength curves and (ii) available DSM-based approaches against L-D interactive failures, which were developed and calibrated exclusively in the context of beams subjected to uniform bending.

Optimal design of cold-formed steel lipped channel beams: Combined bending, shear, and web crippling

The load carrying capacity of cold-formed steel (CFS) beams can be enhanced by employing optimisation techniques. Recent research studies have mainly focused on optimising the bending capacity of the CFS beams for a given amount of material. However, to the best of authors’ knowledge, very limited research has been performed to optimise the CFS beams subject to shear and web crippling actions for a given amount of material. This paper presents the optimisation of CFS lipped channel beams for maximum bending, shear, and web crippling actions combined, leading to a novel conceptual development. The bending, shear and web crippling strengths of the sections were determined based on the provisions in Eurocode 3, while the optimisation process was performed by the means of Particle Swarm Optimisation (PSO) method. Combined theoretical and manufacturing constraints were imposed during the optimisation to ensure the practicality of optimised CFS beams. Non-linear Finite Element (FE) analysis with imperfections was employed to simulate the structural behaviour of optimised CFS lipped channel beams after successful validation against previous experimental results. The results demonstrated that, the optimised CFS sections are more effective (bending, shear, and web crippling actions resulted in 30%, 6%, and 13% of capacity increase, respectively) compared to the conventional CFS sections with same amount of material (weight). The proposed optimisation framework can be used to enhance the structural efficiency of CFS lipped channel beams under combined bending, shear, and web crippling actions.

Uniformly bent CFS lipped channel beams experiencing local-distortional interaction: Experimental investigation

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.

Numerical Modeling and Design of Lipped Channel Beams Subject to Web Crippling under One-Flange Load Cases

Web crippling failure governs the behavior of thin cold-formed steel lipped channel beams (LCBs) used in floor systems. This paper describes a numerical modeling–based research study undertaken to investigate the web crippling behavior of LCBs under one-flange load cases and to develop improved design equations for possible inclusion in the cold-formed steel design standards. Finite-element models were developed to simulate the web crippling behavior of LCBs and their accuracy was verified using 36 web crippling tests of LCBs conducted under one-flange load cases using the new standard test method. A detailed numerical parametric study was then undertaken to investigate the web crippling behavior of LCBs using the verified finite element models of LCBs. This numerical parametric study provided an extensive web crippling capacity database and improved the understanding of the effects of key web crippling parameters such as inside bent radius, bearing length, and yield stress on the web crippling capacity. Using these results, new and improved web crippling design equations were proposed in this paper for LCBs under one-flange load cases. They include both unified web crippling equations and the direct strength method–based equations. This paper demonstrated the improved accuracy of the proposed equations and their potential for inclusion in the cold-formed steel design standards.

Experimental Investigation of Cross-Sectional Bending Capacity of Cold-Formed Steel Channels Subject to Local-Distortional Buckling Interaction

This paper describes an experimental program carried out at the University of Sheffield to investigate the interaction of local and distortional buckling in cold-formed steel lipped channel beams. The channels were arranged in a back-to-back configuration and a total of six tests, including three different cross-sectional geometries, were completed. The specimens were tested in a four-point bending configuration with simply supported boundary conditions while being laterally braced at the loading points. The beams failed in the constant moment span by interaction of local and distortional buckling. The geometric imperfections of the channels were recorded before the test using a specially designed measuring rig employing laser sensors. Tensile coupons were also extracted from the flat portions and the corner regions of the cross sections in order to determine the material properties. Comparisons showed good agreement between the experimental results and the predictions of European design guidelines and current North American provisions, whereas other DSM formulations based on the NLD and NDL concepts resulted in rather conservative predictions.

Shear behaviour and design of Lipped Channel Beams with non-circular web openings

Cold-formed steel Lipped Channel Beams (LCB) with web openings are commonly used as floor joists and bearers in building structures. Their shear behaviour is influenced by the presence of web openings and the shear capacities are considerably reduced. However, the shear behaviour and capacity of LCBs with non-circular web openings (square, rectangular and elliptical web openings) has not been investigated adequately. Hence a detailed numerical study was conducted to investigate the shear behaviour and capacity of LCBs with non-circular web openings. Finite element models of simply supported LCBs under a mid-span load with aspect ratios of 1.0 and 1.5 were developed and validated by using the available shear test results. They were then used in a detailed parametric study to investigate the effects of various influential parameters. Numerical results showed that the current shear design equations in cold-formed steel structures design standards are conservative or unsafe. New shear design equations were therefore proposed for the accurate prediction of the shear capacity of LCBs with non-circular web openings. This paper presents the details of finite element modelling of LCBs with unreinforced non-circular web openings and the development of new shear design rules. The proposed shear design equations in this paper can be considered for inclusion in the future versions of cold-formed steel design standards. Suitable design equations were also developed under the direct strength method.

Local-distortional buckling interaction on cold-formed steel lipped channel beams

This paper deals with the ultimate strength, post-buckling behaviour and design of cold-formed steel lipped channel beams affected by local-distortional buckling mode interaction, subjected to uniform bending of the major axis. The cross-sectional dimensions and length of the beams were chosen to have almost equal local and distortional critical buckling stresses by using the GBTUL-2.0β and CUFSM software. The beams are analysed under pinned with warping free end conditions. 12 sections were selected for this study. The selected sections satisfy the geometric limitations for pre-qualified sections in AISI-S100:2007. Elastic buckling and non-linear finite element analyses were carried out using ABAQUS. The results were compared with corresponding results from experiments available in the literature. The numerical parametric study of 60 analyses of different geometries and yield stress values was undertaken. Based on the comparison of ultimate strengths obtained from the finite element analysis and Direct Strength Method (DSM), a design equation is proposed for lipped channel sections which have their elastic local and distortional buckling moments nearly equal.

Distortional failure and DSM design of cold-formed steel lipped channel beams under elevated temperatures

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).

Experimental and finite element analysis research on cold-formed steel lipped channel beams under web crippling

This article presents the results of an investigation into web crippling behavior of cold-formed steel lipped channel beams subjected to end-one-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF), and interior-two-flange (ITF) loading conditions. A total of 48 cold-formed steel lipped channel beams with different boundary conditions, loading conditions, bearing lengths, and section heights were tested. The experimental scheme, failure modes, concentrated load-general vertical deformation and strain intensity distribution curves are presented in the article. The effect of boundary condition, loading condition, bearing length and section height on web crippling ultimate capacity and ductility of cold-formed steel lipped channel beams was also studied. Results of these tests show that the effect of bearing length on the web crippling ultimate capacity in EOF and ETF loading conditions is more obvious than those in IOF and ITF loading conditions. When bearing length is 50, 100, and 150mm, web crippling ultimate capacity of cold-formed steel lipped channel beams with web slenderness=78 reaches its peak. The middle web enters plasticity and form plastic hinge zone. The values of web crippling ultimate capacity in interior-flange loading conditions are larger than those in end-flange loading conditions. It is shown that the specimens in the interior-flange loading conditions have higher ultimate capacity, larger initial stiffness and better ductility than those of specimens in the end-flange loading conditions. Finite element analysis can simulate experimental failure mode and web crippling ultimate capacity. The calculation equations of web crippling ultimate capacity put forward in the article can accurately predict experimental value.

Improved shear design rules for lipped channel beams with web openings

Cold-formed steel Lipped Channel Beams (LCB) with web openings are commonly used as floor joists and bearers in building structures. The shear behaviour of these LCBs with web openings is complicated and their shear capacities are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a detailed numerical study was undertaken to investigate the shear behaviour and strength of LCBs with unreinforced circular web openings. Finite element models of simply supported LCBs under a mid-span load with aspect ratios of 1.0 and 1.5 were developed and validated by comparing their results with test results. They were then used in a detailed parametric study to investigate the effects of various influential parameters. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative. Improved design equations were therefore proposed for the shear strength of LCBs with web openings based on both experimental and numerical results. This paper presents the details of finite element modelling of LCBs with unreinforced circular web openings, validation of finite element models, and the development of improved shear design rules. The proposed shear design rules in this paper can be considered for inclusion in the future versions of cold-formed steel design codes.

Experiments on Cold-Formed Steel Lipped Channel Beams with Complex Edge Stiffeners and Web Holes

This paper presents an experimental investigation and a numerical analysis on the bending strength and behavior of cold-formed steel C-section and ∑-section beams with complex edge stiffeners and web holes. Local buckling, distortional buckling and interaction between local and distortional buckling were observed in the tests. The experimental results show that the stiffened web has great influence on member's bending strength. Compared with C-section specimens, the stiffness of the web stiffeners of ∑-section specimens reduced the influence of the holes. The finite element analysis results show good agreement with the experimental results in terms of bending strength and buckling mode.

Behaviour and design of cold-formed steel beams subject to lateral–torsional buckling at elevated temperatures

Cold-formed steel beams are increasingly used as floor joists and bearers in buildings and often their behaviour and moment capacities are influenced by lateral–torsional buckling. With increasing usage of cold-formed steel beams their fire safety design has become an important issue. Fire design rules are commonly based on past research on hot-rolled steel beams. Hence a detailed parametric study was undertaken using validated finite element models to investigate the lateral–torsional buckling behaviour of simply supported cold-formed steel lipped channel beams subjected to uniform bending at uniform elevated temperatures. The moment capacity results were compared with the predictions from the available ambient temperature and fire design rules and suitable recommendations were made. European fire design rules were found to be over-conservative while the ambient temperature design rules could not be used based on single buckling curve. Hence a new design method was proposed that includes the important non-linear stress–strain characteristics observed for cold-formed steels at elevated temperatures. Comparison with numerical moment capacities demonstrated the accuracy of the new design method. This paper presents the details of the parametric study, comparisons with current design rules and the new design rules proposed in this research for lateral–torsional buckling of cold-formed steel lipped channel beams at elevated temperatures.

A design rule for web crippling of cold-formed steel lipped channel beams based on nonlinear FEA

This paper presents the details of a research study conducted with the aim of developing an alternative design rule to predict the web crippling strength of cold-formed steel lipped channel beams. Current empirical web crippling design rules are perceived to be only accurate for the type of sections and the section dimensions that have been tested. A large number of experiments are often necessary to validate these design rules for a wider range of section types and dimensions, and these experiments are often expensive and impractical. Hence, a design rule which is based on a theoretical or numerical model has been attempted through this work.Four series of tests, replicating the four web crippling loading conditions namely: Interior-One-Flange (IOF), Interior-Two-Flange (ITF), End-One-Flange (EOF) and End-Two-Flange (ETF), were performed to predict the ultimate strength of one hundred and eight specimens. The test specimens were manufactured to include three distinct corner radii and two different web heights, and the specimens were tested using three different lengths of load bearing plates. Two additional loading scenarios which could arise due to the loading flange restraint namely—fixed-flange and free-flange were also examined. Finite element models were developed to numerically simulate the tests performed in the experimental investigations. Load-deformation curves were obtained from both the tests and FE models, and the FE models were validated using the test results. The validation showed a close agreement of FE results with the test results which provided the confidence of using the FE model for a parametric study beyond the limits of the experiments. Based on the results of the parametric study, a design rule was developed which is much more flexible to adapt for new types of sections and ranges of dimensions.

Behaviour and design of cold-formed steel beams subject to lateral–torsional buckling

Cold-formed steel beams are increasingly used as floor joists and bearers in buildings. Their behaviour and moment capacities are influenced by lateral–torsional buckling when they are not laterally restrained adequately. Past research on lateral–torsional buckling has concentrated on hot-rolled steel beams. Hence a numerical study was undertaken to investigate the lateral–torsional buckling behaviour of simply supported cold-formed steel lipped channel beams subjected to uniform bending. For this purpose a finite element model was developed using ABAQUS and its accuracy was verified using available numerical and experimental results. It was then used in a detailed parametric study to simulate the lateral–torsional buckling behaviour and capacity of cold-formed steel beams under varying conditions. The moment capacity results were compared with the predictions from the current design rules in many cold-formed steel codes and suitable recommendations were made. European design rules were found to be conservative while Australian/New Zealand and North American design rules were unconservative. Hence the moment capacity design equations in these codes were modified in this paper based on the available finite element analysis results. This paper presents the details of the parametric study, recommendations to current design rules and the new design rules proposed in this research for lateral–torsional buckling of cold-formed steel lipped channel beams.

Local/distortional mode interaction in cold-formed steel lipped channel beams

This paper reports a numerical investigation concerning the post-buckling behaviour of cold-formed steel lipped channel beams, subjected to uniform major axis bending, affected by local/distortional mode interaction – the results presented and discussed were obtained through shell finite element analyses performed using the code Abaqus. One analyses simply supported beams (locally/globally pinned and free to warp end sections) (i) with cross-section dimensions ensuring coincident local and distortional critical buckling moments and (ii) having critical-mode initial geometrical imperfections with different shapes and the same overall amplitude – local buckling is triggered either by the compressed flange (most common case) or by the web. The results reported consist of (i) elastic and elastic–plastic post-buckling equilibrium paths, (ii) curves and figures showing how the beam deformed configuration evolves along those paths and, for the elastic–plastic beams, (iii) figures making it possible to visualise (iii 1) the location and growth of plastic strains and (iii 2) the nature of the failure mechanisms detected.