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.

Efficient design of overlapped purlins loaded by gravity

Cold-formed steel represents a competitive solution for a wide range of structural applications due to its efficient use of material and its rapid manufacturing and installation. Concerning the purlin systems, continuous Z-shaped steel purlins overlapping over the intermediate rafters are the best choice to minimise material use. The connection between two purlin segments can be achieved by overlapping the profiles over the supports. Using a finite element model validated against experimental data, an extensive study was performed to identify the parameters that influence the design of overlapped purlins loaded by gravity. The analysis is performed on a two-span continuous beam under gravity loading. To capture as much as possible the real behaviour of the purlin, the sheeting is included in the model. The design of lapped purlins was found to be primarily influenced by the length of the span and the overlap length. The detail of the lapped connection is relevant only for short overlaps. A material efficiency study was performed to determine how the overlapped purlin should be designed to minimise material use. Numerical results demonstrate that short overlaps behave poorly from a material efficiency point of view. The optimal overlap length Lp1 + Lp2 was found to be between 15 and 25 % of the length of the span. Connection details or the use of unsymmetric overlaps do not bring a significant increase in terms of material efficiency. However, the use of higher-grade steels bring great improvements.

Optimization of steel-reinforced wooden purlins

A new structural typology of a Steel-Reinforced Wooden (SRW) purlin made of rectangular laminated wood and C-section type cold-formed steel is presented in this article. The steel C-section profile is fitted onto the wooden purlin so that both work together as a composite unit. Although the wooden sections are weaker and have a lower elastic modulus than the steel sections, the overall dimensions of the SRW purlins are no larger than the steel C-section purlin sizes. The SRW purlins also form lighter structures than either plain steel or wooden purlins and they therefore have lower CO2 emissions. In addition, lighter purlins reduce the load on the main structure, which in turn reduces the material needed for the main structure of the building. So, reinforcement of the wooden purlin with steel sections within certain areas notably improved performance when compared with ordinary single-material purlins. The use of the SRW purlins can, therefore, improve the overall sustainability of a building. The improvements were analyzed in terms of sustainability and lower weight, as a function of span length and design load. The behaviors of the single material purlins and the SRW purlin were also compared. Both material strength and deformation design criteria and their influence were studied using an analytical approach based on loading and span length. The simple, innovative, and reliable design procedure described in this study ensured compliance with all technical requirements. Moreover, the savings relating to material weight were evaluated, neutralizing the carbon footprint in all cases under analysis.

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.

Flexural behavior of light steel purlins reinforced by prestressed CFRP laminates

A reinforcing technology using prestressed carbon fiber-reinforced polymer (CFRP) laminates was proposed for reinforcing steel purlins under bending. The reinforcing system can prestress CFRPs without using a hydraulic jack, which enables convenient construction and high reinforcing efficiency. The flexural behavior of the reinforced steel purlins was studied experimentally and theoretically. First, the flexural failure caused by the local buckling or yielding of the upper flange was successfully delayed by the prestressed CFRPs; the flexural capacity and stiffness were improved by 14% to 18% and 28% to 31% in tests, respectively. Then, a calculation method for determining the flexural capacity and corresponding deflection was proposed, which gave accurate results compared with the test. This study provides useful references for reinforcing cold-formed thin-walled steel beams with prestressed CFRPs.

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.

Web Crippling Behavior of Sigma Purlins

AbstractDue to their thin‐walled nature and complex geometry, cold‐formed steel purlins are prone to a variety of instabilities. In most applications, purlins rely on the attached sheeting to restrain member buckling and hence their cross‐section is optimized to maximize their cross‐sectional resistance to local and distortional buckling caused by sagging bending moments under the action of a uniformly distributed load. 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 local slenderness of the web, however it increases their susceptibility to web crippling in case the purlins are subjected to concentrated transverse loads and hence it may reduce the overall moment resistance. This study reports a series of experimental tests on sigma purlins interior‐one‐flange (IOF) loading condition. The tested specimens employ two different section geometries and three different bearing plate widths. The test results show that all the specimens failed by web crippling, however two distinct failure modes and corresponding load‐deformation curves are observed depending on the section geometry. 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 were numerically tested. Furthermore, the applicability of a novel slenderness‐based design approach previously proposed by Duarte and Silvestre for the web crippling design of channel sections is assessed and design recommendations are proposed.

Numerical Modelling and Optimisation of Cold‐Formed Steel Purlins

AbstractThis paper reports a numerical study on the optimization of the lip size of Z‐sections under gravity loads. Numerical models simulating the structural response of cold‐formed steel Z purlins partially restrained by cladding and angle struts and subjected to sagging moment were developed and validated against a total of nine previously reported experimental results on Z‐sections that failed in local or/and distortional buckling. Models of varying levels of complexity were generated and the key parameters affecting the structural response were determined by means of a sensitivity analysis. The investigated parameters included the magnitude, shape and combination of initial geometric imperfections pertinent to local and distortional buckling and the simplified or explicit modelling of test details such as struts and sheeting. Having determined the appropriate modelling strategy that yields the best balance between accuracy and computational cost, parametric studies were conducted to investigate the effect of decreasing or increasing the lip depth on the sections' moment resistance and corresponding failure mode. Based on the parametric study results, the optimal lip size which maximizes the moment/weight ratio for each section was determined.

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.

Case Study – When A Roof is More Than a Roof

The repurposing of existing buildings is becoming more prevalent. But changing a buildings use is not without concern. A European Company purchased an existing warehouse located north of Chicago, Illinois, USA as the space filled their needs for the layout of their manufacturing equipment. Producing medical grade synthetic mesh requires interior temperatures of 90°F (32.2C) with a relative humidity of 90%. The roof of the facility was low-sloped trapezoidal standing seam metal roof system that was watertight in all types of precipitation: Rain, snow, ice. The insulation, below the roof panels and above the steel purlins, was vinyl face fiberglass batt laid over the structural steel bar joist and pinned by the metal roof panels. Shortly after manufacturing commenced, water build-up in the batt insulation during winter started and was so severe that the vinyl facing would belly downward and split the lap seams, which would release the water, soiling the 2m wide rolls of mesh that then did not meet medical standards and had to be discarded. This case study will review the issues that arose out of repurposing a warehouse to a manufacturing facility and what the solution to correct moisture related issues. Hutchinson Design Group, Ltd. of Barrington, Illinois, was retained to investigate the conditions, determine the causes and develop a corrective solution.

Comparative investigation of the effect of corrosion on the mechanical properties of different parts of thin-walled steel

Abstract To comparatively investigate the effect of corrosion on the mechanical properties of different parts of C-shaped thin-walled steel, the flat and corner parts of C-shaped steel purlin, with a service life of 9 years in an industrial environment, were processed into the tested specimens. The effect of corrosion on the cold-formed effect of C-shaped thin-walled steel was investigated by fracture morphology and stress-strain curves. Thus, three methods for calculating the yield strength of cold-formed steel with corrosion damage were also proposed. Finally, based on reverse reconstruction technology, ABAQUS software was used to analyse the effect of corrosion surface morphology on the stress distribution and for the same specimens with different thicknesses. The results showed that different fracture modes and characteristics occurred in both the flat and corner parts after corrosion, which can be attributed to the corrosion surface and thickness reduction. With an increasing degree of corrosion, the strength of the corner parts obviously decreased more than the strength of the flat parts. When the corrosion ratio was 36%, the yield ratio of the corner parts was as high as 0.99, and the elongation was only 2.8%. The corrosion aggravated the cold-formed effect on the strength and the ductility of cold-formed materials. In addition, the corrosion surface will lead to the unbalanced development of surface stress, resulting in the diversification of fracture paths and locations. Especially when the corrosion surface was more uneven with depth, the stress at the maximum corrosion depth was always greater than the stress at other locations. The effect of the corrosion surface on the mechanical properties was related to the residual thickness of the specimens and increased with thinner residual thickness.

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.