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Suitable Stiffening Systems for LiteSteel Beams with Web Openings Subjected to Shear Poologanathan Keerthan and Mahen Mahendran Science and Engineering Faculty Queensland University of Technology, Brisbane, QLD 4000, Australia Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a simultaneous cold-forming and dual electric resistance welding process. It is commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. A cost effective method of eliminating the detrimental effects of a large web opening is to attach suitable stiffeners around the web openings of LSBs. Experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs with circular web openings reinforced using plate, stud, transverse and sleeve stiffeners with varying sizes and thicknesses. Both welding and varying screw-fastening arrangements were used to attach these stiffeners to the web of LSBs. Finite element models of LSBs with stiffened web openings in shear were developed to simulate their shear behaviour and strength of LSBs. They were then validated by comparing the results with experimental test results and used in a detailed parametric study. These studies have shown that plate stiffeners were the most suitable, however, their use based on the current American standards was found to be inadequate. Suitable screw-fastened plate stiffener arrangements with optimum thicknesses have been proposed for LSBs with web openings to restore their original shear capacity. This paper presents the details of the numerical study and the results. Keywords: LiteSteel beam, Web openings, Finite element analysis, Shear strength, Plate stiffener, LSB stud stiffener, Sleeve stiffener, Transverse stiffener, Hollow flanges, Coldformed steel structures. Corresponding author’s email address: [email protected] 1 1. Introduction The use of cold-formed steel members in low rise building construction has increased significantly in recent times. There are many significant benefits associated with the use of lightweight cold-formed steel sections in residential, industrial and commercial buildings. Thinner cold-formed steel sections with varying geometry are continuously developed to suit various requirements including higher moment capacities. The LiteSteel Beam (LSB) shown n Figure 1(a) is a new cold-formed steel hollow flange channel beam produced by OneSteel Australian Tube Mills [1]. It is manufactured from a single strip of high strength steel using a combined cold-forming and dual electric resistance welding process. The effective distribution of steel in LSBs with two rectangular hollow flanges results in a thin and lightweight section with good moment capacity. The LSB has many applications and has become a very popular choice in the flooring systems as shown in Figure 1(b) [1]. Table 1 shows the details of LSB sections including their dimensions. Current practice in flooring systems is to include openings in the web of floor joists or bearers so that building services can be located within them. Without web openings, services have to be located under the joists leading to increased floor heights. Pokharel and Mahendran [2] recommended the use of circular web openings in LSBs based on an investigation using finite element analyses. Three standard opening sizes of 60, 102 and 127 mm are used with the currently available LSBs [3]. The use of web openings in a beam section significantly reduces its shear capacity due to the reduced web area. Since about 88% of the shear force is supported by the main web element of LSB [4], the use of web openings can lead to significantly reduced shear capacities of LSBs. Keerthan and Mahendran [5,6] investigated the shear behavior and strength of LSBs with circular web openings using experimental and numerical studies. They developed suitable design equations for the shear capacity of LSBs with web openings by including both the enhanced buckling coefficient and the post-buckling strength in shear. Since the loss of shear capacity of LSBs was found to be as high as 60% [5] when the standard 127 mm web openings were used in 200x45x1.6 LSBs, the LSB manufacturers and researchers realized the need to improve the shear capacity of LSB with web openings. There are several methods used to improve the shear capacity of beams with web openings. The most practical method is to increase the web thickness. However, this may not be possible 2 with cold-formed steel sections as the thickness is governed by the manufacturing process. A cost effective way to improve the detrimental effects of a large web opening is to attach appropriate stiffeners around the web openings. Currently available cold-formed steel design standards [7,8] and steel framing standards [9] do not provide adequate guidelines to facilitate the design and construction of stiffeners for LSBs with large web openings. Hence experimental and numerical studies were conducted to develop the most effective and economical stiffener arrangement for LSBs with circular web openings subjected to shear. Details of the experimental study and the results are presented in [10]. In the numerical study, suitable finite element models of LSBs with stiffened web openings were developed to simulate their shear behaviour and capacity, and were validated by comparing their results with experimental results reported in [10]. A detailed parametric study was then undertaken using the validated finite element model to develop the optimum stiffening system for the shear capacity of LSBs with web openings. This paper presents the details of the development of finite element models of LSBs with stiffened circular web openings subject to shear, and the results. It includes a comparison of finite element analysis and experimental results as well as the details of the new optimum plate stiffener arrangement for LSBs. 2. Experimental Study of LSBs with Stiffened Web Openings This section presents the important details of 17 shear tests of simply supported back to back 200x45x1.6 LSBs under a three-point loading arrangement as shown in Figure 2. The main focus was on the use of plate stiffeners with varying fastening arrangements while two tests included the use of LSB stud stiffeners. Table 2 shows the details of test specimens while Figure 3 shows them with various stiffener arrangements. The first four specimens were not stiffened as seen in Table 2. In Specimen 5, the web openings were stiffened with plate stiffeners based on AISI’s [9] minimum stiffening requirements. The plate stiffener thickness was equal to that of 200x45x1.6 LSB while the plate stiffener extended 25 mm beyond the web opening edges. The plate stiffener was fastened to the LSB web with No.12 Tek screws at 25 mm spacing with an edge distance of 12.5 mm as shown in Figure 3 (a). This stiffener arrangement was defined as “Arrangement 1” (20 screws). Test Specimen 6 was assembled similar to Test Specimen 5, but with a total of 8 screws at 63.5 mm spacing along the plate stiffener edges with an edge distance of 12.5 mm (Figure 3 (b)). This screw fastening arrangement was defined as “Arrangement 2”. Since 3 the plate stiffeners with a thickness equal to the LSB web thickness (1.6 mm) did not restore the original shear capacity, two and three 1.6 mm plate stiffeners were used in Specimens 7 and 8, respectively. The plate stiffeners’ heights were also increased to match the clear LSB web height of 168 mm, which led to plate stiffener sizes of 152x168x3.2 mm and 152x168x4.8 mm. These two specimens were fastened using Arrangement 2 with screws located in the middle as implied by AISI [9] recommendations. Hence the edge distance along the horizontal edges was 16.5 mm instead of 12.5 mm while its spacing along the vertical edges was 67.5 mm instead of 63.5 mm due to the increased height of plate stiffeners. In Specimen 9, 200x45x1.6 LSB stud stiffeners were used with 102 mm web openings while 200x45x1.6 LSB stud stiffener and 177x168x1.6 mm plate stiffener were used in Specimen 10 with 127 mm web openings. In these tests, the stiffener heights were again increased to that of clear web. Arrangement 2 of eight screws was used in Specimen 9, but the edge distances and screw spacings were 16.5 mm and 67.5 mm. Improved Arrangement 3 with four additional screws in the diagonal direction (12 screws in total) was used in Specimen 10. The additional screws in the diagonal direction were located at 10 mm from the web opening edge. To increase the shear capacity further, 3 mm thick and 202 mm wide plate stiffeners were used for the full web height of Specimens 11 and 12 (Figures 3 (c) and (d)). As in Specimen 10, four additional screws were used to attach these 202x168x3.0 mm plate stiffeners along the diagonal direction. The screws were located in the middle on each side of the plate stiffener, which led to the edge distances of 25 mm and 16.5 mm and spacings of 67.5 mm and 76 mm in Test 11 (Figure 3 (c)). However, in Specimen 12, the edge distances were 12.5 mm and 16.5 mm (Figure 3 (d)). This stiffener arrangement of using 12 screws with a reduced edge distance of 12.5 mm was defined as “Arrangement 4”. In Specimen 13, 202x168x3.0 mm plate stiffeners were welded to LSBs to determine whether welding instead of screw-fastening would produce higher shear capacities. Specimen 14 was used to investigate the use of thicker (5 mm) and wider (227 mm) plate stiffeners for larger 127 mm web openings. Two 2.5 mm plates of 227x168 mm dimensions were screw fastened using 12 screws in Arrangement 3 as in Specimen 11. Specimen 15 was similar to Specimen 14, but the plate stiffeners were attached using screws located on a circular format as shown in Figure 3 (e) (Arrangement 5). In Specimen 16 the plate stiffener width was reduced to 177 mm based on AISC’s [9] recommendations while three 1.6 mm plate stiffeners were used. Specimen 17 with the smallest web opening of 60 mm was stiffened with only one 1.6 mm plate stiffener. 4 3. Finite Element Analyses of LSBs with Stiffened Web Openings 3.1. Description of Finite Element Model This section describes the development of suitable finite element models to investigate the ultimate shear behaviour and strength of LSBs with stiffened web openings. For this purpose, a general purpose finite element program, ABAQUS Version 6.7 [11], which has the capability of undertaking geometric and material non-linear analyses of three dimensional structures, was used. Finite element models were developed first with the objective of accurately simulating the actual test members’ physical geometry, loads, constraints and mechanical properties reported in the experimental study [10]. However, they were also developed for LSBs with other stiffener types such as transverse and sleeve stiffeners. Shear test results of back to back LSBs were similar to those obtained from single LSBs with a shear centre loading [4]. Hence in this study, finite element models of single LSBs with a shear centre loading and simply supported boundary conditions were used to simulate the shear tests of back to back LSB with stiffened web openings. The cross-section geometry of the finite element model was based on the measured dimensions, thicknesses and yield stresses of 17 tested LSBs reported in [10]. Table 2 gives the measured dimensions of the test beams made of 200x45x1.6 LSBs, where tw and d1 are the base metal thickness and the clear web height. The measured yield stresses of web, and inside and outside flange elements were 452.1, 491.3 and 536.9 MPa, respectively. For LSBs d1 is defined as the clear height of web instead of the depth of the flat portion of web measured along the plane of the web as defined in AS/NZS 4600 [7] for cold-formed channel sections. The reasons for this are given in [4]. Table 2 also provides the diameters of web openings (dwh) used in the models. Since the effect of including the rounded corners in LSBs on the shear buckling behaviour and capacity was found to be negligible [12], right angle corners were used in the finite element models used in this study. ABAQUS has several element types to simulate the shear behaviour of beams with stiffened web openings. The shell element in ABAQUS called S4R5 was selected as it has the capability to simulate the shear behaviour of thin steel beams such as LSBs. This element is 5 thin, shear flexible, isometric quadrilateral shell with four nodes and five degrees of freedom per node, utilizing reduced integration and bilinear interpolation scheme. R3D4 rigid body elements were used to simulate the restraints and loading in the finite element models of LSBs with stiffened web openings. The R3D4 element is a rigid quadrilateral with four nodes and three translational degrees of freedom per node. Finite element modelling was undertaken using MD PATRAN R2.1 pre-processing facilities using which the model was created and then submitted to ABAQUS for the analysis. The results were also viewed using MD PATRAN R2.1 post-processing facilities. In order to fully understand the shear behaviour of LSBs with stiffened web openings, several important issues were considered when deciding these parameters such as the ratio of the depth of web openings to clear height of web (dwh/d1), types and thicknesses of stiffeners, number of self-drilling Tek screws used to fasten the stiffeners to the web and their spacing. 3.2. Finite Element Mesh In finite element analyses (FEA), selection of mesh size and layout is critical. It is desirable to use as many elements as possible in the analysis. However, such an analysis will require excessive computing time and resources. In this research, adequate numbers of elements were chosen for both flanges and web based on detailed convergence studies to obtain sufficient accuracy of results without excessive use of computing time. Convergence studies showed that an element size of 5mm x 5mm provided an accurate representation of shear buckling and yielding deformations. An element length of 5 mm in the longitudinal direction was found to provide suitable accuracy for all the LSB sections. In order to get accurate results, Paver Mesh was applied around the LSB web and stiffener openings. The geometry and finite element mesh of a typical LSB with stiffened web openings is shown in Figure 4. Plate and LSB stud stiffeners were connected to the web elements of LSB using screw fasteners as shown in Figure 5 (c). These stiffeners were modelled using 5mm x 5mm S4R5 elements and were connected to the web of LSB using Tie MPC. Tie MPC makes the global displacements and rotations as well as all other active degrees of freedom equal at the two connected nodes. If there are different degrees of freedom active at these nodes, only those in common will be constrained. This Tie MPC was used to simulate all the screw connections used in installing the stiffeners. 6 3.3. Material Model and Properties of LSB The ABAQUS classical metal plasticity model was used in all the analyses. This model implements the von Mises yield surface to define isotropic yielding, associated plastic flow theory, and either perfect plasticity or isotropic hardening behaviour. When the measured strain hardening in the web element was used in FEA, the shear capacity improvement was less than 1% [4]. Hence it was not considered in our analyses. Tensile coupon tests were conducted for the batch of LSBs from which the test beam specimens were taken. Tensile coupons taken from the web and inside and outside flanges of 200x45x1.6 LSB sections were tested to determine the average yield stresses reported earlier. These measured yield stresses were used in FEA. Since the plate stiffeners were taken from the LSB web, the measured web yield stresses were used in the modeling of plate stiffeners. The LSB stud stiffeners used in the tests were taken from the same batch of LSBs. Hence the measured yield stresses of web, inside and outside flange elements of LSBs were used in the modeling of LSB stud stiffeners. The elastic modulus and Poisson’s ratio were taken as 200,000 MPa and 0.3, respectively. 3.4. Loads and Boundary Conditions Simply supported boundary conditions were implemented in the finite element models of LSBs with stiffened web openings. They were used at the supports to provide the following requirements: Simply supported in-plane - Both ends fixed against in-plane vertical deflection but unrestrained against in-plane rotation, and one end fixed against longitudinal horizontal displacement. Simply supported out-of-plane - Both ends fixed against out-of-plane horizontal deflection, and twist rotation, but unrestrained against minor axis rotation. In order to provide simply supported conditions for the shear panel, the following boundary conditions were employed. x = 1 Mid-span loading point: ux = 1 x = 1 uy = 1 y = 0 uy = 0 y = 0 uz = 1 z = 0 uz = 1 z = 0 Left and right supports: ux = 0 7 Note: ux, uy and uz are translations and θx, θy and θz are rotations in the x, y and z directions, respectively. 0 denotes free and 1 denotes restrained. The vertical translation was not restrained at the loading point. Figure 5 shows the applied loads and boundary conditions of the model. Single point constraints and concentrated nodal forces were used in the finite element models to simulate the experimental boundary conditions and applied loads as closely as possible. In order to prevent twisting, the applied point load and simply supported boundary conditions were applied at the shear centre using rigid body reference node. Shear test specimens included a 10 mm thick and 75 mm wide plate at each support to prevent lateral movement and twisting of the section. These stiffening plates were modelled as rigid bodies using R3D4 elements. In ABAQUS [11] a rigid body is a collection of nodes and elements whose motion is governed by the motion of a single node, known as the rigid body reference node. The motion of the rigid body can be prescribed by applying boundary conditions at the rigid body reference node. Hence simply supported boundary conditions were applied to the node at the shear centre in order to provide an ideal pinned support. 3.5. Fastener Modelling Fasteners play an important role in the shear behaviour of LSBs with stiffened web openings. This study assumed that screw fastener failure is unlikely to occur as confirmed by our experimental study [10]. Considering this observation, the screw fasteners connecting the stiffeners to the LSB were not explicitly modelled. Instead they were simulated using Tie MPCs, which make all active degrees of freedom equal on both sides of the connection. The web side plates at the supports were connected using high strength steel bolts (M16 8.8/S) to avoid bolt failures during testing. Our shear tests [10] confirmed that there were no bolt or plate failures. Therefore these web side plates were modelled as rigid bodies using R3D4 elements. 3.6. Initial Geometric Imperfections The local plate imperfections in LSBs were found to be less than the currently accepted fabrication tolerance of d1/150 [4]. However, the fabrication tolerance limit of d1/150 was 8 used in the numerical modelling of LSBs as the preliminary analyses showed that the effect of local plate imperfection (from d1/300 to d1/150) on the shear capacity of LSB with stiffened web openings was small. The critical imperfection shape was introduced by ABAQUS *IMPERFECTION option with the shear buckling eigenvector obtained from an elastic buckling analysis. 3.7. Residual Stresses The residual stresses in the LSB sections produced using the dual electric resistance welding and cold-forming processes have unique characteristics. The residual stress models of conventional steel sections are therefore not suitable for LSB sections. Details of the residual stress tests and an idealized residual stress model developed for computer analyses are presented in [13]. Preliminary FEA showed that the effect of residual stresses on the shear capacity of LSBs without openings is less than 1% [14]. Therefore the effect of residual stresses on the shear capacity of LSBs with stiffened web openings is also likely to be very small. It was thus decided to neglect the residual stresses in the FEA. 3.8. Analysis Methods Both elastic buckling and nonlinear static analyses were used. Elastic buckling analyses were used to obtain the eigenvectors for the inclusion of initial geometric imperfections. Nonlinear static analyses, including the effects of large deformation and material yielding, were used to investigate the shear behaviour of LSBs until failure. The RIKS method in ABAQUS was also included in the nonlinear analyses. It is generally used to predict geometrically unstable nonlinear collapse of structures. In using the RIKS method in this study, the solution of nonlinear equations was achieved by the Newton-Raphson method, in conjunction with a variable arc-length constraint to trace the instability problems associated with nonlinear buckling of beams. Following parameters were used in the non-linear analyses of LSB with stiffened web openings: Maximum number of load increments = 100, Initial increment size = 0.01, Minimum increment size = 0.000001, Automatic increment reduction enabled, and large displacements enabled. 9 4. Validation of Finite Element Models of LSB with Stiffened Web Openings The accuracy of the developed finite element models of LSBs with stiffened web openings was investigated by comparing the non-linear analysis results with those obtained from the shear tests of LSBs with stiffened web openings [10]. Seventeen finite element models were constructed using the material and geometric properties from experimental testing (Table 2) and the results were compared with test results, with particular attention given to the ultimate load, load-deflection curves and failure modes. These comparisons were intended to establish the validity of the shell element model in the modelling of initial geometric imperfections and shear deformations, and associated material yielding. The accuracy of local plate imperfection magnitude and finite element mesh density was also established. Table 2 presents the ultimate shear capacity results from FEA and a comparison of these results with the corresponding experimental results. The mean and COV of the ratio of test to FEA ultimate shear capacities are 0.97 and 0.021. This indicates that the finite element model developed in this study is able to predict the ultimate shear capacity of LSBs with stiffened web openings with very good accuracy. In the experimental study, five screw fastening arrangements were considered as shown in Figure 3 [10]. Figure 6 shows the FEA results in the form of load versus deflection for 200x45x1.6 LSB with 127 mm stiffened web openings (Test Specimen 14) while Figures 7 (a) and (b) show them for 200x45x1.6 LSB with 102 mm stiffened web openings (Test Specimens 11 and 12) and compare them with corresponding experimental results. Figures 8 and 9 show the shear failure modes of Test Specimens 11 and 12, respectively, while Figures 10 (a) to (c) show the failure modes of Test Specimens 13, 15 and 17, respectively. The shear capacity of Test specimen 13 was considerably increased due to the additional welded plate stiffener. Hence it failed due to combined shear and bending as shown in Figure 10 (a). These figures demonstrate a good agreement between the results from FEA and experiments and confirm the adequacy of the developed finite element model in predicting the ultimate load, deflections and failure modes of LSBs with stiffened web openings. 5. Finite Element Analyses of LSBs with Different Types of Stiffeners The overall objective of this research is to develop the most effective and economical stiffening arrangements for LSBs with web openings subjected to shear. In this section, the 10 use of different types of stiffeners, namely, plate stiffeners, LSB stud stiffeners, sleeve stiffeners and transverse stiffeners, was investigated by using finite element analyses. 5.1. Transverse Stiffeners Transverse stiffeners are generally used in hot-rolled steel sections and are welded to the web. Welding in cold-formed steel sections is difficult and hence this stiffener is not a practical option. However, it was investigated due to its popularity in traditional steel design. Transverse stiffeners improved the shear strength by reducing the aspect ratio of the web panel. The geometry and finite element mesh of a typical LSB with transverse stiffeners is shown in Figure 4 (b), which shows that two steel plates are attached to the web on either side of the opening at 20 mm from the edge of the web opening. Transverse stiffeners can be welded to either the web only or both web and flange elements. Finite element analyses conducted to determine the effect of this variation showed that additional restraint provided by welding the transverse stiffeners to the flanges gave only a 4% increase in the shear capacity. Hence welding the transverse stiffeners to the web of LSBs is considered sufficient. In order to investigate the effect of the thickness of transverse stiffeners on the shear capacity of LSB with web openings, FEA of 200x45x1.6 LSBs with 60 and 127 mm web openings were undertaken with varying transverse stiffener thicknesses. Figure 11 shows the failure modes of LSBs with 3 mm transverse stiffeners while Figure 12 shows the FEA results in the form of shear capacity of LSBs versus thickness of transverse stiffeners. Here the transverse stiffeners were only welded to the web element of LSB. Table 3 shows the shear capacities of LSBs with 5 mm transverse stiffeners. In this table, the shear capacities of LSBs without and with web openings and stiffened web openings are referred to as Vv, Vnl and Vnls, respectively. These results show that the thickness of the transverse stiffeners does not play a significant role on the shear capacity of LSB with web openings (see Figure 12). This is due to the fact that the transverse stiffeners mainly reduces the aspect ratio and does not contribute to increasing the shear area of LSB with web openings. Both Figure 12 and Table 3 show that transverse stiffeners are not adequate to restore the shear strengths of LSBs with larger web openings (127 mm). Hence the use of transverse stiffeners is not recommended for LSBs with large web openings. 11 5.2. Sleeve Stiffeners The sleeve stiffener was proposed based on its ability to restrain the free edge of the web opening. This proposal was adopted from conventional cold-formed steel designs where such stiffeners are used to reduce the local buckling effects of free edges. This stiffener is likely to have a greater effect on the buckling strength of LSBs than the ultimate shear strength. However, increasing the shear buckling capacity is also important. The geometry and finite element mesh of a typical LSB with sleeve stiffeners is shown in Figure 4 (c). In comparison with other stiffeners, the sleeve stiffener is less practical as it requires the sleeve to be formed during manufacturing or welded to the web. However, welding thin cold-formed steel sections is to be avoided as it can be detrimental in terms of heat effects and residual stresses. Hence the use of sleeve stiffeners may complicate the fabrication phase of LSB joists and bearers. The thickness and length of sleeve stiffener that affects its rigidity were considered as possible variables in FEA. The sleeve stiffener thickness was considered to be the same as the LSB web thickness. However, its length was varied (10, 20 and 25 mm) to determine its effect on the shear capacity of 200x45x1.6 LSBs with 60 mm web openings. Table 4 shows the shear capacity results, which show that the sleeve stiffener length (10 to 25 mm) did not play a significant role on the shear capacity of LSB with web openings. Table 5 shows the shear capacities of LSBs with varying web opening sizes and 20 mm sleeve stiffeners, which indicate that sleeve stiffeners are not adequate to restore the shear strengths of LSB with larger web openings (102 and 127 mm). Hence the use of sleeve stiffeners is not recommended for LSBs with large web openings. Figure 13 shows the failure mode of 200x45x1.6 LSB with 60 mm web openings and 20 mm sleeve stiffeners. 5.3. LSB Stud Stiffeners The LSB stud stiffeners are LSBs with web openings that are attached to the web. The LSB stud stiffener is attached to the web around the opening by fastening with No.12 Tek screws. It is capable of both reducing the aspect ratio and increasing the shear area of LSB with web openings. The geometry and finite element mesh of a typical LSB with LSB stud stiffener is shown in Figure 4 (d). 12 Effect of LSB stud stiffeners on the shear capacity of LSBs with web openings was investigated using FEA and Tests 9 and 10, and the results are shown in Table 2. As shown by the experimental study, finite element analyses also showed that LSB stud stiffeners were able to obtain about 80% of the shear capacity of LSB without web openings (52 kN) in the case of 102 mm web openings. Since the thickness of LSB stud stiffener is equal to the web thickness, LSB stud stiffeners are not adequate to restore the shear strengths of LSB with large web openings. Hence LSB stud stiffeners are not recommended for LSBs with large web openings. 5.4. Plate Stiffeners Plate stiffeners are plates with web openings that are attached to the web (see Figures 4 (a) and 5). They are attached to the web around the openings by fastening with No.12 Tek screws. In contrast to the other types of stiffeners, the plate stiffener is capable of both reducing the aspect ratio and increasing the shear area of LSB with web openings. Our experimental studies [10] showed that plate stiffeners were the best stiffener for LSBs with web openings. However, the number of shear tests was limited. Hence in order to determine the optimum plate stiffener sizes, finite element models of LSBs with web openings stiffened with plate stiffeners in shear were developed to simulate their shear behaviour and strength. They were then validated by comparing their results with available test results (Test Specimens 5 to 17) and used in a parametric study (see Section 5.5). In Test Specimen 5, plate stiffener dimensions and screw fastening arrangement were adopted based on AISI [9] (Arrangement 1). However, FEA and experimental results showed that it only reached about 65% of the shear capacity of LSB without web openings (34.8 and 33.6 kN vs 52 kN). Hence FEA and test results showed that the plate stiffeners based on AISI [9] recommendations are not adequate to restore the shear strengths of LSBs. Test Specimens 5 and 6 with 152x152x1.6 mm plate stiffeners were considered to investigate the effect of different screw spacings (Arrangements 1 and 2). Both FEA and tests showed that using more screws (20 versus 8 screws) increased the shear capacity of LSBs by only 5% as shown in Table 2. Test Specimens 7 and 8 were conducted to investigate the effect of using thicker (3.2 and 4.8 mm) plate stiffeners of full web height (152x168 mm). In this case, both FEA and test results showed that the shear capacities increased considerably (Table 2). 13 Tests 11 and 12 of LSBs with 102 mm web openings were considered with 3 mm plate stiffeners that were 202 mm wide (50 mm on either side of the edge of web opening) and 168 mm height (full web height). Both FEA and Test results showed that thicker and wider stiffeners of full web height as used in these tests were able to fully restore the shear capacity of LSBs (56.0 and 55.0 versus 54 kN in FEA and 54.5 and 52.5 kN vs 52 kN in tests). Test and FEA results also showed that Arrangement 4 with reduced edge distances of 12.5 mm led to a small reduction in the shear capacity. Hence screw fastening Arrangement 3 used in Test 11 is recommended. Test Specimen 13 with welded plate stiffeners failed at a higher load due to combined shear and bending as shown in Figure 10. Both FEA and test results (66.5 and 67 kN) showed that the shear capacity of LSB with web openings can be improved to levels beyond the shear capacity of a solid LSB section (54 and 52 kN) by welding suitable plate stiffeners. Generally horizontal, vertical and inclined stiffeners are welded to the web around the openings in hotrolled sections. Our FEA and test results show that plate stiffeners can also be welded to improve the shear capacity of cold-formed sections with large web openings. However, welding is not recommended to avoid excessive heat and residual stress effects on thinwalled cold-formed steel sections. Test Specimens 14 and 15 with larger 127 mm web openings were investigated to determine the required stiffener thickness. Five mm plate stiffeners that were 227 mm wide (50 mm on either side of the edge of web opening) and 168 mm height (full web height) were used. Both FEA and test results showed that these plate stiffeners fastened using Arrangements 3 and 5 were almost able to restore the full shear capacity (93% of the shear capacity of LSB without web openings). In this case, the depth of web opening to the clear height of web ratio (d wh/d1) is 0.75, which is more than the limiting value of 0.7 given in AS/NZS 4600 [7]. Hence it is unlikely that such large openings will be used in practice. Arrangement 5 (Figure 3(e)) is architecturally appealing, however, it is not recommended due to additional installation costs. Test Specimen 16 included 177x168x4.8 mm plate stiffeners, and the shear capacity from FEA was only 36.8 kN due to the use of plate stiffeners with reduced width (177 mm versus 227 mm). However, for Test Specimen 17 with 60 mm web openings, 1.6 mm thick plate stiffeners of 160x168 mm were able to restore the original shear capacity (52.5 and 50.5 vs 14 52 kN). Both FEA and test results show that AISI’s [9] recommendation for the minimum width of plate stiffeners to be based on 25 mm on each side of web openings is not adequate. This research has shown that the plate stiffeners should extend 50 mm beyond all the edges of web openings. In summary, FEA and test results show that plate stiffeners with dimensions equal to web opening width and depth plus 100 mm, screw fastened using Arrangement 3, are needed to restore the original shear strength of 200x45x1.6 LSBs. Their thicknesses have to be a minimum of 1.6 mm and 3.0 mm for these LSBs with 60 mm and 102 mm web openings, respectively. However, detailed parametric studies are needed to determine these parameters for other LSB sections. Details of these parametric studies are given next. 5.5. Parametric Study of LSBs with Stiffened Web Openings (Plate Stiffeners) In this parametric study based on validated finite element models, five LSB sections, 150x45x1.6 LSB, 150x45x2.0 LSB, 200x45x1.6 LSB, 300x75x2.5 and 300x75x2.0 LSB, with four web opening sizes (60, 102, 119 and 127 mm), were selected with an aim to determine the optimum plate stiffener thickness that increases the shear capacity to that of LSB without web openings in each case. The plate stiffener thickness was varied from 1.6 to 8 mm in the models with an aspect ratio of 1.5. The ultimate shear capacities obtained for varying ratios of dwh/d1 are given in Tables 6 (a) to (d). Figure 14 shows the FEA results in the form of shear capacity of LSB with 102 mm stiffened web openings versus number of screws while Figure 15 shows the FEA results in the form of shear capacity of LSB with stiffened web openings versus stiffener thickness for 200x45x1.6 LSB. Figure 14 indicates that plate stiffeners with 12 screws (Arrangement 3) provide the optimum screw fastening arrangement. Figure 15 (b) shows that the optimum thickness of plate stiffener is 3.0 mm for 200x45x1.6 LSB with 102 mm web openings. Similarly, Figures 15 (a) and (c) show that 1.6 mm and 4 mm are the optimum plate stiffener thicknesses for 200x45x1.6 LSB with 60 mm and 119 mm web openings, respectively. Experimental results also confirmed that plate stiffeners with Arrangement 3 (12 screws) provided the optimum arrangement and 1.6 mm and 3.0 mm were the optimum stiffener thicknesses for 60 mm and 102 mm web openings, respectively. Figures 16 (a) to (c) show the FEA results in the form of shear capacity of LSB versus stiffener thickness for 300x75x2.5 LSB and 300x75x2.0 LSB 15 while Figure 17 shows these results for 150x45x1.6 LSB and 150x45x2.0 LSB. The optimum plate stiffener thickness in each case can be obtained from these figures. Table 7 shows the optimum plate stiffener thicknesses for the different LSB sections and web opening sizes. Table 7 and Figure 18 show that 5 mm plate stiffeners fastened using Arrangements 3 were almost able to restore the full shear capacity (93%) of 200x45x1.6 LSB with 127 mm web openings. In this case, the depth of web opening to the clear height of web ratio (dwh/d1) is 0.75, which exceeded the limiting value of 0.7 in AS/NZS 4600 [7]. In order to obtain the full shear capacity, the depth of web opening to the clear height of web ratio (dwh/d1) was limited to 0.7 based on FEA results. 6. Optimum Stiffener Systems for LSB with Web Openings Subjected to Shear In this section the optimum plate stiffener system was proposed based on the numerical and experimental results reported in the previous sections. It is proposed that the width of the optimum plate stiffener is dwh+100 mm and its height is lesser of clear web height (d1) and dwh+100 mm. These dimensions have been chosen for practicality and allow a distance of 50 mm between the free edges of the web opening and the plate stiffener. This optimum stiffener arrangement is an improvement of the recommendations of AISI [9] and Sivakumaran [15]. Table 8 shows the shear capacities of LSBs using optimum plate stiffener arrangement (Arrangement 3 with No.12 screws). It shows that LSBs were able to restore the original shear strength when the optimum stiffener arrangements were used around the web openings. Keerthan and Mahendran [14] proposed suitable predictive equations for the shear capacity of LSB without web opening (Vv). These equations can be used for LSBs with stiffened web openings when the optimum stiffening system proposed here is used around the web openings. Keerthan and Mahendran’s [14] design equations are also given in Appendix A of this paper for the sake of completeness. Figure 19 shows the plot of optimum plate stiffener thickness to web thickness ratio (tSiff/tw) versus depth of web opening to clear height of web (dwh/d1). Figure 20 shows the schematic diagram of optimum plate stiffener arrangement for LSBs with web openings. Suitable equations are also proposed to predict the sizes of optimum plate stiffeners (Equations 1 to 3). Equations 1 to 3 were developed so that they predict the required plate stiffener thickness (tStiff) conservatively and thus ensure a safe design of LSBs with stiffened web openings. 16 d t Stiff 3.52 wh d1 0.035t w 0.24 d wh 0.70 d1 wStiff d wh 100 (1) (2) hStiff Lesser of d1 and d wh 100 (3) where wstiff x hstiff = Width x Height of plate stiffener 7. Conclusions This paper has presented a detailed investigation into the shear behaviour of LSBs with stiffened web openings using finite element analyses. Suitable finite element models were developed and validated by comparing their results with experimental test results. The developed nonlinear finite element model was able to predict the shear capacities of LSBs with stiffened web openings and associated deformations and failure modes with very good accuracy. Both finite element analysis and experimental results show that the plate stiffeners based on the recommendations of AISI [9] are not adequate to restore the shear strengths of LSBs with web openings. New plate stiffener systems with optimum sizes and screwfastening arrangements have been proposed to restore the shear capacity of LSBs with web openings based on both experimental and numerical parametric study results. It was found that the width of the optimum plate stiffener is dwh+100 mm and its height is lesser of the clear web height (d1) and dwh+100 mm while the associated screw fastening is to be based on Arrangement 3 with 12 screws. Suitable predictive equations have been proposed for LSB designers to determine the optimum plate stiffener thickness as a function of dwh/d1. Acknowledgements The authors would like to thank Australian Research Council and OneSteel Australian Tube Mills for their financial support, and the Queensland University of Technology for providing the necessary facilities and support to conduct this research project. They would also like to thank Mr Christopher Robb and Mr Jamie Scott-Toms for their valuable assistance in performing the shear tests of stiffened LSBs. The authors would also like to thank Mr Ross 17 Dempsey, Manager - Research and Testing, OneSteel Australian Tube Mills, for his technical advice and support to this research project. References [1] LiteSteel Technologies (LST), OneSteel Australian Tube Mills, Brisbane, Queensland, viewed 10 March, 2009, <www.litesteelbeam.com.au>. [2] Pokharel, N. and Mahendran, M. (2006), Preliminary Investigation into the Structural Behaviour of LSB Floor Joists Containing Web Openings, Research Report, Queensland University of Technology, Brisbane, Australia. [3] OneSteel Australian Tube Mills, (OATM) (2008), Design of LiteSteel Beams, Brisbane, Australia. [4] Keerthan, P. and Mahendran, M. (2010), Experimental Studies on the Shear Behaviour and Strength of LiteSteel Beams, Engineering Structures, Vol. 32, pp. 3235-3247. [5] Keerthan, P. and Mahendran, M. (2012), Shear Behaviour and Strength of LiteSteel Beams with Web Openings, Journal of Advances in Structural Engineering, Vol. 15, pp.197– 210. [6] Keerthan, P. and Mahendran, M. (2012), New Design Rules for the Shear Strength of LiteSteel Beams with Web Openings, Journal of Structural Engineering, ASCE, In Press. [7] Standards Australia/Standards New Zealand (SA) (2005), Australia/New Zealand Standard AS/NZS4600 Cold-Formed Steel Structures, Sydney, Australia. [8] American Iron and Steel Institute (AISI) (2007), North American Specification for the Design of Cold-formed Steel Structural Members, AISI, Washington, DC, USA. [9] American Iron and Steel Institute (AISI) (2004), Supplement to the Standard for ColdFormed Steel Framing – Prescriptive Method for One and Two Family Dwellings, 2001 Edition, American Iron and Steel Institute, Washington, DC, USA. 18 [10] Mahendran, M. and Keerthan, P. (2012), Experimental Studies of the Shear Behavior and Strength of LiteSteel Beams with Stiffened Web Openings, Research Report, Queensland University of Technology, Brisbane, Australia. [11] Hibbitt, Karlsson and Sorensen, Inc. (HKS) (2007), ABAQUS User’s Manual, New York, USA. [12] Keerthan, P. and Mahendran, M. (2010), Elastic Shear Buckling Characteristics of LiteSteel Beams, Journal of Constructional Steel Research, Vol. 66, pp. 1309-1319. [13] Seo, J.K, Anapayan, T and Mahendran, M. (2008), Imperfection Characteristic of MonoSymmetric LiteSteel Beams for Numerical Studies, Proc. of the 5th International Conference on Thin-Walled Structures, Brisbane, Australia, pp. 451-460. [14] Keerthan, P. and Mahendran, M. (2011), New Design Rules for the Shear Strength of LiteSteel Beams, Journal of Constructional Steel Research, Vol. 67, pp. 1050–1063. [15] Sivakumaran, K.S., (2008), Reinforcement Schemes for CFS Joists Having Web Openings, Research Report, Department of Civil Engineering, McMaster University, Ontario, Canada. 19 Appendix A: Proposed Design Equations for the Shear Strength of LSBs [14] v yw d1 tw for v i 0.25 yw i for EkLSB f yw (Shear yielding) EkLSB d1 EkLSB 1.508 f yw tw f yw (Inelastic shear buckling) v e 0.25 yw e (A-1) for d1 EkLSB (Elastic shear buckling) 1.508 tw f yw (A-2) (A-3) where where yw 0.6 f yw i 0.6 Ek LSB f yw e 0.905 Ek LSB d1 t w d1 tw 2 kLSB kss 0.87(ksf kss ) For LSBs k ss 4 5.34 a d1 2 k ss 5.34 k sf (A-4) for a 1 (A-5) d1 4 for a 1 a d1 2 (A-6) d1 5.34 2.31 3.44 8.39a d1 for 2 a d1 a d1 ksf 8.98 5.61 a d 1 2 1.99 a 1 3 for a d1 d1 a 1 d1 (A-7) (A-8) where kss, ksf = shear buckling coefficients of plates with simple-simple and simple-fixed boundary conditions. 20 Direct Strength Method (DSM) v 1 yw ≤ 0.815 v 0.815 0.815 0.251 yw v 1 1 2 0.251 2 yw (A-9) 0.815< ≤ 1.23 (A-10) > 1.23 (A-11) where yw 0.6 f yw k 2E cr LSB 2 12 1 (A-12) tw d1 2 yw d 0.815 1 cr tw (A-13) f yw EkLSB (A-14) 21