20
Z Y. Shen
and Table 4, respectively. ~ and 6 denote the sectional reduction and elongation of the material,
respectively.
The loading series of the shaking table test are listed in Table 5. The input ground movement in the x-
direction and y-direction of the shaking table are El-Centro N-S and El-Centro E-W, respectively,
taking the time ratio t//~.
/~/.~
TABLE 5
LOADING SERIES OF THE TEST
Series No. 1 2 3 4 5
Amplitude
of the
acceleration
X 0.30g 0.30g 0.50g 0.50g 0.70g
Direction (0.309g) (0.311 g) (0.4976) (0.499g) (0.7046)
Y 0.15g 0.15g 0.25g 0.25g 0.25g
direction (0.163g) (0.1556) (0.258g) (0.2546) (0.2526)
Series No. 6 7
Amplitude X 0.70g 0.60g
of the Direction (0.703g) (0.6036)
acceleration Y 0.25g 0.30g
Direction (0.2546) (0.3036)
( 9 ) is the actual amplitude of the shaking table.
8 9 10
0.60g 0.80g 0.80g
(0.605g) (0.790g) (0.792g)
0.30g 0.35g 0.35g
(0.305g) (0.358g) (0.359~;)
The natural frequencies of the free vibration of the model measured from the experiment are listed in
Table 6. There is no different between the initial frequencies and the frequencies after 4th loading, that

(6=7.23%)
4.883(5.242)
(6 =6.85%)
4.863(5.221)
(6=6.85%)
4.833(5.179)
(6 =6.68%)
4.800(5.155)
(6=6.87%)
9.115(9.243)
(6=1.38%)
9.115(9.220)
(6=1.14%)
9.081(9.202)
(6=1.31%)
9.046(9.164)
(6=1.28%) .
8.870(9.097)
(6=2.49%)
15.462(17.730)
(6=12.79%)
15.462(17.668)
(8=12.49%)
15.339(17.618)
(6=12.93%)
15.304(17.509)
(6=12.59%)
15.200(17.390)
(6=12.60%)
Cumulative Damage Model for the Analysis of Steel

(cm) Cal. with D 1.26 1.28 1.02 1.05 1.30 1.34
Cal. D=-0 1'.24 1.25 0.99 1.00 1.23 1.25
,,
Min Tested -1.30 -1.31 -1.09 -1.09 -1.37 -1.42
(cm) Cal. withD -1.13 -1.14 -1.03 -1.05 -1.31 -1.34
Cal. D=-0 -1.10 -1.11 -1.02 -1.03 -1.28 -1.30
The cumulative damages of the columns of the steel frame model after each loading of the loading
series are shown in Table 8. In the Table the two digits of the end member indicate the column (Figure
5) and the first digit means the end where damage occurs.
TABLE 8
CUMULATIVE DAMAGES OF THE COLUMNS OF THE STEEL FRAME MODEL
Loading End Number
No. 1-5 5-1 2-6 6-2 3-7 7-3 4-8 8-4
4 0.083 0.020 0.080 0.024 0.085 0.020 0.081 0.025
5 0.089 0.023 0.153 0.029 0.091 0.024 0.155 0.029
6 0.112 0.037 0.171 0.032 0.165 0.034 0.172 0.033
7 0.155 0.051 0.196 0.065 0.201 0.063 0.198 0.066
8 0.219 0.073 0.348 0.068 0.265 0.088 0.364 0.068
9 0.242 0.081 0.371 0.080 0.288 0.096 0.387 0.080
10 0.287 0.095 0.395 0.097 0.334 0.111 0.432 0.109
Loading End Number
No. 5-9 9-5 6-10 10-6 7-11 11-7 8-12 12-8 0 0.021 0.005 0.057 0.017 0.021 0.005
0.042 0.013 0.026 0.128 0.042 0.013 0.084 0.007
From Figures 6 to 8 and Tables 7, 8 the following points can be drawn. First, a severe seismic action

Shen Z. Y., Dong B. and Cao W. w. (1998). A Hysteresis Model for Plane Steel Members with
Damage Cumulation Effects. Journal of Constructional Steel Research 48:2/3, 79-87.
Shen Z. Y. and Lu L.W. (1983). Analysis of Initially Crooked, End Restrained Steel Columns, Journal
of Constructional Steel Research, 3:1, 40-48.
RECENT RESEARCH AND DESIGN DEVELOPMENTS IN COLD-
FORMED OPEN SECTION AND TUBULAR MEMBERS
Gregory J. Hancock
Department of Civil Engineering, University of Sydney
NSW, 2006, Australia
ABSTRACT
A major research program has been performed for 20 years at the University of Sydney on cold-
formed open section and tubular structural members. This research has included both members and
connections and has been performed predominantly for high strength steel sections. The open section
members include mainly angles, channels (with and without lips) and zeds, and the tubular members
include mainly rectangular (RHS) and square (SHS) hollow sections. The research has been mainly
incorporated in the Australian Steel Structures Standard AS 4100-1998 and the Australian/New
Zealand cold-formed steel structures standard AS/NZS 4600. The paper summarises the recent
developments in the research and points to on-going and future research needs.
KEYWORDS
Cold-formed, Steel Structures, Structural Design, Open Sections, Tubular Sections, Standards
INTRODUCTION
Cold-formed structural members are being used more widely in routine structural design as the world
steel industry moves from the production of hot-rolled section and plate to coil and strip, often with
galvanised and/or painted coatings. Steel in this form is more easily delivered from the steel mill to
the manufacturing plant where it is usually cold-rolled into open and closed section members. In
Australia, of the approximately one million tonnes of structural steel used each year, 125,000 tonnes is
used for cold-formed open sections such as purlins and girts and 400,000 tonnes is used for tubular
members. Tubular members are normally produced by cold-forming with an electric resistance weld
(ERW) to form the tube. In most applications of open sections, the coil is coated by zinc or
aluminium/zinc as part of the steel supply process. In some applications of tubular members, the

9 Lipped and unlipped channel sections in compression
9 Unlipped channel sections in bearing
9 Lateral buckling of channel sections
9 Bolted and screwed connections in G550 steel
9 Tubular beam-columns
9 Bolted moment end-plate connections
9 Plastic design of cold-formed square and rectangular hollow sections
OPEN-SECTION MEMBERS
Axial Compression of Cold-Formed Angles
A major research program was performed on cold-formed angles formed by cold-rolling and in-line
galvanising so that the final product had a yield stress of 450 MPa (BHP (1996)). Sections ranging
from slender (EA 50*50*2.4 mm) to non-slender (EA 50"50"4.7mm) were tested in pin-ended
concentric compression such that flexural buckling could occur about the minor principal axis.
Detailed measurements of the stress-strain characteristics of the material forming the sections, the
residual stresses and overall geometric imperfections were taken. The results are reported in Popovic,
Hancock and Rasmussen (1999).
The results of the tests are compared with the design rules of AS 4100 (Standards Australia 1998) and
AS/NZS 4600 (Standards Australia 1996) in Figs 1 and 2. Comparison of the angle tests is shown
with AS 4100 in Fig. 1 and AS/NZS 4600 in Fig. 2 which only includes the slender sections. The
slender sections failed in a combination of flexural and flexural-torsional buckling. For the sections
Recent Developments in Cold-Formed Open Section and Tubular Members
27
tested, it can be concluded that the design procedure in AS 4100 is not satisfactory if the design yield
stress is taken from stub column strengths as shown in Fig. 1 but it is satisfactory if it is based on
coupons taken from the flats. The design procedure does not include specific rules for flexural-
torsional buckling. Higher design curves than recommended by AS 4100 can be used for the non-
slender sections which did not include torsional deformations in the failure mode. As demonstrated in
Fig. 2, the design procedure in AS/NZS 4600 is conservative for short length sections where torsional
buckling is included twice by virtue of an effective section for local buckling and torsional buckling
stresses in the column design. For longer length columns, the additional required moment equal to a

0.8
Z
3 0.6
z
0.4
0.2
Long Column Tests L50x50x2.5
AS 4600 and AISI Column Curves (fy = 396 MPa)
l
- Pin-Ended
f-t buckling controls
9 Fixed-Ended
" /
ff-t
X A e NC
/ " 9 /.
,L flexure controls
[
~000
.
9 I
0
20 40 60 80
1 O0 120 140 160 180
200
Le/r
0.0
Fig. 2 Comparison of angle section test strengths with cold-formed design standards
28 G.J. Hancock
Lipped and Unlipped Channels in Compression

comers.
Lateral Buckling of Channel Sections
A research program on the lateral buckling capacities of cold-formed lipped channel-section beams
(CFCs) was undertaken and published in Put, Pi and Trahair (1999a). It has been argued that the
design approximations based on hot-rolled beams may be inappropriate for CFCs, because of the very
different cross-sectional shape and method of manufacture. The paper describes lateral buckling tests
on simply supported unbraced CFCs of two different cross-sections which were undertaken to resolve
the issue. However, the lateral buckling tests showed that the CFCs failed catastrophically by local
and distortional buckling of the compressed element of the cross-section after quite large
deformations. The failure moments were lower when the beam lateral deflection increased the
compression in the compression lip, and higher when they increased the compression in the flange-
web junction.
The results in Fig. 5, which are taken from Put, Pi and Trahair (1999a), show some interesting features
when compared with the predictions of AS 4100 and AS/NZS 4600. The stockier section C10019 is
fairly accurately predicted by AS/NZS 4600 although it is slightly conservative at longer lengths.