Lipped Channel Sections Research Articles

Optimized Design of Cold‐Formed Steel Elements for Serviceability and Ultimate Limit States

AbstractCold‐formed steel (CFS) sections are gaining ever increasing popularity in modern construction practice due to their advantages, such as efficient material use and sustainability. While the manufacturing flexibility of CFS cross‐sectional shapes brings innovative and complex shapes within practical reach, obtaining optimum design solutions can be a challenging task due to the complex mechanical behaviour of CFS elements, which is controlled by local, distortional and global buckling modes, as well as the need to account for manufacturing and end‐use constraints. This study presents a practical framework for the development of optimised CFS beam sections with maximum flexural strength and minimum deflections in ultimate and serviceability limit state conditions, respectively, in accordance with Eurocode 3 (EC3). A population‐based Genetic Algorithm optimisation method is employed to obtain optimum solutions for ten different CFS cross‐section prototypes, while the EC3 geometric restrictions and a number of manufacturing and end‐use constrains are also considered. It is shown that sections optimised based on serviceability limit state (SLS) and ultimate limit state (ULS) requirements can provide up to 44% higher effective stiffness and 55% higher bending moment capacity, respectively, compared to standard commercial lipped channel sections with the same amount of material. The results also indicate that using optimised plain channels and folded‐flange sections generally leads to the best design solution in SLS and ULS optimization, respectively.

Numerical study of LSF walls made of cold-formed steel hollow section studs in fire

Cold-formed steel square and rectangular hollow section (SHS/RHS) studs are often used to replace the conventional lipped channel section studs in light gauge steel frame (LSF) wall systems to meet the required high load demand. To ensure adequate structural fire resistance of SHS/RHS stud walls, four full-scale fire tests were previously completed under standard fire conditions. However, the full-scale fire tests are expensive and time-consuming, while the complex fire performance cannot be adequately explained through test observations and results alone. Hence, a numerical study was undertaken by developing simplified and sheathed stud finite element (FE) models of tested walls. This paper provides the details of the developed models of LSF walls made of SHS/RHS studs at both ambient and elevated temperatures and a comparison with experimental results. The validated models were used to highlight the advantage of using SHS/RHS studs in cavity insulated stud walls and further understand the factors that may affect the fire resistance of LSF walls, such as steel grade and stud depth. In addition to the simplified stud model, advanced modelling techniques were used to explore the effects of sheathing and localised plasterboard fall-off on the wall behaviour in fire. Overall, this paper presents a numerical study of SHS/RHS stud walls and the simplified stud model developed in this paper can be used to predict the fire performance of other SHS/RHS stud walls with similar wall configurations.

Experimental Investigation and Load Capacity of Slender Cold-Formed Lipped Channel Sections with Holes in Compression

The use of cold-formed steel (CFS) channels with circular or rectangular web holes is becoming increasingly popular in building structures. However, such holes can result in sections becoming more susceptible to buckle and display lower load-carrying capacities. This paper presents a total of 42 axial compression tests of CFS lipped channel slender columns with and without circular and rectangular web holes, including different hole sizes and cross sections. The test results show that the axial members with a small ratio of width to thickness were governed by global buckling, while the members with a large ratio of width to thickness were controlled by the interaction of local, distortional, and global buckling. The axial strength decreased maximum by 20.48% and 22.98% for the member with circular holes and rectangular holes, compared to a member without a web hole. Then, a nonlinear elastoplastic finite element model (FEM) was developed, and the analysis results showed good agreement with the test results. The validated FE model was used to conduct a parametric study involving 36 FEMs to investigate the effects of column slenderness, dimension of the hole, and the number of holes on the axial strength of such channels. Furthermore, the formulas to predict the global buckling coefficient and the effective area were modified for such sections with holes by using the verified FEM. Finally, the tests and parametric study results were compared against the design strengths calculated in accordance with the developed method. The comparison results show that the proposed design method closely predicts the axial capacity of CFS channels with circular or rectangular web holes.

Behaviour of cold-formed steel lipped channel sections subject to eccentric axial compression

The use of light-gauge steel framed (LSF) wall systems in low- and mid-rise buildings has increased due to the fast and clean construction and robust structural performance. Cold-formed steel studs used as the primary load-bearing component in LSF walls are often subjected to combined axial compression and bending actions caused by loading eccentricity. Research on the effects of loading eccentricity on the compression capacity has been limited while the currently used AS/NZS 4600 and AISI-S100 DSM design guidelines significantly underestimate the load bearing capacities. In this study, 35 lipped channel columns of 0.6 to 1.5 m lengths were tested under concentric and varying levels of eccentric axial compression loading and the resulting load versus axial shortening curves and failure modes were analysed. Non-linear finite element models of tested columns were developed and validated using the test results. Comparison of the ultimate capacities obtained from the tests and finite element analyses against those predicted by the DSM design guidelines showed that the current DSM design guidelines underestimate the capacities whereas a closer agreement was obtained from the improved DSM design guidelines proposed in a recent research study. This paper recommends the improved DSM design method to enable economical and safe designs.

Web crippling investigations of aluminium lipped channel sections under one-flange loading conditions

Roll-formed aluminium sections have recently been utilised in structural systems as load-bearing members. Commonly used as flexural members, these sections are vulnerable to various buckling instabilities including web crippling failure. The current web crippling design guidelines are imperial in nature and their suitability for newly developed sections may not be accurate and reliable. Therefore, this study aims to investigate the web crippling behaviour of and design considerations for unfastened roll-formed aluminium lipped channel (ALC) sections under one-flange loading conditions. An experimental investigation was conducted for this purpose based on the AISI S909 web crippling test guidelines. Numerical simulations were subsequently conducted to extend the range of geometrical dimensions and aluminium alloy grades. A detailed assessment of the design rules given in the American, Australian, and European specifications was carried out using the acquired experimental and numerical results. Most of these guidelines were found to yield unsafe and unreliable predictions of the ultimate web crippling capacities, and therefore suitable modifications and improvement were proposed. The modified design rules predictions showed a good agreement with both experimental and numerical results. Hence it is recommended to adopt these improved design guidelines in relevant aluminium standards.

Effect of Boundary Condition on Buckling Behavior of Built-up Cold-Formed Steel Members Under Bending

Built-up member constituted by lipped channel sections is often used in cold-formed steel building. But, it has not been clarified yet whether the connection interval of chord members affects the buckling behavior of built-up member. In addition, there are not enough considerations on the end boundary conditions where stress is transmitted only to the web. This study clarifies the influence of the boundary condition and spacing of connection on the local and flexural buckling of builtup cold-formed steel members under bending.

Web crippling capacities of fastened aluminium lipped channel sections subjected to one-flange loading conditions

Recently, a new generation of roll-formed aluminium sections have been produced by BlueScope Permalite Australia and utilized in structural systems. However, limited research has been conducted to investigate their buckling instabilities including web crippling failure. The empirical nature of the current design guidelines may also lead to inaccurate estimation to their web crippling capacities. Therefore, this study aims to investigate the web crippling behaviour of and the design considerations for roll-formed aluminium lipped channel (ALC) sections using a combination of experimental study and finite element analysis (FEA). In total, 40 ALC specimens were tested under one-flange loading conditions with flanges being restrained to the supports (Fastened). Non-linear finite element models were also developed and validated against the experiments. An extensive parametric study was subsequently conducted to extend the range of geometrical dimensions and aluminium alloy grades of ALC sections. Further, the applicability and accuracy of the design rules given in the American, Australian, and European specifications were assessed. It was found that most of these guidelines yield either unconservative or over-conservative predictions of the ultimate web crippling capacities, and hence suitable modifications were proposed. Predictions due to the modified design rules showed a good agreement with both experimental and numerical results, and are hence recommended to be incorporated in relevant aluminium standards.

Constrained shell finite element method of modal buckling analysis for thin-walled members with curved cross-sections

The objective of this study is to develop a constrained shell finite element method (cFEM) for curved cross-sections based on a force-based approach and to enrich the elastic buckling analysis of these thin-walled members for a potentially broader engineering application. These curved thin-walled sections, with significant material efficiency, can experience very complex buckling behaviors that commonly exist for thin-walled members, namely global (G), local (L), and distortional (D) buckling. Given the limitations of the current constrained finite strip method (cFSM) and constrained finite element method for handling curved cross-sections, the cFEM method developed in this study provides a constrained approach to enable buckling mode separation for curved sections. This is a unified method not only applicable to curved sections, but also for straight wall sections. In this study, four criteria utilizing the displacement and force characteristics of modes are defined to separate these mode classes (i.e., G, D, and L). Constraint matrices of G, D, and L mode classes were then constructed and implemented based on the shell element formulations in ANSYS. Numerical examples are presented to demonstrate how the method’s capability in modal decomposition and identification can be applied to the stability analysis of thin-walled structural members, such as circular cylindrical tubes, elliptical cylindrical tubes, and open-branch lipped channel sections with and without rounded corners. All these numerical examples demonstrate the potential of the developed cFEM in advancing structural mechanics to provide an enriched structural analysis capability that can aid the design and enable broad applications of these members.

Cold-formed ferritic stainless steel closed built-up beams: Flexural behaviour and numerical parametric study

The flexural behaviour of cold-formed ferritic stainless steel (CFFSS) closed built-up beam composed of lipped channel sections orientated face to face was examined numerically, using a finite element (FE) package ABAQUS. The developed FE models were first validated against the experimental data collected from the literature before performing the desired parametric study. Thirteen different sections were analysed, with varying plate slenderness, using two different material grades (EN 1.4003, EN 1.4509) with three different material properties and wall thicknesses. The simply supported built-up closed beams were analysed under four-point bending. The moment capacity of the built-up beams dropped with the increase in the compression flange’s plate slenderness. The pool of numerical strengths was used to assess the current DSM’s appropriateness, proposed DSM for cold-formed steel closed built-up beams, and proposed DSM for ferritic stainless steel hollow beams. Based on the above-stated strength comparisons, suitable modifications were proposed for the current DSM specifications, mainly targetting CFFSS closed built-up beams made of lipped channel sections (typically failing by local buckling). Lastly, a reliability analysis was performed to check the reliability of the current and proposed DSM specifications for CFFSS closed built-up beams.

Fire design of slender cold-formed lipped channel and sigma section members with uniform temperature under compression

Steel structural elements with cold-formed thin-walled sections are increasingly common in building structures due to their high strength-weight ratio. These elements can provide adequate resistance to different action efforts, such as bending, axial compression, or compression and bending. Lipped channel sections are the most commonly used sections because the application of sigma sections increase due to their lower slenderness walls.When designing these cold-formed steel profiles, local, distortional and global buckling are key failure modes that should be considered, as these instability phenomena are more susceptible to occur under fire conditions.After validating numerical models at elevated temperatures with experimental tests, this paper presents a parametric study of the lipped channel and sigma cross-section columns in the case of fire, considering different steel grades and cross-section slenderness values. Comparisons are made between the numerical results and analytical design rules from EN1993-1-2 using Annex E and its French National Annex, where a different constitutive law is recommended explicitly for cold-formed steel profiles.It is possible to conclude that Eurocode's simple calculation rules are too conservative and sometimes unsafe. Therefore, to increase the accuracy of existing design formulae, new adjustments to the current fire design rules were developed for these profiles.

Tests and design of built-up section columns

Built-up sections are increasingly used as structural elements in the cold-formed steel (CFS) industry. They are composed of two or more component sections connected by discrete fasteners, typically spaced evenly along the length and potentially with fastener groups at the ends. Conventionally, two singly symmetric C-sections are connected to form a doubly symmetric cross-section, and current design guidelines are limited to this particular application. As a means towards broadening the application of built-up CFS sections, the cross-sections in this study were composed of three or four lipped channel sections. The paper presents an experimental investigation of the strength and behaviour of built-up section columns of various lengths and cross-sectional shapes. As observed in the tests, singly-symmetric columns composed of three channel sections (3C) experienced either local, distortional and/or flexural-torsional buckling failure modes, while doubly-symmetric columns formed by four sections (4C) failed in local, distortional and/or flexural buckling modes. The current AISI Specification specifies the use of a modified slenderness ratio only for built-up sections composed of two sections connected back-to-back, whereas the design proposal in this paper recommends the use of an effective rigidity approach coupled with the Direct Strength Method for predicting the strengths of the test 3C and 4C built-up sections. This proposal also suggests a design procedure for the built-up sections experiencing flexural-torsional buckling, which is neither explicitly stipulated in current design standards nor in previous studies.

Experimental and numerical analysis of cold-formed steel floor trusses with concrete filled compression chord

Floor trusses fabricated from cold-formed steel (CFS) sections offer several advantages over more conventional floor systems. The current paper reports the findings of an integrated experimental and numerical study focusing on the behavior of CFS floor trusses made of lipped channel sections with the compression chord member filled with concrete. This type of configuration occurs when CFS trusses are used together with a cast-in-place concrete slab. The experimental part of the study included load testing of seven full-scale CFS floor trusses, while numerical investigation included three-dimensional finite element modeling of these trusses. An analytical procedure based on a simple linear-elastic mechanics approach was also developed in an attempt to predict the response of steel-concrete composite CFS trusses without the need of detailed FE analysis or physical testing. Test results indicate that presence of concrete infill inside the compression chord member prevented the initiation of chord local/distortional buckling. In these specimens the failure mode was tension yielding of the bottom chord member. With the introduction of concrete infill within compression chord, significant improvement in truss response in terms of increase in stiffness and load capacity was obtained. The increase in load capacity was 41% and 46% depending on the orientation of the compression chord member. Presence of a concrete slab resulted in an additional 27% increase in load capacity. Truss response predicted by nonlinear FE analyses agrees well with the measured response, both in terms of global load-deflection behavior and chord strains.

Bending-shear interaction of cold-formed stainless steel lipped channel sections

The bending-shear interaction response of cold-formed stainless steel lipped channel sections has been given inadequate attention in the past. Therefore, this paper investigates the bending and shear interaction behaviour of cold-formed stainless steel lipped channel sections using numerical studies. Finite element (FE) models were developed and validated against the experimental results found in the literature for three-point and four-point loading tests of lipped channel sections of both cold-formed stainless steel and cold-formed steel. The elaborated FE results were used for a comprehensive parametric study that was conducted comprising 60 FE models of three-point loading simulations of stainless steel lipped channels with five different aspect ratios to study the shear response and the bending-shear interaction response. Another 12 FE models of four-point bending simulations were developed to study the bending response. The numerical results were analysed and it is found that the sections with aspect ratios of 1.5 and 2.0 are subjected to the interaction of bending and shear while there is no interaction effect observed in the sections with other aspect ratios. Eurocode 3 and American specifications interaction equations were then evaluated using the numerical results. These design provisions are found to be too conservative for a higher level of applied shear force. Therefore, revised design equations for bending and shear interaction were proposed aiming better prediction accuracy. Further, a statistical evaluation was conducted for the proposed interaction equations and results suggest improved and consistent predictions.

Web crippling of cold-formed carbon steel, stainless steel, and aluminium channels: Investigation and design

Cold-Formed (CF) structural members have recently drawn significant attention in light gauge steel construction. The employment of the different materials, for example CF carbon steel, stainless steel and aluminium, are becoming more common. These structural members are often subjected to concentrated loading conditions, which ultimately leads to failure through web crippling. A plethora of experimental and numerical studies have investigated the web crippling strength and behaviour of CF carbon steel lipped channel sections. However, only limited studies are available for CF stainless steel and aluminium members.This paper presents the investigation of the web crippling strength of CF lipped channel beams under End Two Flange (ETF) loadings and aims to propose a unified equation considering strength factor. Finite Element (FE) models of CF carbon steel, aluminium, and stainless steel lipped channel beams were developed and validated against the available web crippling ETF load case experimental data. Subsequently, a detailed parametric study was performed based on the validated FE models, to establish a wide-ranging data set. New ETF load case web crippling unified design guidelines were proposed for the CF lipped sections made of carbon steel, stainless steel, and aluminium.

Fire tests of cold-formed steel walls made of hollow section studs

Light gauge steel frame (LSF) walls as primary load-bearing components have been increasingly used in the construction of cold-formed steel (CFS) buildings. Their fire safety has thus become an important consideration for designers. Currently, LSF walls made of lipped channel section (LCS) studs are commonly used in low-rise buildings, but with the expansion of CFS applications to mid-rise buildings, cold-formed steel square and rectangular hollow section (SHS/RHS) studs are being used to meet the higher load capacity demands. However, the fire resistance of LSF walls made of SHS/RHS studs has not been investigated yet, so their fire resistance levels (FRLs) are unknown, restricting their use in mid-rise buildings. Four full-scale load-bearing standard fire tests were therefore conducted to investigate the performance of cold-formed steel SHS/RHS stud walls exposed to fire. The test results showed that CFS SHS/RHS stud walls achieved a higher FRL due to the superior elevated temperature mechanical properties of CFS SHS/RHS, while the temperature development exhibited good similarity with uninsulated LCS stud walls of the same wall configuration. However, a different thermal behaviour was observed when SHS/RHS studs were used in cavity insulated walls, as the hollow cavity reduced the temperature difference between the stud hot and cold flanges. This eliminated the fire resistance reduction caused by thermal bowing deformations and provided an improved fire performance than cavity insulated LCS stud walls. This paper presents the details of the fire tests and the results.

EWM-based design method for distortional buckling of cold-formed thin-walled lipped channel sections with holes.

The distortional buckling is easy to occur for the cold-formed steel (CFS) lipped channel sections with holes. There is no design provision about effective width method (EWM) to predict the distortional buckling strength of CFS lipped channel sections with holes in China. His aim of this paper is to present an proposal of effective width method for the distortional buckling strength of CFS lipped channel sections with holes based on theoretical and numerical analysis on the partially stiffened element and CFS lipped channel section with holes. Firstly, the prediction methods for the distortional buckling stress and distortional buckling coefficients of CFS lipped channel sections with holes were developed based on the energy method and simplified rotation restrained stiffness. The accuracy of the proposed method for distortional buckling stress was verified by using the finite element method. Then the modified EWM was proposed to calculate the distortional buckling strength and the capacity of the interaction buckling of CFS lipped channel sections with holes based on the proposal of distortional buckling coefficient. Finally, comparisons on ultimate capacities of CFS lipped channel sections with holes of the calculated results by using the modified effective width method with 347 experimental results and 1598 numerical results indicated that the proposed EWM is reasonable and has a high accuracy and reliability for predicting the ultimate capacities of CFS lipped channel section with holes. Meanwhile, the predictions by the North America specification are slightly unconservative.

Continuous sizing optimization of cold-formed steel portal frames with semi-rigid joints using generalized reduced gradient algorithm

Abstract The primary aim of this paper is to develop a sizing design optimization framework to address the optimization difficulties associated with semi-rigid Cold-Formed Steel (CFS) portal frames. The paper adopted the mathematical model to embed the influence of semi-rigidity for joints and column bases into the fully automated user-friendly program that was written by the authors to establish a relation between the finite element model, design formulations and optimization model. The paper employed Generalized Reduced Gradient (GRG) algorithm to optimize the cross-sectional areas for CFS Back-to-Back lipped channel sections. These sections used for primary load-carrying elements; in which sections' dimensions treated as continuous variables. The design constraints are set to satisfy design criteria proposed by British Standards and practical constraints from the industry. A systematic approach was followed in the parametric study to investigate the influence of several design parameters on the optimal solutions and performance of proposed buildings. The main parameters considered were the semi-rigidity effect of the apex and eave connections and column bases flexibility. The optimal results reached demonstrate the feasibility and efficiency of applying the proposed framework in solving the sizing optimization problem. GRG algorithm proved its reliability and validity with respect to its ability to achieve the optimal configurations of optimized sections. It showed that the frames modelled their joints as semi-rigid joints have smaller cross-sectional areas compared with the same frames having fully rigid joints. It found that the frames having semi-rigid column bases are lighter compared with their counterparts that modelled their bases as nominally pinned. The written program was effectively able to analyze, design and search the optimal solutions with a promising computational time.

Experimental Study and Proposal to Improve the EWM Design of Cold‐Formed Steel Lipped Channel Columns with Circular Holes under Axial Compression

The cold‐formed steel (CFS) lipped channel section with circular holes has been widely used in low‐rise and multistory building structures as the column. However, the circular hole in the web makes the lipped channel column become susceptible to buckle. A total of 54 CFS lipped channel axial compression columns with and without circular holes were used to study the buckling behavior and the effective width design method. The interaction of the local buckling and the distortional buckling were observed for the short and intermediate columns, while the slender columns were controlled by the interaction of the local buckling, distortional buckling, and flexural buckling or flexural‐torsional buckling. The experimental failure loads were gradually decreased with the increase in the diameter of the circular hole for the specimens with the same section. The failure loads of the specimens with two holes were lower than those of the specimens with one hole with same section and same diameter of holes. Then, the experimental results were used to validate a nonlinear finite element model (FEM) previously developed by the authors. The validated FEM was subsequently used to obtain additional 36 numerical failure results concerning the effects of the length, the section, and the diameter and the number of the circular holes. Furthermore, the proposal to calculate the distortional buckling coefficient of the CFS lipped channel section with circular holes were put forward based on numerical analysis considering the reduction of effect of holes. Finally, a proposal to improve the effective width method (EWM) design approach for CFS lipped channel sections with circular holes under axial compression was presented. The comparisons between experimental and numerical capacities and their calculations provided by the proposed EWM design method illustrate a great application of the proposed approach.

Web crippling tests of cold-formed steel channels with staggered web perforations

Cold-formed steel studs and purlins with slotted webs including staggered perforations are used in building construction to enhance the thermal performance and energy efficiency of buildings. However, the web perforations adversely affect their structural capacities, especially their shear and web crippling capacities. Limited research has been reported on this subject despite its importance and continuing use of channel sections with staggered web perforations. Hence a series of web crippling tests was undertaken to investigate the web crippling behaviour and capacities of cold-formed steel channels with staggered web perforations under two flange load cases with their flanges unfastened to the supports. Forty eight lipped channel specimens with perforated and solid webs were tested to failure. Comparison of the experimental web crippling capacities of slotted and solid channels showed that the presence of staggered web perforations significantly reduced the web crippling capacities of channel sections. New web crippling capacity design equations are proposed to calculate the reduced web crippling capacities of lipped channel sections with staggered web perforations. This paper presents the details and results of this experimental investigation.

Numerical investigation of cold-formed stainless steel lipped channels with longitudinal stiffeners subjected to shear

The shear response of the cold-formed stainless steel lipped channel sections with longitudinal stiffeners has not been investigated adequately in the past. Therefore, this paper presents the details of numerical investigations conducted to study the shear behaviour of longitudinally stiffened cold-formed stainless steel lipped channel sections. Following a validation study of the finite element models of lipped channel sections, the effect of return lips and web stiffeners on the shear response of lipped channel sections was examined through comprehensive numerical parametric studies. In addition, numerical investigations were conducted to study the elastic shear buckling response of the sections and the shear buckling coefficients were back-calculated. It was found that the longitudinal web stiffeners enhance the shear buckling resistance of lipped channel sections considerably with increased stiffener depth. However, the shear capacity increment is not significant compared to plain lipped channel sections. The presence of the web stiffeners is found to be not preventing the out-of-plane buckling of the sections. The evaluation of Eurocode 3 and the direct strength method shear provisions for stainless steel channel sections with longitudinal stiffeners illustrates inaccurate capacity predictions. Therefore, modifications were proposed and comparisons reveal that the proposed provisions enhance the shear resistance predictions with good accuracy over the codified provisions.