30 G.J. Hancock Both the distortional buckling strength Md and section strength Ms reasonably accurately predict the test results at shorter lengths as well as the longer lengths specimens which fail in the lip buckling mode. AS 4100 provides an unconservative estimate of the section strength. However, for the more slender C10010 section, the distortional buckling strength Md and section strength Ms predictions of AS/NZS 4600 are unconservative. By comparison, AS 4100 is more accurate although this may be coincidental since the design method in AS 4100 was not developed for local and distortional buckling of such slender sections and the prediction is based on a very simple model of local buckling. Further, there seems to be a significant interaction between the lateral buckling mode and lip buckling at longer lengths with both AS 4100 and AS/NZS 4600 providing unconservative predictions of the strength. Further investigations of this phenomenon are required for slender sections. A separate paper on the bending and torsion of cold-formed channel beams loaded concentrically and eccentrically at mid-span has been published (Put, Pi and Trahair, 1999b). The tests show that the beam strengths decrease as the load eccentricity increases and that the strength is higher when the load acts on the centroid side of the shear centre than when it acts on the side away from the shear centre. Good agreement is demonstrated between the test results and analytical predictions of the strengths. An extended series of analytical expressions was used to develop simple interaction equations that can be used in the design of eccentrically loaded cold-formed channel beams. Fig. 5 Lateral buckling tests of cold-formed channels compared with design strengths Bolted and Screwed Connections in G550 Sheet Steels Cold-formed structural members are usually fabricated from sheet steels which must meet various material requirements prescribed in applicable national design standards. AS/NZS 4600 allows the use of thin (t< 0.9 mm), high strength (fy = 550 MPa) sheet steels in all structural sections. However, in the design the engineer must use a value of yield stress and ultimate strength reduced to 75% of the minimum specified values, due to lack of ductility exhibited by sheet steels which are cold reduced to thickness. Three papers investigating the ductility (Rogers and Hancock, 1997), bolted connection capacity (Rogers and Hancock, 1998) and screwed connection capacity (Rogers and Hancock, 1999) have recently been published summarising research investigating thin G300 and G550 sheet steels. Recent Developments in Cold-Formed Open Section and Tubular Members 31 Fig. 6 Bearing strength of bolted connections in thin sheet steels compared with design strength 32 G.J. Hancock In general, the problems with these steels were not a reduction in section strength due to the low ductility, but a problem in the bearing capacity of thin sections. This can be clearly seen in Fig. 6 where the bearing capacity of bolted connections in 0.42 mm G550 steel and 0.60 mm G550 and G300 steel are well below the predictions of AS/NZS 4600 and other design standards. The only standard to provide a reasonable prediction of this phenomenon was the Canadian standard for cold- formed steel structural members (CSA, 1994) which had a bearing coefficient which varied with the d/t ratio of the bolt and sheet. Proposals have been made for the Australian standard and American specification to adopt this approach. Similar characteristics were discovered for screwed connections as reported in Rogers and Hancock (1999). The recommended beating coefficients also depend on the screw diameter to sheet thickness ratio and are shown in Fig. 7. Fig. 7 Existing and Proposed Bearing Coefficients for Screw Connections TUBULAR MEMBERS Tubular Beam-Columns A test program was conducted into the behaviour of cold-formed square hollow section (SHS) beam- columns of slender cross-section (Sully and Hancock, 1998). The experimental program follows an earlier test program on compact SHS beam-columns (Sully and Hancock, 1996). The tests were conducted in a purpose built testing rig capable of applying load and moment in a constant ratio. The tests specimens were pin-ended and were loaded at two different ratios of end moment. The results of the testing program have been compared in Sully and Hancock (1998) with the current design rules in AS 4100-1998, the American Institute of Steel Construction Specification and Eurocode 3. From the interaction tests, it is clear that the slender sections collapse more suddenly as a result of inelastic local buckling than do compact sections. The long yielding plateau and associated high curvatures observed in the compact tests (Sully and Hancock, 1996) were not evident for the slender sections. Local imperfections are more easily formed in the slender sections particularly from the welding of the connection components. These local imperfections can have a detrimental effect on the section bending capacity of the member causing premature collapse through local instability. The possibility of this type of failure occurring is of particular concern in structures where maximum moments occur at the member connections. Further research is required in this area. For the long length interaction tests where the maximum load was reached prior to local instability, the design rules in AS 4100 for compact doubly-symmetric sections are applicable. However, this Recent Developments in Cold-Formed Open Section and Tubular Members 33 does not preclude the case of more slender sections than those tested which may locally buckle before reaching maximum load. Further investigation is required to determine if the AS 4100 compact section interaction rules are appropriate for non-uniform moment. Short length interaction tests indicated that local instability affects the beam-column strength more severely for short length specimens. Again, further investigation is required to determine if the AS 4100 interaction rule is appropriate for non-uniform moment. The simple linear interaction rule for non-compact sections in AS 4100 appears satisfactory for all the sections tested. Bolted Moment End Plate Connections Moment end plate connections joining 1-section members are used extensively and considerable documentation on their behaviour exists in the literature. In contrast, research on moment end plate connections joining rectangular and square hollow sections is limited and satisfactory design models are not widely available. The research on tubular end plate connections that has been conducted has concentrated on pure tensile loading or combined compression and bending. An analytical model to predict the serviceability limit moment and ultimate moment capacities of end plate connections joining rectangular hollow sections has been presented in Wheeler, Clarke, Hancock and Murray (1998). The connection geometry considered utilises two rows of bolts, one of which is located above the tension flange and the other of which is positioned symmetrically below the compression flange. Using a so-called modified stub-tee approach, the model considers the combined effects of prying action caused by flexible end plates and the formation of yield lines in the end plates as shown in Fig. 8. The model has been calibrated against experimental data from an extended test program forming part of the research project (Wheeler, Clarke and Hancock, 1995). Of the three types of end plate behaviour considered in the stub-tee model (thick, thin and intermediate), the paper recommends that the end plate connections be designed to behave in an intermediate fashion, with the connection strength being govemed by tensile bolt failure. Thin plate behaviour results in connections that are of very ductile and exhibit extremely high rotations, while connections exhibiting thick plate behaviour are very brittle and may be uneconomical. M M M O O O O O O (a) Mode 1 (b) Mode 2 (c) Mode 3 Fig. 8 Yield line mechanisms for bolted moment end plate connection 34 G.J. Hancock Plastic Design of Cold-Formed Square and Rectangular Hollow Sections Plastic design of cold-formed members has been limited by design standards such as AS 4100 since plastic design methods were verified by tests on hot-rolled steel members, which have notably different material properties compared to cold-formed hollow sections. To investigate the suitability of cold-formed hollow sections for plastic design, a series of bending tests examined the influence of web slenderness on the rotation capacity of cold-formed rectangular hollow sections (Wilkinson and Hancock 1998a). The results indicate that the plastic (Class 1) web slenderness limits in design standards, which are based on tests of I-sections, are not conservative for RHS. Some sections, which are classified as compact or Class 1 by current steel specifications, do not demonstrate rotation capacity suitable for plastic design. The common approach in which the flange and web slenderness limits are given independently is inappropriate for RHS. There is considerable interaction between the webs and the flange, which influences the rotation capacity, as shown by the approximate iso- rotation curves in Fig. 9. A proposal for a bilinear interaction formula between the web and flange slenderness limits for compact RHS is also shown in Fig. 9. ~" 50 r ~- 45 ~40 N 35 II ~ 30 ~ 25 s 20 "~ 10 ~ 5 ~ o 20 Possible new AS 410D I I Compact Limit Compa~:t I Limit ~ < 70- 5~/6 ~~ ~'~ ~f< 30 s , Web Slenderness (AS 4100) ~ - (d-2t)/t-~(J'~/250) 30 40 50 60 70 80 90 Fig. 9 Iso-rotation curves and proposed compact limit for webs of rectangular hollow sections Further research (Wilkinson and Hancock, 1998b,c,d) has recently been completed investigating the plastic behaviour and design of portal frames and connections within the frames. These papers described tests of different types of column-rafter knee connections, and tests of 3 large scale portal frames manufactured from cold-formed Grade C350 and Grade C450 cold-formed RHS. Some welded connections experienced fracture near the heat affected zone caused by welding, before adequate plastic rotation was achieved. A plastic mechanism was formed in each frame and plastic collapse occurred. The ultimate loads of the frames can be predicted by plastic analyses although second order effects and the shape of the stress-strain curve may be important. Recent Developments in Cold-Formed Open Section and Tubular Members CONCLUSIONS 35 A wide ranging research program on cold-formed members which has been performed at the University of Sydney over more than 15 years has been summarised. Emphasis has been placed on test data and comparison of the test results with design standards, particularly the Australian Standard AS 4100-1998 Steel Structures and the Australian/New Zealand Standard AS/NZS 4600:1996 Cold- Formed Steel Structures. The research has been performed mainly on high strength steels with the strength typically ranging from 350 MPa to 550 MPa. Both members and connections have been investigated. There are several general conclusions that can be reached: 1. Open sections such as angles and channels in compression often suffer from structural instability in the elastic range due to the slender nature of the sections and the high yield strength of the sections. Torsional modes or torsional modes combined with flexure can become dominant. Care has to be taken with loading conditions such as fixed or pinned ends and assumptions regarding the line of action of axial load since it can have a large effect on axial load capacity. 2. Laterally unbraced flexural members may undergo lateral buckling with significant interaction with local and distortional modes. Clearly, more research is required in this area as the project described has found certain unconservative behaviour when compared with existing design standards for slender sections. Bearing failure may also be important in flexural members because the cold-formed sections have rounded comers and unstiffened webs. 3. Ductility was not found to be a problem in any of the members or connections tested even with high strength (G550) cold-reduced steel. Of greater importance is the thinness of the material and the types of bearing failures that can occur in bolted and screwed connections. New design rules have been proposed for these cases. 4. Slender tubular members are more likely to undergo inelastic local buckling in compression or combined compression and bending. The design rules for these types of members are included in AS 4100-1998. Care needs to be taken with welded connections to slender cold-formed tubes. Section distortion may occur and aggravate inelastic local buckling of the slender cold-formed sections. 5. Proposals for the design of bolted moment end plates in cold-formed tubular members have been made. This type of connection can be designed for satisfactory performance provided the welding of the tubes to the end plates is carried out to rigorous welding standards. 6. The plastic design of cold-formed tubular (RHS and SHS) members is possible provided the aspect ratio of the sections used for plastic design is chosen carefully. The existing Class 1 section web slenderness limits, which are based on I-section members, are unconservative for RHS members. Revised design rules have been proposed. Care also needs to be taken when designing moment resisting connections in cold-formed tubular members to ensure they have adequate rotation capacity for plastic design. ACKNOWLEDGEMENTS This paper has been prepared based on the research of many people. Permission to use their test data and resulting graphs is appreciated. They were all supplied in electronic form from the original authors which explains the slight change in format between the different figures. The following 36 G.J. Hancock people are gratefully acknowledged: Emeritus Professor NS Trahair, Associate Professor Kim Rasmussen, Dr Murray Clarke, Dr Ben Young, Dr Andrew Wheeler, Dr Colin Rogers, Mr Bogdan Put and Mr Tim Wilkinson. REFERENCES American Iron and Steel Institute (1997). Specification for the Design of Cold-Formed Steel Structural Members, Washington, DC. BHP Structural and Pipeline Products (1997). DuraGal Design Capacity Tables for Structural Steel Angles, Channels and Flats, BHP, Sydney. Canadian Standards Association (1994). "Cold Formed Steel Structures Members", Toronto, Canadian Standards Association. Popovic, D, Hancock, GJ and Rasmussen, KJR (1999). "Axial Compression Tests of Cold-Formed Angles", Journal of Structural Engineering, ASCE, 24:5, 515-523. Pi, Y-L, Put, BM and Trahair, NS (1999a). "Lateral Buckling Tests of Cold-Formed Channel Beams", Journal of Structural Engineering, ASCE, 125: 5, 532-539. Put, BM, Pi, Y-L and Trahair, NS (1999b). "Bending and Torsion of Cold-Formed Channel Beams", Journal of Structural Engineering, ASCE, 125-5, 540-546. Rogers, CA and Hancock, GJ (1997). "Ductility of G550 Sheet Steel in Tension", Journal of Structural Engineering, ASCE, 123:12, 1586-594. Rogers, CA and Hancock, GJ (1998). "Bolted Connection Tests of Thin G550 and G300 Sheet Steels", Journal of Structural Engineering, ASCE, 124:7, 798-808. Rogers, CA and Hancock, GJ (1999). "Screwed Connection Tests of Thin G550 and G300 Sheet Steels", Journal of Structural Engineering, ASCE, 125:2, 128-136. Standards Association of Australia (1991), Structural Steel Hollow Sections, AS 1163-1991. Standards Australia (1993). Steel Sheet and Strip - Hot Dipped Zinc-Coated or Aluminium/Zinc- Coated, AS 1397-1993. Standards Association of Australia. (1998). Steel Structures, AS 4100-1998. Standards Association of Australia/Standards New Zealand (1998). Cold-Formed Steel Structures, AS/NZS 4600:1996. Sully, R and Hancock, GJ (1996). "Behaviour of Cold-Formed SHS Beam Columns", Journal of Structural Engineering, ASCE 122:3, 326-336. Sully, RM and Hancock, GJ (1998). "The Behaviour of Cold-Formed Slender Square Hollow Section Beam-Columns", Proceedings of the Eighth International Symposium on Tubular Structures, Singapore, 445-454. Recent Developments in Cold-Formed Open SeCtion and Tubular Members 37 Wheeler AT, Clarke MJ & Hancock G J, (1995), "Tests of Bolted Moment End Plate Connections in Tubular Members", Proceedings, 14th Australasian Conference on Structures and Materials, University of Tasmania, Hobart, Tasmania, 331-336. Wheeler, AT, Clarke, MJ, Hancock, GJ and Murray, TM (1998). "Design Model for Bolted Moment End Plate Connections Joining Rectangular Hollow Sections", Journal of Structural Engineering, 124:2, 164-173. Wilkinson, T and Hancock, GJ. (1998a). "Tests to Examine Compact Web Slenderness of Cold- Formed RHS", Journal of Structural Engineering, ASCE, 124:10, 1166-174. Wilkinson T and Hancock GJ (1998b). "Tests of Stiffened and Unstiffened Knee Connections in Cold-Formed RHS", Tubular Structures VIII, Proceedings, 8th International Symposium on Tubular Structures, Singapore, 177-186. Wilkinson T and Hancock GJ (1998c)."Tests of Bolted and Intemal Sleeve Knee Connections in Cold-Formed RHS", Tubular Structures VIII, Proceedings, 8th International Symposium on Tubular Structures, Singapore, 187-195. Wilkinson T and Hancock GJ (1998d). "Tests of Portal Frames in Cold-Formed RHS", Tubular Structures VIII, Proceedings of the 8th International Symposium on Tubular Structures, Singapore, 521-529. Young, B and Rasmussen, KJR (1998a). "Tests of Fixed-Ended Plain Channel Columns", Journal of Structural Engineering, ASCE, 124-2, 131-139. Young, B and Rasmussen, KJR (1998b). "Design of Lipped Channel Columns", Journal of Structural Engineering, ASCE, 124-2, 140-148. Young, B and Hancock, GJ (1998). "Web Crippling Behaviour of Cold-Formed Unlipped Channels", 14 th International Specialty Conference on Cold-Formed Steel Structures, St Louis, October, 127-150. Zhao, X-L, Hancock, GJ and R Sully (1996). "Design of Tubular Members and Connections using Amendment No 3 to AS 4100", Steel Construction, Australian Institute of Steel Construction, 30:4, 2- 15. Wheeler, AT, Clarke, MJ and Hancock, GJ (1995)."Tests of Bolted Moment End Plate Connections in Tubular Members", Proceedings, 14 th Australasian Conference on Mechanics of Structures and Materials, University of Tasmania, 331-336. This Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left BlankThis Page Intentionally Left Blank BEHAVIOUR OF HIGHLY ~DUNDANT MULTI-STO~Y BUILDINGS UNDER COMPARTMENT FI~S J.M. Rotter School of Civil and Environmental Engineering, University of Edinburgh, Edinburgh EH9 3JN, UK ABSTRACT In current design practice, structural members under fire are treated as if each member is isolated and determinate, with the strength controlled by material property degradation at high temperature. This treatment might well seem appropriate for compartment fires where only the structural members in the compartment are affected. However, it is seriously misguided for large redundant composite multi- storey building structures, because the major influence of the adjacent cool structure on the behaviour of elements under extreme heating is ignored. The interactions between adjacent parts can completely transform the structural response and invalidate the design assumptions. Key features of the behaviour of a structural element under fire within a highly redundant structure are examined in this paper. The surrounding cool structural components restrain thermal expansion and provoke other displacements. Several examples are presented of the behaviour of quite simple structures which illustrate the roles of thermal expansion, loss of material strength, the relative stiffness of adjacent parts of the structure, the development of large deflections, post-buckling and temperature gradients. Although simple, the relevance of these examples to complete structures is clear. Several counter-intuitive phenomena are noted. From these discoveries, some significant implications are drawn for the philosophy of design to be used for large buildings under fire. KEYWORDS Compartment fires, composite, fire, floor systems, large deflections, membrane effects, multi-storey, non-linear response, plasticity, post-buckling, restraint, thermal buckling, thermal expansion. INTRODUCTION For fire control reasons, the spaces within large buildings have long been divided into compartments to ensure that the fire does not spread and that its effects can be contained locally. The consequence for the structure is that only a local part is severely heated, whilst its surroundings remain comparatively cool. The result is that a very hot weakening and expanding local region is contained within a large cool mass. The interaction between these two regions is the subject of this paper. The full scale fire tests on the composite building at Cardington (Kirby, 1997; Moore, 1997) showed that very high temperatures could be sustained in the steel joists. Since the temperatures were so high that the steel strength was effectively destroyed, and yet runaway failures did not occur, researchers are presented with a significant task to explain why; this paper sets out some fundamental parts of that explanation. Current assessment methods for the fire resistance of a building structure (ENV 1994-1-2, 1995) are based on the fire testing of single elements, evaluated in terms of the time to failure. Naturally, these 39 . Cold-Formed Steel Structures, AS/NZS 460 0:19 96. Sully, R and Hancock, GJ (19 96) . "Behaviour of Cold-Formed SHS Beam Columns", Journal of Structural Engineering, ASCE 122:3, 32 6- 3 36. . Australia (1993). Steel Sheet and Strip - Hot Dipped Zinc-Coated or Aluminium/Zinc- Coated, AS 139 7-1 993. Standards Association of Australia. (1998). Steel Structures, AS 410 0-1 998. Standards. summarising research investigating thin G300 and G550 sheet steels. Recent Developments in Cold-Formed Open Section and Tubular Members 31 Fig. 6 Bearing strength of bolted connections in thin sheet