Cold-formed Steel Purlins Research Articles

On the Stresses in Thin-Walled Channels Under Torsion

Thin-walled channel beams such as cold-formed steel purlins are primarily used to withstand wind forces in the roofing and walling systems of buildings. Traditionally, these types of members are usually designed for bending moments, with the effects of torsion ignored. However, the loading on thin-walled channels can be much more complicated than simple bending actions. Because of the position of the shear centre outside the section, channels can undergo bending and torsion when subjected to vertical load on the top flange. The applied torsion may cause significant stresses in the channel, which may need to be accounted for in design. There appears to be no research on quantifying the effects of torsion on thin-walled channels subjected to a uniformly distributed load acting on the top flange. In this paper, a theoretical solution is derived for calculating the longitudinal stresses in thin-walled channels subjected to torsion caused by a uniformly distributed load acting on the top flange. The theory is validated by modelling the channels in a finite-element analysis. The theoretical results include calculations of the twist rotation, bimoment, sectorial coordinate and longitudinal stresses, while the results from the finite-element analysis include the twist rotation and longitudinal stresses. The results show that the longitudinal stresses caused by torsion can significantly exceed those caused by the bending moment. Practical advice is also given for engineers on how to minimize torsion in cold-formed steel purlins.

Verification of Numerical Models of High Thin-Walled Cold-Formed Steel Purlins.

High thin-walled cold-formed steel purlins of the Z cross section are important elements of large-span steel structures in the construction industry. The present numerical study uses the finite element method to analyse the 300 mm and 350 mm high Z cross sections in-depth. The prepared numerical models are verified and validated at several levels with experiments that have been previously published. Significant agreement between the numerical models and the experimental results regarding Mises stress, proportional strain, failure mode, and force-deformation diagram have been obtained. With the verification, the presented procedure and partial findings can be applied to other similar problems. The results can be used to help research and corporate groups optimise the structural design of cold-formed thin-walled steel structures.

Numerical Investigation of Cold Formed Z Purlins with Lap Bolted Connection

Abstract The main aim of this paper is to investigate the flexural rigidity of lapped cold-formed steel (CFS) purlin connections under monotonic loading, using a numerical model developed with finite element software ABAQUS. The purlins are made up of CFS Z-section, while high strength bolts of diameter 12 mm and grade 8.8 have been used. The test setup consists of simply supported two Z-section that are connected together using overlap connection, where load is being applied at mid span. Furthermore, a parametric study has been conducted to investigate various parameters including, length of lapped connections, thickness, and depth of CFS section and arrangement of bolts, to end up with a total of 15 case specimens. All case specimens were examined in detail in terms of load carrying capacity and deflection characteristics. The results showed that overlap connection is capable of transmitting moment and acts as semi-rigid connection. Moreover, results proved that increasing the ratio of overlap length to beam span resulted in an increase in connection moment capacity. Additionally, decreasing the ratio of lap length to section thickness increases the flexural capacity. Finally, the specimens with bolts in both flange and web at the position of overlap connection were found to have the highest moment capacity.

The analysis of web opening configuration on cold-formed steel hat purlin under torsion behaviour

PurposeCold-formed steel has been used extensively as secondary elements such as purlins and girts in building frames. Purlin is critical to the structure of the roof because it supports the weight of the roof deck and aids to make the entire roof structure more rigid. Furthermore, cold-formed steel purlin is a replacement for wood purlin because steel purlins are light weight and more economical. Hence, the purpose of this study to investigate the effect of opening due to torsion behaviour.Design/methodology/approachThis analysis used cold-formed steel hat purlin with and without openings (WOs) under different opening shape, location and spacing by using finite element LUSAS software.FindingsThe finite element results showed that purlin with openings had higher angle of rotation than section WO, with a percentage difference of not more than 6%. When the opening was located at mid-span, the angle of rotation reduced. Angle of rotation increased when the opening spacing increased. Number of openings also affected the torsional behaviour of the purlin. Five opening shapes, which were circle, diamond, C-hexagon, square and elongated circle, were studied. Among all the shapes, purlin with diamond opening was more resistance to torsion.Originality/valueThe use of cold-formed steel section with web openings (rectangular or circular) is a practical solution when it is required to pass service ducts through the structural member. However, the presence of opening gives minor effect on the structural behaviour of cold-formed steel hat purlin.

Boosting machines for predicting shear strength of CFS channels with staggered web perforations

Cold-formed steel (CFS) purlins and studs with staggered web perforations have been used in construction to improve the thermal efficiency of buildings. The perforations adversely affect structural properties of the members, especially their shear strength. Accurate shear strength predictions of such members is a challenging task, which is not easily solved by the traditional methods. This paper explores five machine learning (ML) boosting algorithms, including gradient boosting regressor (GBR), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), gradient boosting with categorical features support (CatBoost), and adaptive boosting (AdaBoost), as tools for predicting the elastic shear buckling loads and the ultimate shear strength of CFS channels with staggered web perforations. The models were developed using open-source software and a large dataset of finite element simulation results with 3512 samples for each property. The models’ optimal hyperparameters were established through an extensive tuning process to ensure their best performance measured using the robust ten-fold cross-validation method. The elastic buckling loads and the ultimate shear strengths predicted by the developed models compared excellently with the simulation results, with CatBoost being the most accurate model in predicting both properties. The models’ accuracy exceeded the accuracy of the existing descriptive equations. The CatBoost models were inspected by evaluating the relative feature importance and partial dependence of the model-predicted targets from features, which aligned well with the mechanics-based knowledge and confirmed the ability of the models to capture the underlying physics. The predictions of the developed boosting machines were compared with those of previously developed ML models, which allowed for ranking the models and selecting the most accurate ones. Resistance and safety factors for the shear strength predicted by the ML models were determined using the AISI S100-16 w/S2-20 provisions. A Python-based interactive notebook was created for rapid and accurate predictions of the elastic shear buckling loads and the ultimate shear strengths of the slotted channels using the developed models.

Improving the GBT-based buckling analysis of restrained cold-formed steel members by considering constrained deformation modes

This paper reports the development, numerical implementation and practical application of a novel/improved approach to perform the buckling analysis of braced/restrained cold-formed steel members by means of Generalised Beam Theory (GBT). The novelty consists of a cross-section analysis procedure that incorporates elastic restraints and, therefore, leads to a set of constrained deformation modes with clear structural meaning for the member under consideration. The potential of the developed GBT-based approach is illustrated by presenting and discussing numerical results concerning cold-formed steel (i) purlins restrained by sheeting and (ii) studs braced by sheathing. For validation and assessment purposes, several GBT-based results are compared with values provided by the programs GBTul2.0 (conventional GBT), CUFSM (finite strip method) and/or Ansys (shell finite elements). It is shown that the proposed GBT-based approach is much more efficient than the conventional one, as it offers the possibility of obtaining accurate buckling results with very few (constrained) deformation modes – this feature makes it possible to derive semi-analytical formulae to calculate critical buckling loadings of braced/restrained members. This capability is used in this work to derive GBT-based semi-analytical formulae providing critical length and buckling loading estimates for cold-formed steel purlins and studs restrained by panels (sheeting or sheathing).

Shape optimisation of singly-symmetric cold-formed steel purlins

This paper presents the results of a study aiming at shape optimising singly-symmetric cold-formed steel purlins. The “self-shape” optimisation algorithm previously developed, proven to be robust and to converge to known solutions is used for this purpose. Eight optimisation cases are considered, consisting of 1.5 mm and 1.9 mm thick purlins, spanning either 3000 mm or 8000 mm and drawn with either 4, 6 or 8 elements per half cross-section. The aim of the algorithm is to minimise the cross-sectional area subjected to the following constraints: (i) the sections must at least match the second moment of area, and the inward and outward bending capacities of commercial purlins used as reference profiles, (ii) be readily manufacturable using existing roll-forming process, (iii) can be connected similarly to existing purlins by offering vertical and horizontal flat elements long enough and strategically positioned to bolt the purlins to gusset plates and screw the roof to them, respectively, and (iv) have an opening wide enough to run services. The restraints provided by the roof sheeting is considered in the algorithm when calculating the bending capacities. Results show that the algorithm converges to consistent solutions and satisfactory satisfies all constraints, resulting in manufacturable and useable purlins. When compared to the reference purlins, the optimised solutions result in saving up to 6.6% of steel. This cost saving in material is quite significant for a mass-produced product such as purlins. The efficiency of the optimised purlins relative to the reference sections were further validated with FE analysis. The FE analyses confirm that the optimised 1.5 mm thick purlins are superior to the reference section. The optimised purlins may therefore benefit the cold-formed steel industry as they represent more economical solutions without compromising on the usability and performance of the products. However, the FE model shows that the 1.9 mm thick purlins may not have the expected performance and experimental testing is fully validate the optimised sections.

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.

Slenderness-based design for sigma sections subjected to interior one flange loading

Due to their thin-walled nature and complex geometry, cold-formed steel purlins are prone to a variety of instabilities. Sigma purlins are a family of cold-formed steel members with folding-lines along their webs. The non-straight geometry of their web is beneficial in terms of reducing the susceptibility of the web to local buckling, however, it increases their susceptibility to web crippling when the purlins are subjected to concentrated transverse loads and hence it may reduce their overall moment resistance. This paper reports a series of experiments on sigma purlins under the interior-one-flange (IOF) loading condition. Two different section geometries and three different bearing plate widths were examined. To investigate further the effect of web geometry on the IOF web crippling strength of sigma sections, an FE model was developed and validated against the reported test results. Following successful replication of the experimental observations, a comprehensive parametric study was performed, and several sigma sections covering a wide range of cross-sectional geometries and slenderness were numerically modelled. Finally, a slenderness-based (or direct strength) design approach previously developed for the web crippling design of channel and hat sections is extended to sigma sections.

Experimental Analysis of Cold Formed Steel Purlin and Comparison of C and Z Section Using Ansys

Experimental Analysis of Cold Formed Steel Purlin and Comparison of C and Z Section Using Ansys

Comparison of strength and stiffness parameters of purlins with different cross-sections of profiles

Abstract The article presents comparative analyzes aimed at determining the optimal cross-section used in cold-formed steel purlins. The geometrical characteristics, bending resistance and self-weight of channel, zeta and hat cross-sections were compared. The calculations were made using Dlubal SHAPE-THIN software for the bending by the main axis y-y and z-z. The characteristics for the gross and effective cross-section were determined. Based on the first stage analyzes, a significant decrease in cross-sectional bending resistant was observed as a result of a local buckling. The solution to this problem may be the use of intermediate stiffeners. In the second stage, analysis of the impact of the intermediate stiffeners’ locations on the characteristics of hat sections were conducted. Additional intermediate stiffeners on the webs, on the upper chord, and on the webs and upper chord (together) were considered. A significant effect on the bending resistant with a small increase in the element’s self-weight has been demonstrated. In the third stage, the characteristics of a channel, zeta and hat profile with intermediate longitudinal stiffener in the middle of the web were compared. The performed analyzes demonstrated that the hat cross-section shows a significant advantage in bending by the main axis z-z. This advantage can be used in case of lack of protection against lateral torsional buckling and a larger degree of roof slope.

Longitudinally stiffened web purlins under shear and bending moment

Abstract This paper aims to better understand the influence of longitudinal web stiffeners in the structural behavior of cold-formed steel purlins. A set of specimens with stiffened web and plain web cross-sections were tested on predominantly shear, combined bending and shear, and bending only. Numerical analyses carried out in CUFSM and ANSYS investigated the buckling behavior of the sections, allowing the determination of elastic critical stresses and the calculation of the resistance for the tested specimens by Direct Strength Method (DSM). Numerical results showed that the intermediate web stiffeners improve the buckling strength in loading cases of pure bending and pure shear. Experimental and numerical data were used to evaluate the interaction between bending moment and shear force, and showed that the circular interaction diagram was conservative and the results were closer to the trilinear interaction diagram. The comparison between experimental data and DSM predictions demonstrated that DSM provides accurate estimates for shear and flexural strengths of purlins with stiffened web cross-section.

Combined bending and shear behaviour of slotted perforated steel channels: Numerical studies

Cold-formed steel studs and purlins with staggered slotted perforations in webs are used in building structures to produce a better thermal performance of the profiles and for the energy efficiency of structures. On the other hand, the slotted webs result in an unfavourable effect in terms of the structural performance of the element, prominently their shear, bending and combined bending and shear strengths. Relatively little research has been reported on this subject despite its importance. Many research studies have been undertaken to examine the behaviour of conventional cold-formed steel (CFS) channel sections subject to combined bending and shear. To date, however, no research has been carried out to investigate how CFS channels with staggered slotted perforations behave under combined bending and shear actions. An extensive study on this area is therefore essential. Finite element (FE) models of CFS channels with staggered slotted perforations were developed to investigate their combined bending and shear capacity. A parametric study was conducted in detail by developing FE models based on the validation process with available experimental data. This paper presents the FE analysis details of CFS channels with staggered slotted perforations subject to combined bending and shear actions and the FE results. New design equations were also proposed to predict the combined bending and shear capacity of steel channels with staggered slotted perforations.

Stability and moment-rotation behavior of cold-formed steel purlins with sleeved bolted connection

Long runs of cold-formed steel Z-section purlins are often segmented due to assemblage and transportation issues. The segments are commonly connected by bolts to a short cold-formed steel member similar to the purlin; this short member is typically called a sleeve; from a structural point of view, it does not guarantee a state of full continuity to the purlin. This study reports a series of 15 experiments on cold-formed steel Z-sections purlins with sleeved bolted connections tested in bending. These experiments vary cross-section height, thickness and length of sleeve, and span. This parametric experimental study seeks to better understand the flexural-buckling strength, collapse mechanism, and moment-rotation behavior of purlin-sleeve systems. Since the design of purlins with sleeved bolted connections is often limited by the serviceability limit state, in this case excessive displacement, special attention is given to accurately determining and understanding the moment-rotation behavior of purlin-sleeve systems. Based on the experimental results, an expression is proposed to predict non-linear moment-rotation behavior; the proposed expression is compared to expressions previously proposed in the literature. The proposed moment-rotation expression, when used in a simple rotation spring-beam model, leads to accurate prediction of displacement and bending moment in the purlin-sleeve system at any load stage.

Moment redistribution in cold-formed steel sleeved and overlapped two-span purlin systems

Cold-formed steel purlin systems with overlapped or sleeved connections are alternatives to continuous two-span systems and exhibit different degrees of continuity. Both connection types are highly favourable in practice since they are both strategically placed over an interior support to provide additional moment resistance and rotational capacity where the corresponding demands are at their largest, thus improving the overall structural efficiency. Until recently, full-scale testing has been the most common way of investigating the structural behaviour of such systems. In this study, numerical modelling, capable of capturing the complex contact interactions and instability phenomena, is employed. The developed finite element models are first validated against data from physical tests on cold-formed steel beams featuring sleeved and overlapped connections that have been previously reported in the literature. Following their validation, the models are employed for parametric studies, based on which the structural behaviour of the examined systems is explored, while the applicability of conventional plastic design as well as of a previously proposed design approach is investigated. Finally, the efficiency of these systems in terms of load-carrying capacity is compared with their equivalent continuous two-span systems.

Finite Element Analysis of Cold Formed Steel Purlin Bolted Connections

Finite Element Analysis of Cold Formed Steel Purlin Bolted Connections

Advanced numerical investigation into structural behaviour of high-strength cold-formed steel lapped Z-sections with different overlapping lengths

In order to improve buildability of cold-formed steel structures, a series of research and development projects have been undertaken by the authors to examine structural behaviour of bolted moment connections between cold-formed steel sections. In this article, a systematic numerical investigation with advanced finite element modelling technique into the structural behaviour of high-strength cold-formed steel lapped Z-sections under gravity loads is presented, and details of the modelling techniques are presented thoroughly. It aims to examine deformation characteristics of these lapped Z-sections with different overlapping lengths. After careful calibration of advanced finite element models of lapped Z-sections against test data, it is demonstrated that the predicted moment rotation curves of these models follow closely the measured data not only up to the maximum applied moments but also at large deformations. In general, all of these lapped Z-sections are unable to resist sustained loadings after section failure under combined bending and shear, and they exhibit sudden unloadings once the maximum applied loads are attained. Hence, the proposed finite element models are able to simulate highly non-ductile deformation characteristics of these Z-sections. While long overlapping lengths over internal supports in multi-span cold-formed steel purlin systems are often advantageous in terms of both ‘stiffness and strength’, more steel materials are used at the same time. Hence, it is very desirable to establish an efficient use of the lapped Z-sections with optimal overlapping lengths. A total of six models with different overlapping lengths are then extended to simulate the structural behaviour of lapped double-span beams, and extensive material and geometrical non-linear analyses have been carried out. It is found that lapped double-span beams with practical overlapping lengths tend to behave superior to continuous double-span beams in terms of both load resistances and deformations. Depending on the overlapping lengths of the lapped Z-sections, different system failure mechanisms have been clearly identified after significant moment redistribution within the beams, and their structural behaviour has been compared in a rational manner. Consequently, these models will be readily employed to investigate the structural behaviour of high-strength cold-formed steel lapped Z-sections under a wide range of practical loading and boundary loading conditions for possible development of effective design rules.

Strength and stiffness of cold-formed steel purlins with sleeved and overlapped bolted connections

This paper aims to analyze the strength and stiffness of semi-continuous cold-formed steel purlins subjected to flexure. A series of nine cold-formed steel Z sections with sleeved and overlapped bolted connections were tested in bending. Results show that strength is often limited by a plastic mechanism failure, which reduces the web rigidity and induces an early development of local buckling in the compressed flange. In addition to the experiments, this paper presents a numerical and analytical study of the strength and stiffness of semi-continuous purlins, as well as, an analytical method to predict vertical displacement.

Lateral buckling of C-section purlins with one anti-sag bar at middle span section

Anti-sag bar is frequently adopted to enhance the lateral stiffness of cold-formed steel purlins. In existing studies, the anti-sag bar is normally treated as the rigid lateral restraint of cold-formed steel purlins, while according to the previous study of the authors', the local deformation of purlin web near the location connecting the anti-sag bar may significantly reduce the efficiency of anti-sag bar for providing the lateral restraint to cold-formed steel purlins. The lateral buckling of C-section purlins with one anti-sag bar at their middle span section is investigated in this paper, where the effective stiffness of the anti-sag bar taking into account the local deformation of purlin web is adopted. Two representative total potentials for the lateral buckling of C-section purlins are discussed with the differences between highlighted. Based on the proposed total potential, a hand-calculation solution for the lateral buckling load of C-section purlins is developed. The total potential and the solution for buckling load proposed in this study are verified by comparing their results with those from the finite element (FE) analysis using the shell element modeling of ANSYS or the FE program developed. The influences of the key parameters on the lateral buckling load of the C-section purlins are discussed in the parametric study.

Stress analysis on cold-formed C-purlins subjected to wind suction load considering the effective stiffness of anti-sag bar

The anti-sag bar is frequently adopted as an effective solution to enhance the lateral stiffness of cold-formed steel purlins. In many existing methods (e.g. EC3 method), the anti-sag bar is treated as the rigid lateral bracing for cold-formed steel purlins, which may overestimate its bracing efficiency due to the local deformation of purlin web near the position connecting the anti-sag bar, which may significantly reduce the effective stiffness of anti-sag bar. This paper presents an investigation on the effective stiffness of anti-sag bar in bracing the cold-formed steel purlins accounting for the effect of the local deformation of purlin web, based on which an accurate approximation is also proposed. The influence of the effective stiffness of anti-sag bar on the out-of-plane bending moment over the purlin span is then studied using the analytical model presented in EC3. Subsequently, new solutions for the maximum compressive and tensile stresses for purlins with one anti-sag bar at their mid-span section are then proposed with the influence of the effective stiffness of the anti-sag bar taken into account. The results of the proposed solutions are verified by comparing their predictions with the results from the finite element (FE) analysis. Comparisons with FE results made in this study also indicate that the predictions of the EC3 solution may significantly overestimate or underestimate the controlling stresses of cold-formed steel purlins with anti-sag bar in many cases.