Experimental investigations at ambient temperature into the behaviour of bolted moment-connections between cold-formed steel members have previously been described. Full-scale joint tests have demonstrated that the channel-sections being connected are susceptible to premature failure, the result of web buckling caused by the concentration of load transfer from the bolts. The results of non-linear elasto-plastic finite element analyses have been shown to have good agreement. No consideration, however, has been given to the behaviour of such connections at elevated temperatures. This paper describes non-linear elastoplastic finite element parametric studies into the effects of elevated temperatures on bolted moment-connections between cold-formed steel members; simple design rules are proposed that will enable designers to take into account the effects of elevated temperatures.postprin

Lim, JBP

Young, B

HKU Scholars Hub

TitleEffects of elevated temperatures on ultimate moment capacity ofbolted moment-connections between cold-formed steelmembersAuthor(s) Lim, JBP; Young, BCitationThe 19th International Specialty Conference on Cold-FormedSteel Structures, St. Louis, MO., 14-15 October 2008. InConference Proceedings, 2008, p. 547-561Issued Date 2008URL http://hdl.handle.net/10722/63255Rights Creative Commons: Attribution 3.0 Hong Kong License547  Nineteenth International Specialty Conference on Cold-Formed Steel Structures St. Louis, Missouri, U.S.A, October 14 & 15 2008    Effects of elevated temperatures on ultimate moment capacity of bolted moment-connections between cold-formed steel members   James B.P. Lim1 and   Ben Young2    Abstract   Experimental investigations at ambient temperature into the behaviour of bolted moment-connections between cold-formed steel members have previously been described. Full-scale joint tests have demonstrated that the channel-sections being connected are susceptible to premature failure, the result of web buckling caused by the concentration of load transfer from the bolts. The results of non-linear elasto-plastic finite element analyses have been shown to have good agreement. No consideration, however, has been given to the behaviour of such connections at elevated temperatures. This paper describes non-linear elasto-plastic finite element parametric studies into the effects of elevated temperatures on bolted moment-connections between cold-formed steel members; simple design rules are proposed that will enable designers to take into account the effects of elevated temperatures.                                                      1 Lecturer, Dept. of Civil Engineering, The University of Strathclyde, Glasgow, UK 2 Associate Professor, Dept. of Civil Engineering, The University of Hong Kong, Hong Kong, China 548  Introduction   Bolted moment-connections between cold-formed steel members, formed through brackets bolted to the webs of the cold-formed steel sections being connected (see Fig.1), are used for the joints of portal frames [Ref. 1, 2], multi-storey frames [Ref. 3, 4], and racking systems [Ref. 5]. The behaviour of such joints, however, has only been considered at ambient temperature, with no consideration being given to joint behaviour at elevated temperatures.    Figure 1. Details of typical bolted moment connection   The lack of design information for elevated temperatures means that it is not always possible to design safely cold-formed steel frames having such joints in fire, without resorting to the use of fire protection. Conservative design recommendations are normally based on simple modifications to the fire design rules of hot-rolled steel structures. However, in the case of hot-rolled steel, local buckling is generally not a problem. On the other hand, with cold-formed steel, both local and distortional buckling is common, making the design of these structures in fire problematic. Whilst ideally full-scale fire tests should be conducted, the cost of these tests will be prohibitive. In fact, it has only been in recent years that cold-formed steel coupon tests have been conducted at elevated temperatures.  549  Chen and Young recently have conducted a series of such tests [Refs 6, 7]. From the results of these tests, equations were developed that predict the stress-strain curves at elevated temperatures. In this paper, the stress-strain curves proposed by Chen and Young [Ref 6] are applied to a numerical investigation on the strength of bolted-moment connections between cold-formed steel members at elevated temperatures.  In this paper, the strength in fire of the channel-sections at the joints are investigated, which are susceptible to premature web buckling, induced by concentrated load transfer from the bolt-group. Curves are presented that illustrate how this mode of failure is affected by elevated temperatures. For cold-formed steel frames, where failure is generally non-ductile, the failure load of the joints is more important than for hot-rolled steel frames, where the frames continue to exhibit increased strength after the formation of the first plastic hinge. Simple design rules are proposed, from the results of this study, which will allow designers to take into account the effects of elevated temperatures.   Stress-strain curves at elevated temperatures   Fig.2 shows stress-strain curves for cold-formed steel at eight temperatures ranging from 22oC to 700oC. In this paper, the effects of elevated temperatures at these eight temperatures will be considered. The stress-strain curves are obtained from equations proposed by Chen and Young [Ref. 6]. Table 1 summarises the Young’s modulus and yield stress, calculated from equations also proposed by Chen and Young [Ref. 7].  In this paper, the general purpose finite element program ABAQUS [Ref. 8] is used for the numerical investigations. In the numerical models, non-linear stress-strain material curves are modelled. The first part of the engineering stress-strain curve represents the elastic part up to the proportional limit stress with measured elastic modulus and Poisson’s ratio. In this study, the Poisson’s ratio is taken as 0.3 under fire conditions. Generally, the Poisson’s ratio is assumed to be independent of temperature [Refs 9, 10]. Since the analysis of post-buckling involves large in-elastic strains, the engineering stress-strain curve has been converted to a true stress and logarithmic plastic strain curve for the different temperatures. These true stress and plastic true strain curve equations are specified in ABAQUS.    550   Figure 2. Stress-strain curves at different temperatures    Table 1. Summary of material properties at different temperatures  Temp -erature T (oC) Young’s modulus E (N/mm2) Yield stress fy (N/mm2) 22 210000 515 250 171696 494 400 146496 454 450 138096 409 500 100609 347 550 68632 267 600 41427 170 700 16200 48.9  551  Ultimate strength of bolted moment-connections   Phenomenon of premature web buckling When designing bolted moment-connections, two modes of failure can easily be prevented:  i. Overall lateral-torsional buckling of the joint. This type of buckling may be prevented through the provision of sufficient lateral restraint around the joint  ii. Buckling of the bracket. Adopting the design recommendations of Ref. 11 would ensure that the bracket has a higher moment capacity than the channel-sections being connected.  A third mode of failure, which cannot be prevented as easily, is concerned with the reduction in strength of the channel-sections at the vicinity of the joints, caused by concentrated load transfer from the bolt-group (see Fig.3). This mode of failure, referred to as premature web buckling [Ref. 12], has been observed as the governing mode of failure in a number of laboratory tests on cold-formed steel bolted moment-connections [Refs 1, 13, 14 and 15]. A full-review of all of these tests is given in Ref. 12, in which it is demonstrated some of the joints tested failed at a moment-capacity 20% lower than the calculated moment-capacity of the channel-sections.  Fig.4 shows an example of premature web buckling induced failure. As can be seen, the mode involves buckling of the web of the channel, accompanied by sympathetic flange distortion. While the resulting failure mode shape is similar to distortional buckling, the mode of failure is initiated by premature web buckling. Premature web buckling is not covered by BS5950: Part 5 [Ref. 16], or any of the other codes of practice.     Figure 3. Free body diagram of channel-section when joint is in pure bending M 552  Figure 4. Typical web buckling induced failure [Ref. 14]  Ref 12 describes a combination of laboratory tests and finite element analyses used to investigate this mode of failure. However, while good agreement was demonstrated between the measured ultimate moment-capacity and that predicted by using the finite element analyses, the study was only concerned with the behaviour at room temperature. In this Section, a numerical study on the influence of elevated temperatures on premature web buckling is described.   Finite element model   Details of the finite element model used to investigate premature web buckling in Ref. 12 are shown in Fig.5. As can be seen, the model consists of only a single channel-section loaded under pure bending. The parameters used to describe the dimensions of the bolt group are shown in Fig.5. A full description of the model is given in Ref. 12.      Figure 5. Details of parameters used to describe the bolt-group array A A Section AA aB bB 553   Figure 6. Dimensions of channel-section used in parametric study   Parametric study   A parametric study was conducted to investigate the effects of elevated temperatures on premature web buckling. Fig.6 shows the dimensions of the channel-section used for the purposes of the parametric study; the same dimension of channel-section was also used in Ref. 12.  In the parametric study described in this Section, the thickness of channel-section was varied between 2 mm and 8 mm. Three bolt-group lengths (aB) were considered, namely, 200 mm, 500 mm and 1000 mm.  Fig.7(a) shows the reduction in moment capacity Mu,T/Mu,normal for a bolt-group length of 200 mm. For each temperature, the values of Young’s modulus, yield stress and ultimate stress are also normalised their respective values at room temperature.  From Fig.7(a), it can be seen that the value of Mu,T/Mu,normal decreases with the thickness of the channel-section. This is to be expected since plate buckling is a function of the thickness cubed. For the channel-section of thickness 8 mm, the reduction in moment capacity closely follows that of the reduction in yield stress (fy,T/fy,normal). However, for the channel-section of thickness 2 mm, the value of Mu,T/Mu,normal is much lower. For example, in the case of a temperature of 400oC, the reduction in strength of the 2 mm channel-section is 13% lower than that of 554  the 8 mm section. A lower bound to the reduction in strength can be seen to be ET/Enormal.    It is interesting to note from Fig.7(a) that the greatest variation in Mu,T/Mu,normal between the different thicknesses of channel-section is 13% and occurs at a temperature 450oC. At this temperature, the difference between ET/Enormal and fy,T/fy,normal is also 13%. Similarly, at a temperature of 600oC the variation in Mu,T/Mu,normal between the different thicknesses of channel-section is 6%. At this temperature, the difference between the same material properties is also 6%.  Since comparisons of the roundness of the stress-strain curves at these temperatures show no noticeable difference, it may therefore be concluded that the value of Mu,T/Mu,normal is a function of both ET/Enormal and fy,T/fy,normal.  Fig.7(b) and Fig.7(c) show the same results for values of aB = 500 mm and 1000 mm, respectively. As can be seen, the same general trends as for Fig.7(a) can be observed, even though the value of aB has been increased significantly from 200 mm to 1000 mm. In Ref. 12, the effect of increasing aB from 200 mm to 1000 mm resulted in a 20% increase in moment capacity. While this increase in moment capacity has been taken into account when comparing the curves of Fig.9, owing to the fact that normalised results are presented, it is interesting to note that the results have no additional sensitivity to the value of aB.  In general, as the value of aB increases, the values of Mu,T/Mu,normal also increase but the range of variation between the different thicknesses of channel-sections decreases. The fact that the values of Mu,T/Mu,normal are not sensitive to the value of aB is important for the design recommendations that follow. 00.20.40.60.811.20 100 200 300 400 500 600 700Temperature (oC)Normalised results against ambient temperaturet=2mm t=3mmt=4mm t=5mmt=6mm t=8mmYoung's modulus yield stressultimate stress (a) Bolt-group having aB = 200 mm555   00.20.40.60.811.20 100 200 300 400 500 600 700Temperature (oC)Normalised results against ambient temperaturet=2mm t=3mmt=4mm t=5mmt=6mm t=8mmYoung's modulus yield stressultimate stress(b) Bolt-group having aB = 500 mm   00.20.40.60.811.20 100 200 300 400 500 600 700Temperature (oC)Normalised results against ambient temperaturet=2mm t=3mmt=4mm t=5mmt=6mm t=8mmYoung's modulus yield stressultimate stress(c) Bolt-group having aB = 1000 mm Figure 7. Comparison of variation of moment capacity with material properties  Design recommendations   In the parametric study, it was observed that the reduction factor Mu,T/Mu,normal is sensitive to both ET/Enormal and fy,T/fy,normal but not to the values of aB. As the moment capacity of the channel-section is a function of both ET and fy,T, a design recommendation based on the reduction in moment capacity may be appropriate.  The direct strength method specified in the supplement to the North American Specification [Ref. 17] and the Australian/New Zealand Standard [Ref. 18] is 556  used to predict the moment capacity of the cold-formed steel channel-sections. The nominal design strengths at elevated temperatures were calculated by substituting the reduced yield stress (0.2% proof stress) and Young’s modulus into the design rules. The nominal design strengths were calculated using the cross-section and the reduced material properties as those used in the parametric study of the finite element analysis.  It should be noted that the current direct strength method is developed based on cold-formed steel structural members at normal room temperature by Schafer and Peköz [Ref. 19]. In this study, the direct strength method is used for cold-formed steel channel-sections subjected to bending at elevated temperatures.  Fig.8 shows the comparison of the reduction factor Mu,T/Mu,normal with the reduction factor predicted using the direct strength method (MDSM,T/MDSM,normal). The value of MDSM,T/MDSM,normal has been calculated for values of thickness of 2 mm and 6 mm. It is shown that the values of the reduction factor Mu,T/Mu,normal plots closely to the values of MDSM,T/MDSM,normal within an acceptable range.  MDSM,T/MDSM,normal is therefore appropriate for a design recommendation for the reduction in strength of a cold-formed steel channel-section undergoing premature web buckling at elevated temperatures.  00.20.40.60.811.20 100 200 300 400 500 600 700Temperature (oC)Normalised results against ambient temperaturet=2mm t=3mmt=4mm t=5mmt=6mm t=8mmDSM (t=2mm) DSM (t=6mm)(a) Bolt-group having aB = 200 mm 557  00.20.40.60.811.20 100 200 300 400 500 600 700Temperature (oC)Normalised results against ambient temperaturet=2mm t=3mmt=4mm t=5mmt=6mm t=8mmDSM (t=2mm) DSM (t=6mm)(b) Bolt-group having aB = 500 mm     00.20.40.60.811.20 100 200 300 400 500 600 700Temperature (oC)Normalised results against ambient temperaturet=2mm t=3mmt=4mm t=5mmt=6mm t=8mmDSM (t=2mm) DSM (t=6mm)(c) Bolt-group having aB = 1000 mm Figure 8. Comparison of variation of moment capacity with direct strength method       558   Concluding remarks   A simple design recommendation has been proposed that will allow premature buckling to be taken into account at elevated temperatures, by applying a reduction factor to the moment capacity determined at ambient temperature. This reduction factor is based on the moment capacity of the section, calculated using the direct strength method.    Acknowledgements   The work described in this paper was supported by the William M.W. Mong Engineering Research Fund provided by The University of Hong Kong. The authors are also thankful to Mr Ran Feng for the assistance of this research project.                       559  Appendix. - References    1 Kirk, P. ‘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, 1986, p295. 2 Lim, J.B.P. and Nethercot, D.A. ‘Design-development of a general cold-formed steel portal framing system’, The Structural Engineer, 80, No. 21, 2002, p31. 3 Wong, M.F. and Chung, K.F. ‘Experimental investigation of cold-formed steel beam-column sub-frames’, Proc. 15th International Specialty Conference on Cold-formed Steel Structures, St. Louis, University of Missouri-Rolla, 2000, p607-618. 4 Chung, K.F. and Shi, Y.J. ‘Lateral torsional buckling of gusset plates in bolted moment connections among cold-formed steel members’, Jour. Constr. Steel Res., 46, Nos. 1-3, 1998, p418, Oxford, Elsevier Applied Science. 5 Baldassino, N. and Bernuzzi, C. ‘Analysis and behaviour of steel storage pallet racks’, Thin-Walled Structures, 37, No.4, 2000, p277. 6 Chen J and Young B. ‘Experimental investigation of cold-formed steel material at elevated temperatures’, Thin-Walled Struct., 2007; 45(1), p96-110. 7 Chen J and Young B. ‘Mechanical properties of cold-formed steel at elevated temperatures’, Proceedings of the 17th International Specialty Conference on Cold-Formed Steel Structures, Orlando, 2004, p437-465. 8  ABAQUS standard user's manual, Version 6.5. ABAQUS, Inc.; 2004. 9 Kaitila O. ‘Finite element modeling of cold-formed steel members at high temperatures’, Licentiate thesis, Helsinki University, 2002.  10 Zha XX. ‘FE analysis of fire resistance of concrete filled CHS columns’, Journal of Constructional Steel Research, 2003; 59(6), p769-779.  11 Lim, J.B.P. and Nethercot, D.A. ‘F.E.-assisted design of the eaves bracket of a cold-formed steel portal frame’, Journal of Steel and Composite Structures, 2, No. 6, 2002, p411. 560  12 Lim, J.B.P. and Nethercot, D.A. ‘Ultimate strength of bolted moment-connections between cold-formed steel members’ Thin-Walled Struct., 41(11), 2003, p1019. 13 Lim, J.B.P. and Nethercot, D.A. ‘Finite element idealisation of a cold-formed steel portal frame’, Journal of Structural Engineering, ASCE, 130(1), 2004. p78-94 14 Chung, K.F. and Lau, L. ‘Experimental investigation on bolted moment connections among cold-formed steel members’, Engng Struct, 21, 1999, p898. 15 Wong, M.F. and Chung, K.F. ‘Structural behaviour of bolted moment connections in cold-formed steel beam-column sub-frames’, Jour. Constr. Steel Res., Oxford, Elsevier Applied Science, 58, No. 2, 2002, p253. 16 BS5950: Part 5. Code of practice for design of cold-formed sections, London, British Standards Institution, 1998. 17 Supplement to the North American Specification for design of cold-formed steel structural members, American Iron and Steel Institute, Washington, D.C., 2004. 18 AS/NZS 4600:2005. Cold-formed steel structures, Australian/New Zealand Standard, Standards Australia, Sydney, Australian, 2005. 19 Schafer, B.W. Peköz, T. ‘Direct strength prediction of cold-formed steel members using numerical elastic buckling solutions’, Proceedings of the 14th International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, 1998; p69-76.            561   Appendix. - Notation    aB length of bolt-group bB breadth of bolt-group D depth of web of channel-section Enormal Young’s modulus at normal room temperature  ET Young’s modulus at temperature T°C fy  yield stress fy,normal yield stress at normal room temperature fy,T  yield stress at temperature T°C  fu  ultimate stress fu,normal ultimate stress at normal room temperature fu,T  ultimate stress at temperature T°C MDSM,normal moment capacity calculated using direct strength method at normal room temperature MDSM,T moment capacity calculated using direct strength method at temperature T°C Mu ultimate moment capacity Mu,normal ultimate moment capacity at normal room temperature Mu,T ultimate moment capacity at temperature T°C t thickness of channel-section or plate    

Effects of elevated temperatures on ultimate moment capacity of bolted moment-connections between cold-formed steel members

Young, Ben

Lim, J. B. P.

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

English

Effects of Elevated Temperatures on Ultimate Moment Capacity of Bolted Moment-connections Between Cold-formed Steel Members

https://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=1315&context=isccss

Effects of elevated temperatures on ultimate moment capacity of bolted moment-connections between cold-formed steel members

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