See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/285994139 Optimum Joint Detail for a General Cold-Formed Steel Portal Frame Article in Advances in Structural Engineering · September 2012 DOI: 10.1260/1369-4332.15.9.1623 CITATIONS READS 15 938 3 authors: Andrzej M Wrzesien James B.P. Lim University of the West of Scotland University of Auckland 25 PUBLICATIONS 103 CITATIONS 218 PUBLICATIONS 1,681 CITATIONS SEE PROFILE D.A. Nethercot Imperial College London 370 PUBLICATIONS 6,181 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Composite Cold-Formed Steel - Wood-based Flooring Systems View project Stability in Elastic-plastic States of Columns View project All content following this page was uploaded by Andrzej M Wrzesien on 06 April 2017. The user has requested enhancement of the downloaded file. SEE PROFILE OPTIMUM JOINT DETAIL FOR A GENERAL COLDFORMED STEEL PORTAL FRAME A.Wrzesiena, James B.P. Limb,*, D.A. Nethercotc a Department of Civil Engineering, The University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, U.K. b SPACE, David Keir Building, Queen's University Belfast, BT9 5AG, U.K. c Department of Civil and Environmental Engineering, Imperial College, London SW7 2BU, U.K. Synopsis In cold-formed steel portal framing systems that use bolted moment connections, formed through brackets, for the eaves and apex joints, it is well-known that the joints are semi-rigid, have finite connection-lengths and limited moment capacity. For such frames, it is therefore necessary for these joint effects to be taken into account when conducting frame design and analysis. However, as the semi-rigidity and the finite connection-lengths of each joint influence the bending moment distribution as well as the deflected profile of the frame, the joint detail for the eaves and the apex should not be designed independently of the frame. In this paper, a method of determining the optimum joint detail is described. It is demonstrated that careful selection of the joint detail can result in as much as a 25% increase in efficiency of the frame. Including joint effects explicitly into the design process provides better opportunities to devise the most appropriate balance between joints and member properties and thus reduce material use and construction costs. Keywords Cold-formed steel sections, portal frames, semi-rigid joints, serviceability limit states, optimisation criterions, rotational stiffness. * Corresponding author. Tel.: +44(0)28 9097 5456. E-mail address: [email protected] 1 Notation aB length of bolt-group bB breadth of bolt-group bec bB pertaining to eaves to column connection ber bB pertaining to eaves to rafter connection db diameter of bolt dh diameter of bolt hole EA axial rigidity of back-to-back channel used for column and rafter members of portal frame EI flexural rigidity of back-to-back channel used for column and rafter members of portal frame ff height to apex less height to eaves hf height to eaves of portal frame kab rotational stiffness of apex bracket kar rotational stiffness of apex to rafter connection kb bolt hole elongation stiffness determined from the initial gradient of load versus bolt hole elongation curve kB rotational stiffness of bolt-group keb rotational stiffness of eaves bracket kec rotational stiffness of eaves to column connection ker rotational stiffness of eaves to rafter connection lar effective length of bracket pertaining to apex to rafter connection lec effective length of bracket pertaining to eaves to column connection ler effective length of bracket pertaining to eaves to rafter connection Lf span of portal frame S bay spacing Smax maximum permissible bay spacing sf length of rafter of portal frame t thickness of plate f pitch of portal frame 2 1 Introduction Cold-formed steel portal frames (Fig.1) can be a viable alternative to conventional hot-rolled steel portal frames for low-rise commercial, light industrial and agricultural buildings with spans of around 12m. The advantages of constructing a portal framing system using cold-formed steel sections instead of conventional hotrolled sections include: (1) sections delivered to site that have been marked, cut to length, and punched at the factory to design specifications (2) smaller foundations (3) maintenance-free pre-galvanised cold-formed steel sections that do not require painting to prevent rusting (4) reduced transportation costs due to efficient stacking of cold-formed steel sections (5) reduced acquisition costs as the cold-formed steel sections used for the secondary members can be purchased from the same manufacturer/supplier (6) frames erected manually by semi-skilled labour without the need for an on-site crane. Over the past three decades, various researchers have undertaken tests on joint arrangements that can be used for the eaves and the apex joints of cold-formed steel portal framing systems. Table 1 summarises the joint tests reported in the literature, including the moment capacity of the cold-formed steel sections being connected, and the number of components and fasteners required to form the joints. In chronological order, a brief description of each joint arrangement is given in Section 1.1 below. However, while the joints tests reported in the literature review are mainly concerned with determining joint detail that increase the moment capacity of the joints, the majority of the joints are semi-rigid. In this paper, it will be shown that in the case of cold-formed steel portal frames, in order to obtain optimum frame performance, the joint detail for the eaves and apex should not be designed independently of the frame, and that taking joints effects explicitly into the design process provides better opportunities to devise the most appropriate balance between joints and member properties and thus reduce material use and construction costs. 1.1 Literature review The earliest tests reported in the literature on cold-formed steel portal frame joints are those by Baigent and Hancock (1982). Details of this joint are given in 3 Fig.2. As can be seen, the joints were formed through the web of the channel-sections used for column and rafter members. The moment capacity of the channel-sections being connected was 9.19 kNm. The thickness of the channel-sections was 1.86 mm while the thickness of the plate used to connect the joints was 12 mm. Due to the use of high-tensile grip bolts, the joints could be considered as being rigid. The next set of tests reported were those by Kirk (1986) on the Swagebeam portal framing system. These tests were undertaken by Professor Bryan at Salford University. Fig.3 shows details of the joints. As can be seen, back-to-back channel sections were used for the column and the rafter members. The joints were formed through back-to-back brackets bolted between the webs of the channel-sections. The moment capacity of the back-to-back channel-sections was 32 kNm; the thickness of the channel-sections was 2.4 mm and the thickness of each bracket was 3.0 mm. The primary innovation was that the joints could be formed through the swages rolled in the brackets which connected with matching swages in the webs of the channelsections. This produced stiff connections. Mäkeläinen and Kankaanpää (1996) described tests on a portal framing system constructed from back-to-back sigma sections connected though the web via brackets. To provide additional stiffness to the frame, a tie bar (double angle 50 x 50 x 2.5 mm) was bolted to both eaves brackets (Fig.4a). The depth of the sections used for the tests were 250 mm, 300 mm, and 400 mm while the thicknesses of 2.5 mm and 3.0 mm were considered. Fig.4 shows details of the joint brackets. These included a single plate of thicknesses of 8 mm, 10 mm and 12 mm (see Fig.4a), four cold-formed plates with a thickness of 2.5mm each (see Fig.4b), and four cold-formed plates with two outer plates outwardly lipped (see Fig.4c). Although the moment capacities of the sections were not provided, similar compound members made from back-to-back standard sigma sections of 300 mm deep, 75 mm wide, and 3.0 mm were calculated to have a moment capacity of 77 kNm. Chung and his co-workers (Chung and Lau (1999), Wong and Chung (2002), Yu et al (2005)) and Lim and Nethercot (2002, 2003a, 2003b, 2004a, 2004b) independently reported tests on an arrangement where the joint was formed through back-to-back brackets bolted between the webs of the channel-sections being connected. In the tests described by Chung, the maximum moment capacity of the sections was 17.88 kNm, while that of Lim and Nethercot was 82.8 kNm. Fig.5a to Fig.5d shows the different shapes of the brackets studied by Chung. In the case of the 4 joint details shown in Fig.5c and Fig.5d, the joints were tested twice. In the first stage, the joints were formed through a hot-rolled steel single gusset plates of thickness 6mm. In the second phase, the joints were formed through two back-to-back coldformed steel brackets, each 2.5mm thick and with lip stiffeners along the cathetus and hypotenuse of the bracket respectively (Fig.5c and Fig.5d). Unlike Chung, the joints tested by Lim and Nethercot (Fig.6) isolated failure of the brackets from that of the channel-sections. Having ensured that the brackets themselves would not fail, research was focused on the strength and stiffness of the channel-sections, as influenced by the bolt-group size. Mills and LaBoube (2004) conducted experimental studies on joints currently used in Australia for cold-formed steel portal frame sheds. The joints were constructed from single channel-sections with a moment capacity of 10.84 kNm. Popular joints included an end plate connection bolted to the column and welded to the rafter (Fig.7a), and a mitred joint (Fig.7b). Self-drilling screws were used as an alternative to conventional bolting. A similar arrangement for the apex joint was also studied, in which double lipped channel-sections were used as the gusset plate and screwed back-to-back to the rafters. Dubina et al (2004) described three different type of joints (Fig.8). As can be seen from Fig.8a and Fig.8c, the channel-sections were bolted only through the web of welded I-section brackets (KIS, KIP) and spaced gussets bracket (KSG). In second variant, bolts were located both on the web and on the flange (Fig.8b) of I-section bracket (KIS) and I-section bracket with plate bisector (KIP). The moment capacity of the channel-sections being connected was 117.8 kNm. It should be noted that unlike Chung and Lau (1998), the joint was formed through hot-rolled steel sections instead of back-to-back brackets. However, as the strength of the hot-rolled steel sections is much greater than that of the channel-sections, the behaviour of the joints is dominated by that of the channel-sections. Dundu and Kemp (2006) conducted research on single channels connected back-to-back (Fig.9). Such an arrangement is similar to that of Mills and LaBoube (2004). Dundu and Kemp were concerned with the development of a plastic hinge, and so concentrated on the ductility of the joints. A novel method for providing lateral restraint was introduced through an angle connection between the web of the rafter and that of the purlin. It was demonstrated that this arrangement eliminated the 5 lateral-torsional buckling failure mode successfully, since both the top and the bottom flanges were effectively restrained. Kwon et al (2006) reported a research on applications of closed sections produced by a combination of cold-rolling and clinching techniques. The sections used for the tests were 150 mm deep, 40 mm wide and 0.8 mm thick. The moment capacity calculated from the gross section modulus was 3.55 kNm. Connection brackets for the eaves and the apex joints were constructed from 2.3 mm thick mild steel plates through combination of folding and welding, with four different connection types. The bracket of Connection Types 1 and 2 were produced by cutting the bottom flange of a C-shape bracket and welding lipped plate to build a haunch stiffener, with and without a lip on the flange respectively. However the bracket was made by press-breaking 3 mm thick cold-formed steel strips. Fig.10a and Fig.10b show the general joint arrangement of Connection Type 3 with a lip on the flange. In Connection Type 4, the bracket of the same shape lip on the flange was not provided. Rhodes and Burns (2006) conducted extensive component tests on the eaves joints of a cold-formed steel portal framing system that used a knee-brace arrangement, formed through back-to-back channel-sections bolted to the flanges of the column and the rafter through a welded bracket. Fig.11 shows details of the joint. The columns and the rafters were formed from back-to-back channel-sections having a moment capacity of 128.54 kNm and 76.68 kNm, respectively. In the joints described in the literature, the general joint arrangement comprises back-to-back channel-sections for the members, connected through gusset plates bolted to the web of the channel-sections. Table 1 summaries the moment-capacities of the sections used for the joints. If it is assumed that a moment capacity of at least 50 kNm is required in order for a joint to be considered feasible for use in a coldformed steel portal frame of medium span (about 12 m) then only the joints described by Rhodes and Burns (2006) do not share this general joint arrangement; in the case of the joints by Rhodes and Burns, the resistance to moment is provided through a knee-brace, which adds considerable expense in terms of fabrication and on-site erection. In the joints described by Dubina et al (2004), the gusset plates are replaced by hot-rolled steel sections. However, the connection of the back-to-back channelsections to the hot-rolled steel sections remains through bolts in the webs of the channel-sections. The main difference between the joint described by Dubina et al 6 and the general joint arrangement are that there are also bolts through the flanges of the channel-sections to the hot-rolled steel sections; such bolts would increase the moment capacity and the rotational stiffness of the bolt-groups. On the other hand, in the joint described by Dundu and Kemp (2006) while there is no gusset plate, the connection is still through bolts in the webs of the channel-sections. However, the lack of gusset plates means that the moment capacity and the stiffness of the boltgroups in the webs are limited by the depth of the channel-sections. 1.2 Objectives and scope of work Previous research indicates that virtually all practical forms of joints are semirigid and have finite connection-lengths, and that both of these effects should be taken into account in design since the semi-rigidity and the finite connection-length of the joints influence the bending moment distribution as well as the deflected profile of the frame. Furthermore, it is incorrect to treat joints as rigid, since such a treatment will result in a very different pattern of moments and will severely underestimate frame deflections. No previous research has therefore considered the interaction between the rotational stiffness and finite connection-length of the eaves joint, relative to those of the apex joint, in terms of economy of design of a portal frame. This paper investigates this interaction and the optimum joint detail for the general joint arrangement described by Lim and Nethercot (2002, 2003a, 2003b, 2004a, 2004b) will be determined for practical frames. These frames will be designed to the British code of practice; the effect of different span-to-height ratios, pitch, and column base fixity will be investigated. It will be demonstrated that material savings of the column and rafter members can be made through careful selection of the sizes of the eaves and apex brackets, as influenced by their respective bolt-group sizes. Whilst any of joint arrangements described in the literature review above could have been used for the study, the same general conclusions would apply. In order to analyse the frames, it is necessary to first determine the rotational stiffness of the cold-formed steel bolted moment connections used for the eaves and the apex joints, and to be able to incorporate this within a frame analysis. This rotational flexibility can be attributed to elongation of the bolt holes, and Section 2 summarises work previously undertaken that describes and validates a method for determining bolt hole elongation stiffness and the rotational stiffness of the joints. 7 Section 3 presents the design loads and serviceability requirements of the frame that will be considered in the optimisation study of Section 4. 2 Frame idealisation 2.1 Full-scale tests In order to quantify the effect of different joint details on frame behaviour, Lim and Nethercot conducted two full-scale frame tests: Frames A and B. Both frames were of span 12 m and column height 3 m with a roof pitch of 10o, but used different sizes of brackets and bolt arrangements (Fig.12). Fig.13 and Fig.14 show the general test arrangement and arial view, respectively, of Frame B. Fig.15 shows the experimental variation of load against apex deflection for both frames. As can be seen, the effect of increasing the bolt-group size from 315 mm x 230 mm (Frame A) to 615 mm x 230 mm (Frame B) increases the gradient of load against deflection by approximately a factor of three. Fig.15 also shows the gradients obtained using a simple beam idealisation, described in Section 2.2. It should be noted that the gradients of the beam idealisation, against which the experimental gradients can be compared, are plotted with an initial offset along the deflection axis to account for the deflection due to misalignment of the bolt holes, and so to enable the experimental and the analytical results to be compared at loads when all the bolt shanks are in full bearing contact against the connected plates. The values of the initial offsets were determined from a line of best fit drawn for the load-deflection curve of each frame. From the results of these two tests, it can be concluded that the joints of coldformed steel portal frames were semi-rigid and of finite connection-length. Further details of these tests can be found in Lim and Nethercot 2004b. 2.2 Beam idealisation for the frame Details of the simple beam idealisation of the eaves joints used by Lim and Nethercot for the purposes of frame analysis are shown in Fig.16. As can be seen, the column and rafter members are each connected at the eaves joint through rotational spring elements of stiffness kec and ker, respectively. Each rotational spring is of zero size and connects two coincident nodes, with one node belonging to the member and the other node to the eaves bracket. The values of kec and ker for the spring elements depends on the bolt-group size, the number of bolts used and the bolt-hole elongation 8 stiffness, kb. The rotational stiffness values are presented in Table 2, where subscript a denotes the apex joint and subscript e denotes eaves joints. Essentially, each boltgroup is assumed to rotate around its centre of rotation as described by (Davies (1991) and Kulak et al (1987)) (see Fig.17). The finite connection-length of the eaves joint is idealised using two rigid beam elements. As can be seen in Table 2, the column and rafter connections at the eaves have finite connection-lengths of lec and ler, respectively. The apex joint is idealised in a similar manner to the eaves joint as shown in Fig.18. Fig.19 shows details of the beam idealisation of the whole portal frame. For the convenience of obtaining results and plotting graphical output, six elements are used for the column and twelve elements for the rafter; an additional element is used for each leg of the eaves and the apex brackets. 2.3 Joint effects on bending moments Fig.20 shows bending moment diagrams of the frame under vertical loads. As can be seen, three bending moment diagrams are provided, these being for the case of a rigid-jointed frame, Frame A and Frame B, respectively. All three frames are subjected to the same vertical load. While the magnitude of this vertical load is not important, as the analysis is elastic and it is the relative differences in bending moments that are important, the magnitude of the vertical load corresponds to the serviceability load of a rigid-jointed frame. As can be seen, the bending moment at the eaves of Frames A and B is less than that of the rigid-jointed frame while the bending moment at the apex is larger than that of the rigid-jointed frame for vertical load cases. 2.4 Joint effects on deflections Fig.21 shows the effect of different values of kb, assuming linear load-extension characteristics of bolt-hole elongation, on the deflections predicted by the beam idealisation for Frames A and B. For the sake of comparison, the results have been plotted on the same scale as Fig.15. It can be seen that the apex deflection of Frame A is more sensitive than that of Frame B to the value of kb because any change in the value of kb has a greater effect on the magnitude of deflections of Frame A as the rotational stiffness of its joints are lower. 9 2.5 Concluding remarks The results of full-scale tests previously reported show that semi-rigid design should be used for cold-formed steel portal frames as the rotational flexibility of the joints has a large effect both on the bending moment distribution of the frame as well on frame deflections. It may be noted, however, that semi-rigid joint design has the advantage that the ratio of the bending moment at the eaves to the bending moment at the apex can be controlled by the designer through choosing suitable connection rotational stiffnesses and connection-lengths for the joints. On the other hand, the joint detail also needs to chosen to control deflections under serviceability load. The following sections of this paper concentrates on using the beam idealisation to take joint effects explicitly into the design process, providing an opportunity to design the most appropriate joint detail for a given frame. 3 Design loads and serviceability requirements in typical applications In the previous Section, a simple beam idealisation model was described that can be used for the purpose of frame analysis in the optimisation study of Section 4. In this Section the frame geometry, loads and serviceability requirements will be used for the study will be described. The parameters of the frame are shown in Fig.22. The frame is pinned at its column bases, and its span is 12m while its height to the eaves is 3m. The pitch of the frame is 10o. The member flexural rigidity is 11.264x109 kNmm2, while the member axial rigidity is 0.679x106 kN. The bay spacing is to be determined. 3.1 Dead and live loads The dead and the live loads applied to the frame are as follows Dead load due to the self-weight of the frame (DL) 0.27kN/m Dead load due to the self-weight of the cladding (DL) 0.09kN/m2 Live load due to snow and services (LL) 0.75kN/m2 3.2 Wind load In this section the British code of practice CP3 (1972) will be used. The Authors are aware that CP3 has been superseded by BS 6399-2, however, it is well known that frames designed to both CP3 and BS 6399-2 result in similar size sections. CP3 is used owing to it being easier to implement in a computer program. 10 A basic wind speed of 46m/s is assumed as this is the average basic wind speed in the U.K., which leads to a wind load pressure, q, of 0.55kN/m2. Four wind load combinations (WLC1 to WLC4) are considered. In accordance with CP3 the pressure coefficients are shown in Table 3 and the coefficient of pressure given by WLC1 are shown in Fig.23. It is usually sufficient to consider only wind load combination 1 (WLC1) (Morris and Plum (1988)); However, the frame is checked for all four wind load combinations in the optimisations study described in Section 4. 3.3 Load combinations In accordance with BS5950:Part 1, the frame is checked at the ultimate limit state for the following two ultimate load combinations: Load combination ULC1 = 1.4 × DL + 1.6 × LL Load combination ULC2 = 1.0 × DL + 1.4 × WLC The frame is also checked at the serviceability limit state for the following two serviceability load combinations: Load combination SLC1 = 1.0 × LL Load combination SLC2 = 1.0 × WLC 3.4 Serviceability requirements In general, it should be noted that the design of hot-rolled steel portal frames is often dominated by serviceability requirements. As there is no codified mandatory deflection limits for portal frames, deflection limits need to be defined for the design of cold-formed steel portal frames. Table 4 presents deflection limits proposed by Lim and Nethercot (2003b) for cold-formed steel portal frames and these deflection limits will be adopted in the optimisation study. 4 Optimum joint detail In Section 2, two frames were described: Frames A and B. From Fig.15, it can be seen that the deflections of Frame B, having a larger bolt-group size, are smaller than those of Frame A. A similar conclusion can also be reached from Equation 4, from which it can be seen that Frame B has a higher rotational stiffness for the joints than Frame A. Using the design loads and the serviceability requirements described in Section 3, it can be shown that the bay spacing permitted for Frame B is 2.5 times larger than 11 that for Frame A. In other words, Frame B can be designed to carry a load that is 2.5 times larger than the design load of Frame A. As the only difference between Frames A and B is the detail of the joints, the efficiency of the frame is therefore controlled by the rotational stiffness and the connection-length of the joints. The bending moment distribution and the deflected profile of the frame are affected by both the rotational stiffness as well as the connection-lengths of the eaves and the apex joints. The eaves and the apex joints should therefore not be designed independently of one another. For a frame of a given span and height, the optimum joint detail of the eaves and the apex joints has to be determined. The optimum joint detail maximises the ultimate load carrying capacity of the frame while also limiting frame deflections within prescribed serviceability requirements. 4.1 Optimisation criteria In order to optimise the design of a portal frame, it is necessary to decide on an optimisation criterion. An obvious criterion, in an economic sense, is that of minimum cost. However, in order to obtain the minimum cost design of a portal frame, the costs of material, fabrication, transportation and erection will all need to be considered. Such an optimisation is found to be too complex. As an alternative, the minimum-weight criterion is adopted to optimise the design of the portal frame subject to a design constraint that only 3 mm thick back-toback channel sections (see Fig.24) can be used for column and rafter members. For such frames, the moment capacities of the column and the rafter members are then fixed. The problem therefore reduces to one of varying the size of the bolt-group to give the maximum permissible bay spacing, Smax. The values of Smax for various frame geometries is determined by a program called MAXBAY which was written by the Author using the ANSYS parametric language. The maximum permissible bay spacing for various geometries of frame will be determined by a program called MAXBAY which was written by the Author using the ANSYS parametric language. 4.2 Practical constraints To facilitate ease of handling and erection of the joints on site, practical constraints on joint details should also be imposed on the bracket size as well as on 12 the number of bolts used in each connection. Fig.25 shows the constraints imposed on the size of the eaves and the apex brackets which limit the length of the edges of the brackets to 1000mm. Similarly, the number of bolts per connection is limited to nine. Hence, the rotational stiffness and the connection-length required for a beam idealisation of the joint detail prescribed above are given in Table 5. It must be emphasised that while these constraints result in practical sizes of brackets having a practical number of bolts, either of the constraints can be increased. 4.3 Different combinations of practical constraints For each frame, the maximum permissible bay spacing (to the nearest 0.5m), Smax, is determined under each of the following design constraint combinations (DCC) with the program MAXBAY: Constraint DCC1: Ultimate limit state The frame is designed to the ultimate limit states. No practical constraints are imposed on the joint details. The rotational stiffness of the eaves and the apex joints are varied until the bending moments at both the eaves and the apex are equal. The bay spacing so obtained is therefore the upper bound of the bay spacing, S. Constraint DCC2: Ultimate + serviceability limit states The frame is designed to both the ultimate and the serviceability limit states. No constraints are imposed on the joint details. The rotational stiffness of the eaves and the apex joints are varied until the bending moments at both the eaves and the apex are equal and while the deflections satisfy the deflection limits. Constraint DCC3: Ultimate + serviceability limit states + joint detail constraint This is the practical design constraint combination (DCC) and the frame is designed to both the ultimate and the serviceability limit states. The constraints shown in Fig.25 are imposed on the joint details. Constraint DCC4: Ultimate + serviceability limit states + rigid-joint constraint This is the rigid-jointed design constraint combination (DCC) and the frame is designed to both the ultimate and the serviceability limit states with both the eaves and the apex joints assumed to be rigid. Fig.26 shows the results of various design and analyses on the effects of different combinations of practical constraints on the maximum permissible bay spacing for frames having Lf/hf = 4 and f = 10o. The critical load combination that 13 controls the maximum permissible bay spacing for the frame under constraints DCC3 and DCC4, are also shown. It is found that: (1) The bay spacing for frames designed to constraint DCC2 is almost identical to that determined under constraint DCC1. This is expected as the program MAXBAY has increased the rotational stiffness of the eaves and the apex joints until serviceability requirements are satisfied while at the same time keeping the bending moments at the eaves and the apex joints equal. (2) The bay spacing determined under constraint DCC3 is smaller than that determined under constraint DCC2 as a result of the constraints imposed on the joint details. The program MAXBAY has increased the sizes of the eaves and the apex joints until the prescribed maximum sizes has been reached. (3) The bay spacings determined under the constraint DCC3 are higher than or equal to that for constraint DCC4. (4) The maximum permissible bay spacing for the 9m span frame is limited by the bending moments at the eaves under load combination ULC1. The maximum permissible bay spacing for frames having spans between 12m and 18m is limited by the apex deflection under load combination SLC1. 4.4 Different frame geometries The effects of different frame geometries on the maximum permissible bay spacings are also examined, and the results are described as follows: 4.4.1 Frames with Lf/hf = 3 Fig.27 shows the maximum permissible bay spacings for frames with Lf/hf = 3 and f = 10o and the critical load combinations that control the maximum permissible bay spacings for the frames under constraints DCC3 and DCC4. It can be seen from Fig.27 that the bay spacings for both 15 m and 18 m span frames under constraint DCC3 are less than those of rigid-jointed frames and frames with Lf/hf = 3. Moreover, the apex deflection under load combination SLC1 is generally critical. 4.4.2 Frames with Lf/hf = 2 Fig.28 shows the maximum permissible bay spacings for frames with Lf/hf = 2 and f = 10o. It can be seen from Fig.28 that the bay spacings for all frames designed under constraint DCC3 are less than those for rigid-jointed frames under constraint DCC4. Moreover, the eaves deflection under load combination SLC2 is critical. 14 4.4.3 Frame with increased pitch Fig.29 shows the maximum permissible bay spacings for frames with Lf/hf = 4 and f = 20o. Compared to frames with Lf/hf = 4 and f = 10o (Fig.26), it can be seen that the maximum permissible bay spacings increase under all the practical constraints considered. 4.4.4 Frames with fixed column bases Fig.30 shows the maximum permissible bay spacings of frames using fixed column bases instead of pinned column bases. In all the frames under constraint DCC£, the presence of fixed column bases increases the maximum permissible bay spacings by approximately 40%. 5 Conclusions In this paper, different arrangements in bolted-moment connections between cold-formed steel members have been reviewed. As can be seen, almost all the joints comprise channel-sections for the members, connected through gusset plates bolted to the webs of the channel-sections. The most general arrangement involves a bolt-group in a regular grid with each bolt passing through the webs of the channel-sections. Variations to this arrangement include connections with bolts through the flanges of the channel-sections, or with more bolts located away from the centre of rotation of the bolt-group. Using a general joint arrangement comprising a 3x3 array of bolts, a method for determining the rotational stiffness of the joints is described, which can then be incorporated into a frame analysis. An optimisation study on portal frames is carried out, in which the size of the brackets is the key parameter of interest under different load combinations and constraints. It can be seen that in some cases, semi-rigid joints of finite connection lengths having a practical joint detail can actually result in a frame with a higher load carrying capacity than an equivalent rigidly jointed frame. Moreover, the optimisation study allows the efficiency of the joint details to be compared against that of a joint detail without constraint. It is shown that for an 18 m span frame with a height of 4.5 m and a pitch of 10o, a frame designed with a practical semi-rigid joints is as efficient as an equivalent rigidly jointed frame. However, for the same frame, relaxing the practical joint constraint will allow as much as a 25% increase in material savings. 15 As the semi-rigidity and the finite connection-length of each joint influences the bending moment distribution and the deflected profile of the frame, the joint details for the eaves and the apex should not be designed independently of one another, and they should be designed in conjunction with a frame analysis. 16 6 References Baigent, A.H. and Hancock, G.J. (1982). The behavior of portal frames composed of cold-formed members. Thin-walled structures - Recent technical advances and trends in design, research and construction, Oxford, Elsevier Applied Science, p209-222. BS5950: Part 1 (2000): Code of practice for design in simple and continuous construction: Hot rolled sections, London, British Standards Institution. BS6399: Part 1 (1996): Code of practice for dead and imposed loads, London, British Standards Institution. BS6399: Part 2 (1997): Code of practice for wind loads, London, British Standards Institution. CP3 (1972): Code of basic data for the design of buildings: Chapter V: Part 2: Wind loads, London, British Standards Institution. Chung, K.F. and Lau, L. (1999). Experimental investigation on bolted moment connections among cold-formed steel members. Engineering Structures, 21(10), p898-911. Dubina, D., Stratan, A., Ciutina, A., Fulop, L. and Zsolt, N. (2004). Monotonic and cyclic performance of joints of cold formed steel portal frames. Fourth International Conference on Thin-Walled Structures, p381-388. Dundu, M. and Kemp, A. R. (2006). Plastic and lateral-torsional buckling behavior of single cold-formed channels connected back-to-back. Journal of Structural Engineering, 132(8), p1223-1233. Kirk, P. (1986). Design of a cold-formed section portal frame building system. Proc. 8th International Specialty Conference on Cold-formed Steel Structures, St. Louis, University of Missouri-Rolla, p295-310. Kwon, Y. B. Chung, H.S. and Kim, G. (2006). Experiments of cold-formed steel connections and portal frames. Journal of Structural Engineering, 132(4), p600-607. Lim, J.B.P. and Nethercot, D.A. (2002). F.E.-assisted design of the eaves bracket of a cold-formed steel portal frame. Journal of Steel and Composite Structures, 2(6), p411-428. Lim, J.B.P. and Nethercot, D.A. (2003a). Ultimate strength of bolted momentconnections between cold-formed steel members. Thin-Walled Structures, 41(11), p1019-1039. Lim, J.B.P. and Nethercot, D.A. (2003b). Serviceability design of a cold-formed steel portal frame having semi-rigid joints. Steel and Composite Structures, 3(6), p451-474. 17 Lim, J.B.P. and Nethercot, D. A. (2004a). Stiffness prediction for bolted momentconnections between cold-formed steel members. Journal of Constructional Steel Research, 60(1), p85-107. Lim, J.B.P. and Nethercot, D.A. (2004b). Finite element idealisation of a cold-formed steel portal frame. Journal of Structural Engineering, ASCE, 130(1), p78-94. Mäkeläinen, P. and Kankaanpää, J. (1996). Structural design study on a light-gauge steel portal frame with cold-formed sigma sections. Proc. 13th International Specialty Conference on Cold-Formed Steel Structures, St. Louis, University of Missouri-Rolla, p349-371. Mills, J. and LaBoube, R. (2004). Self-Drilling Screw Joints for Cold-Formed Channel Portal Frames. Journal of Structural Engineering, ASCE, 130(11), p17991806. Morris, L.J. and Plum, D.R. (1988): Structural Steelwork Design to BS5950, London, Longman Scientific and Technical. Rhodes, J. and Burns, R. (2006). Development of a portal frame system on the basis of component testing. Proc. 18th International Specialty Conference on Cold-Formed Steel Structures, St. Louis, University of Missouri-Rolla, p367-385. Yu, W. K., Chung, K. F. and Wong, M. F. (2005). Analysis of bolted moment connections in cold-formed steel beam-column sub-frames. Journal of Constructional Steel Research, 61(9), p1332-1352. Wong, M.F., and Chung, K.F., (2002). Structural behaviour of bolted moment connections in cold-formed steel beam-column sub-frames. Journal of Constructional Steel Research, 58(2), p253-274. Zadanfarrokh, F and Bryan, E. R. (1992). Testing and design of bolted connections in cold formed steel sections. Proc. 11th International Specialty Conference on ColdFormed Steel Structures, St. Louis, Missouri, U.S.A., p625-662. Ho, H.C. and Chung, K.F. (2006). Analytical prediction on deformation characteristics of lapped connections between cold-formed steel Z sections. ThinWalled Structures, 44(1), p115-130. 18 Table 1 Joints reported in the literature Sections Principal author Baigent (1982) Bracket Fasteners No. of brackets Description No. of fixings/ joint - 1 M19mm H.T. bolts 8 3 280 2 M16 G.8.8 8 12 355 1 M16 G.8.8 20 depth x breadth x t σy Mc le tb σyb (mm) (N/mm2) (kNm) (mm) (mm) (N/mm2) 153x79x1.86 325.8 9.2 260 12 * 32.0 620 77.0 - Kirk (1986) 220x65x2.4 280 Mäkeläinen (1996) 300x75**x3.0 350* h Chung (1999) 150x64x1.6 450* 17.9 460 460hs 6 2.5 343 475 1 2 M16 G.8.8 8 Lim (2002) 340x90x3 280* 82.8 746hs 3 209 2 M16 G.8.8 16 Mills (2004) 200x76x1.5 450* 10.8 Bolts Bolts Screws 2 2 12 Dubina (2004) 350x100x3 452 117.8 M20 G.6.6 32 Dundu (2005) 300x75x3 468.9 51.6 M20 G.8.8 M20 G.8.8 4 8 Kwon (2006) PRY 150x40x0.8 570* 3.6 Screws ø 4.8mm 16 342x97x2.5 rafter 343 76.7 M16 G.8.8 32 Rhodes (2006) End plate joint Mitred joint Sections screwed back-to-back 940 10 235 1 Sections bolted back-to-back 261.6 2.3 Connection angles 240 1 275* 2 C 202x69x2 352 128.5 350* knee brace * design yield strength, ** dimensions are not reported but standard sizes are assumed, h denotes a haunch, hs denotes a haunch with stiffeners 402x97x3.2 column 1 2 Table 2 Parameters pertaining to Frames A and B in analysis using beam idealisation Frame lec ler lar (mm) (mm) (mm) kec ker kar keb kab x10-3 x10-3 x10-3 x10-3 x10-3 (kNm/ (kNm/ (kNm (kNm/ (kNm/ rad) rad) rad) rad) rad) A 400.1 400.1 287.5 2.4 2.4 2.4 70.0 39.4 B 550.1 550.1 446.5 6.8 6.8 6.8 93.6 32.6 Table 3 Coefficients of pressure corresponding to different wind load cases Wind load combination Description WLC1 Coefficient AB BC CD DE Wind on side + internal pressure 0.5 -1.4 -0.6 -0.45 WLC2 Wind on side + internal suction 1.0 -0.9 -0.1 0.05 WLC3 Wind on end + internal pressure -0.7 -1.0 -0.8 -0.7 WLC4 Wind on end + internal suction -0.2 -0.5 -0.3 -0.2 Table 4 Recommended deflection limits for cold-formed steel portal frames under both live and wind loads Deflection category Reason for limit Deflection limit Lateral eaves deflection Damage to side cladding hf/100 Damage to roof cladding hf/150 Vertical apex deflection Ponding of water Visual acceptability 1 s 2 s f / 125 2 Lf/240 Table 5 Parameters pertaining to practical sizes of eaves and apex brackets with nine bolts lec ler lar (mm) (mm) (mm) 525 525 525 kec ker -3 x10 x10-3 (kNm/ (kNm/ rad) rad) kar x10-3 (kNm rad) 5.905 10.744 5.905 2 Fig.1. Cold-formed steel portal framing system Fig.2. Eaves joint after Baigent and Hancock (1982) Fig.3. Swagebeam eaves joint after Kirk (1986) 3 a) single layer b) four layers c) four layers with lip stiffeners Fig.4. Eaves joint with different configurations after Mäkeläinen and Kankaanpää (1996) a) triangular b) rectangular c) L-shape with stiffener d) haunched with stiffener Fig.5. Eaves joint brackets after Chung and Lau (1998) Fig.6. Eaves joint after Lim and Nethercot (2002) a) bolted end plate joint b) mitred joint c) self-drilling screw joint Fig.7. Eaves joints after Mills and LaBoube (2004) 4 KIS KIP a) bolts on the web (KIS, KIP) KSG b) bolts on the web and on the flange (KIS, KIP) c) bolts on the web (KSG) Fig.8. Eaves joints after Dubina et al (2004) Fig.9. Bolted joints after Dundu and Kemp (2006) a) joint arrangement b) self drilling screws configuration Fig.10. Eaves joint (Connection Type 3) after Kwon et al (2006) 5 Fig.11. Eaves joint after Rhodes and Burns (2006) bolt-group A of size 315 x 230 (a) Frame A bolt-group B of size 615 x 230 (b) Frame B Fig.12. Details of the bolt-groups and the corresponding sizes of eaves and apex brackets 6 x x x x x x x x x x x x x x x 3000 back-toback channelsections jack x reaction beam 12000 x reaction column (schematic representation only) x location of lateral restraint Fig.13. General test arrangement of Frame B Fig.14. ‘Aerial’ view of Frame B 7 120 120 120 120 Experimental result 100 100 100 100 (kN) Load (kN) Load (kN) Load (kN) Load 80 80 80 80 60 60 60 60 Beam idealisation result using linear spring to represent bolt hole elongation Beam idealisation result using nonlinear spring to represent bolt hole elongation 40 40 40 40 20 20 20 20 0 0 0 0 0 0 0 0 50 50 50 50 100 100 100 100 150 200 150 200 150 200 150 200 Apex deflection deflection (mm) (mm) Apex Apex deflection (mm) Apex deflection (mm) 250 250 250 250 300 300 300 300 (a) Frame A 120 120 100 100 120 80 80 100 Load (kN) Load (kN) Load (kN) Experimental result 60 40 60 80 40 60 20 20 40 0 0 20 0 150 0 50 100 Beam idealisation result using nonlinear spring to represent bolt hole elongation Apex deflection (mm) 0 0 (b) Frame B Note: The linear results plot on the same curve as the nonlinear results 200 50 250 100 300 150 Apex deflection (mm) 50 100 150 Apex deflection (mm) Fig.15. Variations of applied loads against apex deflections for Frames A and B 8 200 200 ler ler bolt-group of size aer x ber lec lec ker keb centre of rotation kec bolt-group of size aec x bec coincident nodes connected by rotational spring of zero size Fig.16. Details of beam idealisation of eaves joint centre of rotation i di Fi bB B M aB (a) (b) Fig.17. Details of a typical bolt-group with nine bolts 9 lar bolt-group of size aer x ber lar centre of rotation lar coincident nodes connected by rotational spring of zero size kB lar kab kB Fig.18. Details of beam idealisation of an apex joint lar ler kar 2kab C L lec keb ker kec Fig.19. Details of beam idealisation of a portal frame 10 9.39kNm 5.30kNm 9.39kNm (a) Rigid frame 6.14kNm 6.14kNm 6.98kNm 7.13kNm 7.13kNm (b) Frame A 6.21kNm 6.21kNm 5.69kNm 7.40kNm 7.40kNm (c) Frame B 6.21kNm 6.21kNm Fig.20. Comparison of bending moment diagram of frames under vertical load 11 120 100 Load (kN) 80 60 kb=5.00 x 103kN/mm kb=6.21 x 103kN/mm 40 kb=10.00 x 103kN/mm kb=15.00 x 103kN/mm 20 kb=rigid 0 0 50 100 150 200 250 300 250 300 Apex deflection (mm) (a) Frame A 120 100 Load (kN) 80 kb=5.00 x 103kN/mm 60 kb=6.21 x 103kN/mm kb=10.00 x 103kN/mm kb=15.00 x 103kN/mm 40 kb=rigid 20 0 0 50 100 150 200 Apex deflection (mm) (b) Frame B Fig.21. Sensitivity of apex deflection to kb for test frames 12 sf C ff D B θf Other parameters: EI = flexural rigidity EA = axial rigidity S = bay spacing hf E A Lf Fig.22. Diagram showing various portal frame parameters 1.4 C 0.6 D B 0.5 0.45 E A Fig.23. Coefficients of wind pressure for load combination WLC1 13 C L Fig.24. Back-to-back channel-sections used for column and rafter members bolt-group of size 565 x 230 bolt-group of size 790 x 230 Fig.25. Various constraints on bracket sizes 14 25 DCC1: Ultimate limit state Ultimate limit state ULC1 (eaves) 5 SLC1 (apex) SLC1 (apex) 10 ULC1 (eaves) DCC4: Ultimate + serviceability limit states + rigid Ultimate & serviceability limit states with joint rigid constraint joint constraint ULC1 (eaves) 15 DCC3: Ultimate + serviceability limit states + joint constraint Ultimate & serviceability limit states with detail joint detail constraint SLC1 (apex) Maximum bay spacing bf (m) 20 ULC1 (eaves) ULC1 (eaves) DCC2: Ultimate + serviceability limit states Ultimate & serviceability limit states 0 9 12 15 18 Span of frame Lf (m) Fig.26. Effect of different combinations of practical constraints on maximum permissible bay spacings for different spans of frames with Lf/hf = 4 and f = 10o DCC3: Ultimate + serviceability limitlimit states + joint Ultimate & serviceability states withdetail joint constraint detail constraint ULC1 (eaves) 5 SLC1 (apex) SLC1 (apex) 10 ULC1 (eaves) DCC4: Ultimate + serviceability limitlimit states + rigid Ultimate & serviceability states withjoint rigidconstraint joint constraint SLC1 (apex) 15 DCC2: Ultimate + serviceability limitlimit states Ultimate & serviceability states ULC1 (eaves) ULC1 (apex) DCC1: Ultimate limitlimit state Ultimate state ULC1 (eaves) Maximum bay spacing bf (m) 20 0 9 12 15 18 Span of frame Lf (m) Fig.27. Effect of different combinations of practical constraints on maximum permissible bay spacings for different spans of frames with Lf/hf = 3 and f = 10o 15 20 DCC1: Ultimate limitlimit state Ultimate state SLC2 (eaves) SLC2 (eaves) 5 SLC2 (eaves) SLC2 (eaves) 10 SLC2 (eaves) DCC4: Ultimate + serviceability limitlimit states + rigid Ultimate & serviceability states withjoint rigidconstraint joint constraint SLC2 (eaves) SLC2 (eaves) 15 DCC3: Ultimate + serviceability limitlimit states + joint Ultimate & serviceability states withdetail joint constraint detail constraint SLC2 (eaves) Maximum bay spacing bf (m) DCC2: Ultimate + serviceability limitlimit states Ultimate & serviceability states 0 9 12 15 18 Span of frame Lf (m) Fig.28. Effect of different combinations of practical constraints on maximum permissible bay spacings for different spans of frames with Lf/hf = 2 and f = 10o 5 ULC1 (eaves) SLC2 (eaves) ULC1 (eaves) DCC4: Ultimate + serviceability limitlimit states + rigid Ultimate & serviceability states withjoint rigidconstraint joint constraint SLC2 (eaves) 10 DCC3: Ultimate + serviceability limitlimit states + joint Ultimate & serviceability states withdetail joint constraint detail constraint ULC1 (eaves) 15 DCC2: Ultimate + serviceability limitlimit states Ultimate & serviceability states SLC2 (eaves) Maximum bay spacing bf (m) 20 DCC1: Ultimate limitlimit state Ultimate state ULC1 (eaves) ULC1 (eaves) 25 0 9 12 15 18 Span of frame Lf (m) Fig.29. Effect of different combinations of practical constraints on maximum permissible bay spacings for different spans of frames with Lf/hf = 4 and f = 20o 16 ULC1 (eaves) DCC2: Ultimate + serviceability limitlimit states Ultimate & serviceability states DCC3: Ultimate + serviceability limitlimit states + joint Ultimate & serviceability states withdetail joint constraint detail constraint 5 ULC1 (eaves) SLC1 (eaves) 10 ULC1 (eaves) 15 SLC1 (eaves) 20 DCC4: Ultimate + serviceability limitlimit states + rigid Ultimate & serviceability states withjoint rigidconstraint joint constraint ULC1 (eaves) ULC1 (eaves) Maximum bay spacing bf (m) 25 DCC1: Ultimate limitlimit state Ultimate state SLC1 (eaves) 30 0 9 12 15 18 Span of frame Lf (m) Fig.30. Effect of different combinations of design constraints on maximum permissible bay spacing for different spans of frames with Lf/hf = 4 and f = 10o and fully fixed column bases 17 View publication stats
