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.
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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.
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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