Prepared for a lecture series given by Professor Greg Hancock
and Dr Xiao-Ling Zhao, organised by the Australian Institute of
Steel Construction, June 2000.
Research into the Behaviour and Design of Cold-Formed
Tubular Members and Connections
Gregory Hancock and Tim Wilkinson
Centre for Advanced Structural Engineering
Department of Civil Engineering, University of Sydney
NSW, 2006, Australia
Xiao-Ling Zhao
Department of Civil Engineering, Monash University
Clayton, Victoria, Australia
ABSTRACT
For nearly 20 years, a major research program has been performed at the University of Sydney
investigating the structural behaviour and design of cold-formed tubular structural members and
connections. This research has been progressively incorporated in the Australian Standard AS 4100
Steel Structures. In the last 5 years, several major steel structures have been built for the Olympics
2000 and these have been made mainly from cold-formed tubular members designed to AS 4100.
Hence the Olympic structures have benefited from the research and design developments.
Cold-formed tubular members are manufactured in Australia to the Australian Standard AS 1163
Structural Steel Hollow Sections. In 1990, the Australian Steel Structures Standard was published as
AS 4100 in limit states format and included the University of Sydney research available at that time.
In 1998, a revision of AS 4100 was published and included all of the latest research on cold-formed
tubular members
The lecture summarises the research which has been performed to date including plate strength,
compression members, flexural members, beam-columns, portal frames, and welded and bolted
connections. Emphasis is placed on the experimental data and its use in formulating design equations
for use in AS 4100-1998.
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 some applications of tubular members, the sections are in-line galvanised
1
with a subsequent enhancement of the tensile properties. The resulting product is called DuraGal
(BHP (1997)). In Australia, the total quantity of cold-formed products now exceeds the total quantity
of hot-rolled products.
Structural steel hollow sections are normally produced to the Australian Standard AS 1163 (1991).
They are all cold-formed and usually have stress grades of 250 MPa (called C250), 350 MPa (called
C350) and 450 MPa (called C450). The most common grade is C350 which has the yield strength
enhanced from 300 MPa to 350 MPa during the forming process. The C450 grade is often achieved
by in-line galvanising (BHP, 1997) but may be achieved by alloying elements in the steel feed.
The Australian Standard for the design of steel structures AS 4100 was first published in limit states
format in 1990 and permitted the use of cold-formed tubular members to AS 1163. Cold-formed
tubular members had been permitted to be designed to the permissible stress steel structures design
standard AS 1250 (Standards Australia 1981) since an amendment in 1982. However, the research on
cold-formed tubular members was limited in many areas, particularly flexural members and
connections, and so a significant research program was undertaken.
This paper summarises research in the following areas:
•
•
•
•
•
•
•
•
Plate slenderness limits for tube faces in both compression and bending (Section 1)
Compression members (Section 2)
Flexural members including lateral buckling (Section 3)
Web crippling under bearing and combined bending and web crippling under bearing (Section 4)
Combined compression and bending (beam-columns) for both compact and slender sections
(Section 5)
Welded connections less than 3 mm thick (Section 6)
Bolted moment end-plate connections (Section 7)
Plastic design of portal frames (Section 8)
1.
PLATE SLENDERNESS LIMITS
1.1
Flange Slenderness Limits in Compression
Design rules for the plate slenderness limits (yield slenderness limit 8ey and plastic slenderness limit
8ep) of cold-formed tubular sections are included in AS 4100-1998. These plate slenderness limits
were based on tests of C350 SHS and RHS produced by BHP Structural and Pipeline Products. The
test results were published in Hasan and Hancock (1989), Key and Hancock (1985) and Key, Hasan
and Hancock (1988). To ascertain whether these plate slenderness limits were applicable to C450
tubular sections, compression tests on stub columns and plastic bending tests on beams were
performed on sections produced by Palmer Tube Mills (Aust) Pty Limited. The test results were
published by Zhao and Hancock (1991a).
1.2
Yield Slenderness Limit for Flange in Compression
The yield slenderness limit (8ey) defines a plate element slenderness (8e) below which the plate can be
considered as fully effective when subjected to compression. The effective width (be) of a flat
element of clear width (b) is defined as:
λ t
 λ ey 
 = ey
be = b

fy
 λe 
250
(1)
2
in which fy is the yield stress used in design.
The nominal section capacity of a concentrically loaded compression member is defined in Clause 6.2
of AS 4100-1998 as:
Ns = kf An fy
(2)
in which An is the net area of the cross-section and kf is the form factor defined as:
kf =
Ae
Ag
(3)
where Ag is the gross area of the section. Ae is the effective area which is calculated from the gross
area by summing the effective areas of the individual elements, whose effective widths are given by
Eq. 1.
For SHS and RHS, the formulae for kf are given in Zhao and Hancock (1991a). They are summarised
below, where E = 200000 MPa, < = 0.3 and kb = 4.0 (the adoption of 4.0 for the elastic buckling
coefficient was explained in Key et al. (1988).
For SHS:
kf =
be 0.01858λ ey
=
b
Sc
(4)
For RHS:
0.01858λ ey
kf =
Sc
+
b
d
b
1+
d
(5)
where
2
 b  f y (1 − ν )
Sc =  
2
 t  Eπ k b
(6)
The parameter Sc is called the modified plate slenderness. For RHS, d (the clear depth of RHS)
should be used for the calculation of Sc in place of b (the clear width of RHS). Eq. (5) assumes that
for RHS only the more slender face is not fully effective.
For 8ey = 40, from Eq. (4) for SHS:
kf =
0.743
Sc
(7)
and from Eq. (5) for RHS:
3
0.743 b
+
Sc
d
kf =
b
1+
d
(8)
in which Sc is given by Eq. (6).
The dimensionless stub column failure strengths (Pu / AmFyf) have been plotted in Fig. 1 against the
modified plate slenderness S c = (bm / t m ) σ yf 12(1 − ν 2 ) / Eπ 2 k b . Fig. 1(a) compares the results for
the
1.2
1.0
k f for RHS
with b/d =0.6
100 x 100 x 3.8 SHS
100 x 100 x 3.3 SHS
100 x 100 x 2.8 SHS
75 x 75 x 3.3 SHS
75 x 75 x 2.8 SHS
75 x 75 x 2.3 SHS
65 x 65 x 3.3 SHS
125 x 75 x 3.8 RHS
125 x 75 x 3.3 RHS
100 x 50 x 2.8 RHS
0.8
Pu /A m σyf 0.6
0.4
0.2
k f for SHS
Elastic Local Buckling
k b = 4.0
(a) C450 SHS and RHS
0
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Modified Plate Slenderness (S c )
1.6
1.8
2.0
1.2
1.0
k b for RHS
with b/d =0.6
0.8
Pu /A m σyf 0.6
C450
C350
0.4
k f for SHS
0.2
(b) C350 and C450 SHS and RHS
Elastic Local Buckling
k b = 4.0
0
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Modified Plate Slenderness (S c )
1.6
1.8
2.0
Fig. 1 Section Strength versus Modified Plate Slenderness
different section sizes for C450 SHS and RHS, whereas Fig. 1(b) compares the results for the C350
tests and for the C450 tests. The form factor kf is also plotted in Figs 1(a) and (b) for SHS and RHS
with a b/d ratio equal to 0.6. The comparison is based on the measured yield stress (Fyf) and the
measured dimensions (bm,, tm and Am). From Fig. 1(b), it can be concluded that the plate yield
slenderness limit (8ey = 40) specified in AS 4100-1998 is adequate for both C350 and C450 SHS and
RHS. The reason for some tests having Pu / AmFyf greater than 1.0 is a result of the fact that Fyf is
based on the face yield strength whereas the average yield strength is greater than Fyf as a result of the
higher yield in the corners.
1.3
Plastic Slenderness Limit for Flange in Compression
For SHS and RHS, the plastic slenderness limit (8ep) defines a flange plate slenderness below which
the section can be used for plastic design. The usual method to judge whether a section can be used
4
for plastic design is to check its plastic hinge rotation capacity (R) as defined by Korol and Hudoba
(1978) and Hasan and Hancock (1989). A value of R equal to 4.0 was assumed to be sufficient to
allow redistribution of moment for plastic design.
From the measured plastic hinge rotation capacity (Rt) determined in tests for a range of sections, a
value of b/t = 25 was obtained for C350 RHS by Hasan and Hancock (1989), and a value of b/t = 22
was obtained for C450 RHS by Zhao and Hancock (1991) as the satisfactory lower bound limits for
defining the maximum flange slenderness of cold-formed RHS that may be used for plastic design.
From Clause 5.2 of AS 4100-1998
λe =
b fy
≤ λ ep
t 250
(9)
Hence, for C350 RHS, using b/t = 25, Eq. (9) gives 8ep = 29.6, and for C450 RHS, using b/t = 22, Eq.
(9) gives 8ep = 29.5.
A direct comparison of 8e versus Rt is shown in Fig. 2 using the measured values of bm, tm and Fyf. It
can be seen that at an Rt value of 4.0, both the C350 and C450 give a similar plate element plastic
slenderness limit (8ep) of approximately 30. If a higher value of Rt was required, then the C450 RHS
would require a lower plate element plastic slenderness limit than the C350 RHS.
bm σyf
-----Plate Element Slenderness -----tm √( 250 )
50
Linear Regression (C450)
40
Linear Regression (C350)
30
Lower Bound
20
0
Lower Bound
C450
C350
10
0
2
4
6
8
Plastic Hinge Rotation Capacity (R t )
10
12
Fig. 2 Plate Element Slenderness versus Plastic Hinge Rotation Capacity
It can be concluded that the plate element plastic slenderness limit (8ep = 30) specified in AS 41001998 is adequate for both C350 and C450 SHS and RHS. It should be noted that at this stage, plastic
design of SHS and RHS is not permitted by AS 4100-1998 so that the 8ep value is currently used to
define the limit for compact sections which can resist the plastic moment Mp without moment
redistribution.
1.4
Plastic Slenderness Limit for Web in Bending
To further investigate the suitability of RHS sections with low b/d 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 (1998). 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
5
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. 3 where the numbers next to the
markers are the value of Rt. A proposal for a bilinear interaction formula between the web and flange
slenderness limits for compact RHS is also shown in Fig. 4. The reference to “this paper” in Fig. 3
means Wilkinson and Hancock (1998).
50
0
Flange Slenderness (AS 4100) λf
45
0.8
40
2
2.7
35
9.0
25
1.8
5.0 4.3
6.5
8.0
1.2
3.5
4.2
30
1.5
0.8
1.2
5.6
0
4.8
9.0
8.5
1.3
6.0
20
3.8
7.4
7.1
12
15
13
10
AS 4100
Compact Limit
R =1
1.4
14
11
2.3
5.7
2.6
R =2
This Paper Grade C450
This Paper Grade C350
11
Zhao & Hancock (1991) Grade C450
R =4
5
R =6
0
20
30
40
50
Hasan & Hancock (1988) Grade C350
60
70
80
90
Web Slenderness (AS 4100) λw
Flange Slenderness (AS 4100) λw = (d -2t )/t ·√(f y/250)
Fig. 3 Rotation Capacity and Isorotation Curves for Tests of RHS
50
Possible new
Compact Limit
λw < 70 - 5λf /6
λf < 30
45
40
AS 4100
Compact
Limit
35
30
25
20
R =2
15
R =1
R =4
10
5
R =6
0
20
30
40
50
60
70
80
90
Web Slenderness (AS 4100) λw = (d -2t )/t·√(f y/250)
Fig. 4 Iso-rotation Curves and Proposed Compact Limit for Webs of RHS
2.
COMPRESSION MEMBERS
The formulae for column design adopted in AS 4100-1998 are based on the ‘modifying factor’
method for multiple column curves described by Rotter (1982). The nominal member capacity (Nc) of
a column is defined in Clause 6.3.3 of AS 4100-1998 as:
6
Nc = αs Nc ≤ Ns
(10)
in which Ns is given by Eq. (2). The member slenderness reduction factor "c is determined by the
following formulae:
2

 90  

α c = ξ 1 − 1 −   
 ξλ  

(11a)
λ 
  +1+η
90
ξ= 
2
λ 
2 
 90 
2
(11b)
λ = λ n + α aα b
(11c)
η = 0.00326(λ − 13.5) ≥ 0
(11d)
L 
λn =  e  k f
 r 
αa =
fy
250
2100(λ n − 13.5)
λ − 15.3λ n + 2050
2
n
(11e)
(11f)
The appropriate member section constant ("b) is given in Table 6.3.3(1) or 6.3.3(2) of AS 4100-1998.
The form factor (kf) is given by Eq. (3). The effective length (Le) is the product of the actual length
(L) and the member effective length factor (ke) determined in accordance with Clause 4.6.3 of AS
4100-1998.
The results of long column tests on SHS sections performed by Key, Hasan and Hancock (1988) are
compared in Fig. 5 with three column curves with different values of the appropriate member section
constant ("b). The test strengths are nondimensionalised with respect to the stub column strength (kf
Pyf) based on the measured yield stress of each specimen and the measured dimensions. The curves
with "b = -1.0 and 0.0 correspond approximately with the SSRC1 and SSRC2 column curves
respectively.
7
1.0
Euler (PE )
α b = - 1.0
- 0.5
0.0
Pmax
----------k f Pyf
76 x 76 x 2.0 SHS - Concentric
76 x 76 x 2.0 SHS - Eccentric (e = L/1000)
152 x 152 x 4.9 SHS - Concentric
152 x 152 x 4.9 SHS - (Eccentric (e = L/1000)
203 x 203 x 6.3 SHS - Concentric
203 x 203 x 6.3 SHS - Eccentric (e = L/1000)
0.5
0
0
0.5
1.0
k f Pyf
√( -----P---E------ ) (Non-Dimensional Slenderness)
1.5
Fig. 5 Comparison of AS 4100 Column Curves with Test Results
The test results on the loaded columns with load eccentricity equal to L/1000 have been adopted in AS
4100-1998 for the design of cold-formed SHS and RHS columns. The use of an eccentricity of
L/1000 resulted from the fact that the SHS tested were particularly straight and so no significant
geometric imperfections existed in the columns. The curve chosen in AS 4100-1990 for non-stress
relieved SHS and RHS is "b = -0.5
3.
FLEXURAL MEMBERS
Lateral Buckling Beam Curves
The beam design curve in AS 4100-1998 is very conservative when applied to RHS sections, since it
was based on the lower bounds of tests on I-sections. Inelastic lateral buckling tests on RHS sections
were performed and formulae for member capacity of RHS beams were proposed (Zhao, Hancock and
Trahair (1995) and are shown in Fig. 6. A finite element (FE) model was developed to simulate the
lateral buckling behaviour of RHS sections. The analysis included the effects of the prebuckling
deflections, material inelasticity, residual stresses and initial imperfections (Pi and Trahair, (1994))
and Zhao, Hancock, Trahair and Pi (1995)). The proposal of Pi and Trahair (1994) is shown in Fig. 6.
An alternative lateral buckling moment (Mbx) under uniform bending moment is given by:
(
)
M bx = 1.056 − 0.278λ2 M px
for 0.45 ≤ λ ≤ 1.40
(12)
M bx = M yz
for λ > 1.40
(13)
λ=
M px
M yz
π 
M yz =   EI y GJ
L
(14)
(15)
8
in which Mpx is the fully plastic moment capacity, 8 is the nondimensional slenderness ratio, Myz is the
elastic buckling moment, E is the elastic modulus, G is the shear modulus, Iy is the second moment of
area about minor y-axis and J is the torsion constant of the tubular section. The alternative proposal
given by Eqs 12 and 13 is also shown in Fig. 6 as ”This Paper”. The proposal is very much higher
than the AS 4100-1998 beam curve. It has not been incorporated in AS 4100-1998 at this time.
1.0
0.8
0.6
M bx /M px
RH S Beam s (uniform m om ent)
Test Values (m axim um )
Test Values (at ∆ t )
Basic FEM M odel (Pi and Trahair)
Proposed (Pi and Trahair)
AS 4100 - 1990
This Paper
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Non-D im ensional Slenderness λ
1.6
1.8
2.0
Com parison w ith AS 4100 and Proposed Design Rules for RH S Beam s
Fig. 6 Proposed Design Rules for RHS Beams
4.
WEB CRIPPLING UNDER BEARING
4.1
Beams under Bearing
Tests were performed on a range of cold-formed RHS subject to transverse bearing force (Zhao and
Hancock (1992a, 1995a). Two types of failure modes were observed for RHS sections under a
transverse bearing force. They are web buckling failure and flange-face yielding failure. The loadcarrying capacities of RHS under transverse bearing force depend on the following key parameters
(where the symbols are defined in Fig. 7).
q
q
q
q
Loading position, ie interior bearing (when bd ≥ 1.5d 5 ) or end bearing (when bd < 1.5d 5 )
Ratio (() of bearing length (bs) to section width (b)
Ratio of web depth (d – 2t) to section thickness (t)
External corner radius of the section (rext)
9
b
rext
d5 = d -2rext
d
rext
(a) Section
bd
bs
rext
bb = bbf + 2 bbw
2.5
1
bbf = bbs + 5rext
1
d5 /2
1
bbw
bbf
bbw
bbw = d5 /2
bb
(b) Interior force
bs
rext
2.5
bb = bbf + bbw
1
1
d5 /2
1
bbw
bbf
bbf = bbs + 2.5rext
bbw = d5 /2
bb
(c) End force
Fig. 7 RHS Sections under Transverse Bearing Forces
Fig. 8 End Bearing Failure
10
The load carrying capacity of RHS under end-bearing force was found to be less on average than half
of that of RHS under interior bearing force. The effect of reducing the bearing length in end-bearing
tests was found more severe than in interior bearing tests. Reducing the bearing length by one-half in
end-bearing tests reduces the bearing capacity by 30%, while reducing the bearing length by one-half
in interior bearing tests reduces the bearing capacity by 8% to 20% depending on the web slenderness.
A typical end bearing specimen after testing is shown in Fig. 8 for RHS under transverse bearing
forces.
The design rules for calculating web bearing capacities (bearing yield capacity and bearing buckling
capacity) in AS 4100-1990 were based on tests of hot-rolled I-sections. It was found that the
predictions in AS 4100-1990 were too high to be used for RHS sections under transverse bearing
force, since the formulae in AS 4100-1990 applied to webs of I-sections that are loaded
concentrically, while in the case of RHS sections the bearing load is applied eccentrically as a result of
the corner radii. The eccentric loading produces primary bending of the web out of its plane and a
subsequent reduction in capacity.
Plastic mechanism analysis was used to establish design formulae for bearing yield capacity. The
mechanism models were based on experimental observations. The nominal bearing yield capacity
(Rby) of both webs can be calculated using Clause 5.13.3 of AS 4100-1998. They are summarised
below, where most of the symbols are defined in Fig. 7.
Rby = 2bb tf yα p
(16)
in which fy is the yield stress of the material, bb and "p can be determined as follows:
q
for interior bearing ( bb ≥ 1.5d 5 )
bb = bs + 5rext + d 5
[
]
2
α p = (0.5 / k s ) 1 + (1 − α 2pm ) {1 + k s / k v − (1 − α pm
) × 0.25 / k v2 }
q
for end bearing ( bb < 1.5d 5 )
bb = bs + 2.5rext + d 5 / 2
α p = 2 + k s2 − k s
in which
α pm = 1 / k s + 0.5 / k v
k s = 2rext / t − 1
kv = d 5 / t
The design rules for bearing buckling capacity of RHS sections are similar to those for I-sections in
AS 4100. The nominal bearing buckling capacity of a web shall be taken as the axial load capacity
determined in accordance with Section 6 of AS 4100-1998 using ab = 0.5 and kf = 1.0 for a
compression member of area twbb and slenderness ratio Le / r = 3.5d 5 / t w for interior bearing and
Le / r = 3.8d 5 / t w for end bearing. The term tw is web thickness and bb is defined in Fig. 7. The
higher values of slenderness Le / r used for tubular sections when compared with other sections
reflects the smaller degree of restraint provided by the flanges to the web.
11
4.2 Beams under Combined Bending and Bearing
A series of interaction tests of bending and transverse concentrated force were performed, where the
concentrated force was applied either by a welded SHS branch to form a T-joint or by a bearing plate
(Zhao and Hancock, 1991b, 1992a). The interaction curves for the RHS sections under bending and
bearing force are compared in Fig. 9 with those of similar tests on RHS with welded branch. The
interaction is more severe for the tests with bearing plate whereas the interaction is less for the welded
T-joints due to the restraint against web rotation provided by the welded branch. It was found that the
interaction behaviour depends on the ratio (() of bearing length (bs) to section width (b) and the ratio
of web depth (d – 2t) to section thickness (t) (Zhao and Hancock, 1992b).
A new clause was added to AS 4100-1998 to account for combined bearing and bending. It can be
summarised as follows.
Rectangular and square hollow sections to AS 1163 subjected to combined bending and bearing force
shall satisfy either:
 R*   M * 
 ≤ 1.5
 + 
1.2
 φRb   φM s 
(17)
for b s / b ≥ 1.0 and (d − 2t w ) / t w ≤ 30
or
 R*   M * 
 + 
 ≤ 1.0 otherwise
0.8
 φRb   φM s 
(18)
where
N
Rb
Ms
=
=
=
bs
b
tw
=
=
=
capacity factor = 0.9
nominal bearing capacity of webs specified in Clause 5.13.2 of AS 4100-1998
nominal section moment capacity determined in accordance with Clause 5.2 of
AS 4100-1998
stiff bearing length
total width of section
web thickness
12
1.6
Dash (T-Joint)
1.4
S3B1C11
S3B1C12
S3B1C13
Solid (Bearing)
Dimensionless Moment M / Mf
1.2
S3B1C11
S3B1C12
S3B1C13
1.0
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Dimensionless Loading P/Pf
Fig. 9 RHS Sections under Combined Bending and Transverse
Bearing Force
5.
BEAM-COLUMNS
5.1
Introduction
The design rules in AS 4100-1998 Section 8 for members subject to combined actions have a two tier
approach. For both the section capacity rules in Clause 8.3, and the member capacity rules in Clause
8.4, simple linear interaction formulae are specified. However, for doubly symmetric, compact Isections, more advanced interaction rules were specified as higher tiers in AS 4100-1990. Recently, a
detailed research program (Sully and Hancock, 1996) was performed on compact cold-formed SHS to
AS 1163 to ascertain whether the more advanced interaction rules are applicable to these sections.
Further research has also been performed on slender cold-formed SHS sections (Sully and Hancock,
1995). The results of this research, which are described briefly in this section, have been used to
extend the applicability of the advanced interaction rules in AS 4100-1998 to compact rectangular and
square hollow sections. In particular, Clause 8.3.2 for the section capacity for uniaxial bending about
the major principal axis, Clause 8.3.3 for the section capacity for uniaxial bending about the minor
principal axis, Clause 8.4.2 for the member in-plane capacity using an elastic structural analysis have
been extended in AS 4100-1998 to allow the advanced rules for compact I-sections to be used for
rectangular and square hollow sections to AS 1163.
In the USA, in the AISC Specification (AISC 1993), there is an advanced interaction rule which
applies to all sections, whether I- or tubular. This design curve, which is invariant with end-moment
ratio, is higher than the Australian curve in some cases and lower in others. This section describes the
Australian theoretical and experimental research used to support the Australian extensions.
5.2
Test Program on Compact Sections
A test rig was purpose-built for this test program. It consisted of a 2000 kN hydraulic actuator used to
apply compressive axial force and a 250 kN hydraulic actuator used to apply bending moment to the
specimen as shown in Fig. 10. The moment was applied to the specimens by the bending actuator via
lever arms attached to each end of the specimen. The layout of the rig allowed for a range of end
moment ratios ($) from around $ = - 1 / 4 to $ = -1 (ie specimen bent in single curvature). The rig did
not allow for positive values of $ (ie specimens bent in double curvature).
13
The two actuators could be operated independently or coupled depending on the loading type being
investigated. For this test program, the actuators were linked together so that by controlling one, in
either load or displacement, loads would be applied in a constant ratio.
Southern end frame
(roller joint with floor)
Spherical joint
Pin joint
Lever arm
Rigid joint
SHS Test specimen
Support frames
(stainless steel on
teflon pads to allow
movement in horizontal
plane)
High tensile
steel bars
Rigid joint
Lever arm
A
Ball joint
250 kN
MTS jack
A
Spherical joint
2000 kN
dartec jack
Channel
Transfer
plates
Packing
plates
SHS test
specimen
Northern Head stock
(fixed to floor)
Section A-A
Fig. 10 Plan View of Test Rig Layout
The specimens tested were 125 × 125 × 6.0 SHS in Grade C350 which could be classified as compact
according to AS 4100-1998. In order to determine the section axial compression capacity of the
specimens, two stub column tests were carried out in a 2000 kN hydraulic actuator. Both specimens
reached similar ultimate loads (1173 kN and 1196 kN). A plastic bending test was conducted using a
2000 kN hydraulic actuator in a four point bending test configuration. The plastic bending test
reached a moment of 53 kNm at ultimate and, after substantial deformation, was concluded when a
local buckle had formed in the specimen.
A column test was conducted in the test rig by application of the compression actuator only. The
column specimen was 3000 mm long. Adding this to the 225 mm at each end of the test rig, from the
centre of the pins to the ends of the test specimen, gave the columns an effective length of 3450 mm
between the pinned bearings. This length was chosen because it gave a non-dimensionalised
14
slenderness (8) of approximately 1 when the nominal yield stress (Fy = 350 MPa) and nominal
dimensions were used.
λ=
Lc
r
 σy 
 2 
π E 
(19)
An eccentricity of 3mm was added at each end in the plane of bending. This was considerably greater
than the measured geometric imperfection of 0.4 mm. The specimen exhibited stable unloading
characteristics, after reach an ultimate axial load (Puc) of 632 kN.
Interaction tests were performed using the test rig in Fig. 10. All of the specimens tested were 3000
mm long which was the same as the column tests. Two series of interaction beam-column tests were
conducted. For the first series with $ = -1 (referred to as B1 series), four tests were conducted with
varying ratios of applied load and moment. In order of descending applied load/moment ratio they are
B1R1 to B1R4. For the second series with $ = -0.5 (referred to as B2 series), three tests were
conducted, known as B2R1 to B2R3, again in descending order of applied load/moment ratio. Plots
of load versus central moment for the four B1 series of tests are shown in Fig. 11. This central
moment is the sum of the moment applied directly from the bending actuator and the moment
indirectly applied via the P - ) effect from both the compression and bending actuators.
700
Test results
Finite element analysis
(NIFA)
600
500
Load (kN)
B1R1
400
B1R2
300
200
B1R3
100
B1R4
0
0
10
20
30
40
Maximum Moment (kNm)
50
60
Fig. 11 Maximum Moment versus Load for B1 Series of Compact Interaction Tests
Unlike the B1 series, the region of maximum moment for the B2 series shifted during the tests. At
low loads, the peak moment was at the point of application of greatest applied moment, ie at the
southern end. As the deflections increased, the P - ) effect increased and the peak moment shifted
towards the centre of the specimen. The extent to which the shift occurred was dependent on the
applied load/moment ratio.
5.3
Finite Element Analysis of Compact Sections
An advanced finite element nonlinear analysis, developed at the University of Sydney (Clarke 1993)
was used to simulate each of the tests. The advanced analysis could include the effects of large
deflections, residual stresses, material nonlinearity, gradual yielding, elastic unloading and geometric
15
imperfections. Material properties for the finite element analysis were taken from the results of the
tensile coupon tests and residual stress tests. Material curves were multi-linear functions derived
directly from the stress-strain curves. Membrane residual stresses were taken as zero. The end
platens were included as a third material type to account for their increased stiffness. Measured
eccentricities between the specimens and the end platens were included. Geometric imperfections
were taken as sinusoidal over the length of the specimen with a mid-span deflection of 0.4 mm.
Comparison of analysis and tests results for the B1 series of interaction tests is shown in Fig. 11.
There is good agreement especially for tests B1R3 and B1R4. Similar good agreement has been
achieved for the B2 series. Hence it was concluded that the finite element analysis is able to
accurately simulate the test results.
To compare the test sections with current design rules, for a wider range of parameters that was tested,
further finite element analyses were undertaken for $ = -1, $ = -½, $ = 0, $ = ½, $ = 1. From each of
these analyses, the maximum applied load was found with the corresponding maximum applied end
moment. Using the equations from Trahair and Bradford (1998), the equivalent maximum second
order elastic moment within the section was calculated:




P 
 π P 
+
cot
M m = M 1 +  β cosec  π

Px 
Px 



2
(20)

P 
for β < − cos  π
, and
Px 

Mm = M
(21)

P 
for β ≥ − cos  π
Px 

where
Mm
M
P
Px
$
=
=
=
=
=
maximum second order elastic moment
maximum applied end moment
Maximum applied axial load
Euler buckling load for the section
ratio of applied end moments
This is of course very different from the actual maximum moment within the section, which is the
sum of the applied maximum end moment and moment due to the mid-span deflection and load.
These maximum second-order elastic moments are compared with the current interaction design rules
in Clause 8.4.2.2 of AS 4100-1998, for doubly symmetric compact I-sections and the interaction rule
from the AISC Specification (AISC-US 1993). Graphs of these plots for β = −1, β = 0, β = 1 are
shown in Fig.12.
3
  1 + β  3  
Ν 
1+ β 


M = M s 1 − 
  1 −
 + 1.18  2 
  2    φN c 

Ν  
1 −
 
 φN c  
(22)
16
M
Ms
N
Nc
$
N
=
=
=
=
=
=
Maximum allowable applied end moment
section moment capacity = Ze fy
applied compressive axial load
member axial load capacity given by Eq. 10
ratio of applied end moments
0.9
The graphs have been non-dimensionalised against the short column load (Psq) and the plastic moment
(Mpt) capacity, Psq is calculated from the measured cross-sectional area and the proof stress of the
material from the flats, determined from the tensile coupon tests. Mpt is calculated using the measured
section dimensions to determine the actual plastic section modulus, and the proof stress of the material
from the flats, determined from the tensile coupon tests.
The cold-formed, compact square hollow sections tested showed adequate ductility and adequate
capacity to absorb moment past the maximum axial load. Comparing the equivalent second order
elastic moments with the design rules shows that even at $ = -1 there is some capacity to absorb small
axial forces without reducing the moment capacity. This effect increases with an increase in $. The
current interaction design rules in AS 4100 for doubly symmetric I-sections are applicable to coldformed RHS as specified in AS 4100-1998. They are however conservative for larger values of $ and
there is scope for improved design rules to be developed. The current interaction rules in the AISCUS Specification (AISC 1993) are more conservative than the theoretical and experimental values
except for the $ = -1 case.
5.4
Test Program on Slender Sections
The same test rig and loading arrangements as used for the compact sections were used for a second
test series on slender sections. The slender square hollow sections tested were of nominal overall
dimension 200 mm square with nominal thickness 5 mm and nominal yield stress 350 MPa. The
slenderness (b/t) of the faces was 38 based on the clear width of the flanges. Two specimen lengths
were tested. The distance between the centres of the pinned bearings in Fig. 10 were 5550 mm for the
long sections and 1246 mm to 1560 mm for the short specimens. The length of the long specimens
was chosen to produce a non-dimensional column slenderness of approximately 1.0. Two different
ratios of end moment were used for the long specimens both producing overall bending in single
curvature. These were equal and opposite end moment (β = −1.0) and the moment at one end half the
other (β = −0.5). The tests are labelled B1 and B2 respectively as for the compact sections. However
a symbol ‘s’ has been included to indicate that the test is on a slender section. The full set of results is
given in Sully and Hancock (1995) and summarised in Sully and Hancock (1998).
17
0.7
AS 4100 interaction rule
AISC interaction rule
SHS interaction curve, flats only
SHS interaction curve, flats and corners
0.6
Load (P/Psq )
0.5
0.4
0.3
0.2
0.1
(a) Comparison of Design Rules with Interaction Surface for β = -1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Maximum Moment (M/M pt )
0.8
0.9
1.0
0.7
0.6
AS 4100 interaction rule
AISC interaction rule
SHS interaction curve
Load (P/Psq )
0.5
0.4
0.3
0.2
0.1
(b) Comparison of Design Rules with Interaction Surface for β = 0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Maximum Moment (M/Mpt )
0.8
0.9
1.0
0.7
AS 4100 interaction rule
AISC interaction rule
SHS interaction curve
0.6
Load (P/Psq )
0.5
0.4
0.3
0.2
0.1
(c) Comparison of Design Rules with Interaction Surface for β = 1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Maximum Moment (M/Mpt )
0.8
0.9
1.0
Fig. 12 Comparison of Design Rules with Interaction Surface
18
1000
AS4100
AISC-LRFD
Eurocode3
Tests
900
LC1s
800
Axial Load (kN)
700
B1R1s
600
B1R2s
500
B1R2as
400
300
B1R3s
200
100
0
PB1NTs
0
PB4PT
10 20 30 40 50 60 70 80 90 100
Moment, M me = δb M e, (kN.m)
Fig 13 Slender Long SHS Axial Force/Moment Interaction ($ = -1.0)
1000
900
AS4100
AISC-LRFD
Eurocode3
Tests
LC1s
800
Axial Load (kN)
700
B2R1s
600
500
B2R2s
400
300
200
B2R3s
100
0
PB1NTs
0
10
20 30 40 50 60 70 80
Moment, M me = δ b M e , (kN.m)
PB4PTs
90 100
Fig. 14 Slender Long SHS Axial Force/Moment Interaction ($ = -0.5)
19
1600
1400
AS4100
AISC-LRFD
Eurocode3
Tests
STC
Axial Load (kN)
1200
1000
S1T1
800
600
S1T2
400
S1T3
200
PB1NTs
0
0
10
20 30 40 50 60 70 80
Moment, M me = δ b M e , (kN.m)
PB4PTs
90
100
Fig. 15 Slender Short SHS Axial Force/Moment Interaction ($ = -1.0)
The axial force-moment interaction graphs are shown in Figs 13, 14 and 15 where the moment on the
horizontal axis is the second-order elastic moment. The second order moment was derived for the test
results by amplifying the applied end moment from the tests by the appropriate amplification factor
which depends on the ratio of the applied axial load to the Euler buckling load of the member based
on the length between the pinned ends. The amplification factor is specified in Clause 4.4.2.2 of AS
4100-1998 as
δb =
Cm
1− N / NE
(22)
where N is the applied axial load, NE is the Euler buckling load, and Cm is a moment distribution factor
equal to unity in the case of uniform moment (β = −1.0) and 0.8 in the case of the moment at one end
half the other (β = −0.5).
On the vertical axis of Fig. 15, the ultimate load for a test of a column with no end moment is shown
where the column strength of the specimen STC is a stub column test. On the horizontal axes of Figs
13, 14 and 15, the results of two different tests with pure bending and no axial force are shown. The
test labelled PB4PT is a four point bending test where a region of pure moment derived from lateral
loads on a beam section is achieved. The test labelled PBINT was performed using the test rig in Fig.
10 to achieve pure bending by applying a tension through the 250 kN MTS actuator and a balancing
compression through the 2000 kN Dartec actuator. This test failed by inelastic local buckling in the
compression flange and webs of the SHS section adjacent to the point where the loading plates were
welded to the webs of the section. The applied moment at failure for the PBINT test was significantly
below the PB4PT test probably as a result of the different method of application of the end moment.
In the case of the P4PBT test, the moment was applied by the section of SHS extending beyond the
interior loading point whereas in the PBINT test, the moment was applied by the channel lever arms
through the plates welded to the webs. It is clear from these results that the method of connection of
slender tubes can play an important part in the strength of the section, particularly in bending.
20
The results for the interaction tests are compared in Figs 13, 14 and 15 with the predictions by AS
4100-1998, the AISC-LRFD Specification (AISC-US (1993)) and Eurocode3 (Eurocode (1992)). In
computing these standards, the mean measured section geometry and mean measured yield stress of
the flat material have been used. All three specifications are conservative except for the PBINT test
result. A line fitted between the column test strength and the PB4PT test for each case is
approximately aligned with the test results indicating that a linear interaction graph between axial
force and moment is most appropriate for slender sections. The conservatism of the code predictions
is mainly a consequence of the conservatism of the prediction of the pure axial and pure moment
cases.
In AS 4100-1998 a linear interaction curve has been retained in Clause 8.4.2.2 for slender sections
unlike the compact sections described in Sections 5.2 and 5.3 above.
6.
WELDED CONNECTIONS
The Australian Standard AS 4100-1990 when originally produced only applied to steel that is 3 mm or
thicker. Tubular sections less than 3 mm thick could not be designed to this standard, and had to be
designed to the Australian Cold-Formed Steel Structures Standard AS 1538-1988 (now in Limit State
Format as AS/NZS 4600:1996). Since the design rules for welded connections in AS/NZS 4600 are
based on tests on sheet steel performed in the USA in the early 1980s (Pek`z and McGuire (1981)),
they may be inappropriate when applied to RHS sections. Consequently, a large number of tests were
performed on butt welds, transverse fillet welds and longitudinal fillet welds in both C350 and C450
RHS members (Zhao and Hancock (1995b, 1995c, 1996)). Proposed design rules were calibrated
using reliability analysis method. They are now included in AS 4100-1998.
6.1
Butt Welds
The dominant failure mode found in the tests of butt welds in C350 RHS members was tube tearing
failure. Significant necking of RHS was observed at the failure cross section. Most of the tearing
occurred along the seam of the RHS as shown in Fig. 16. This may be due to the lower ductility of
the seam. The dominant failure mode in the tests of butt welds in C450 RHS members was tube
failure in the heat affected zone as shown in Figure 17. No significant necking of RHS was observed.
21
Fig. 16 Butt Weld in C350 SHS – Typical Failure
Fig. 17 Butt Weld in C450 SHS – Typical Failure
The complete penetration butt weld along a full perimeter was found to be stronger than the RHS
itself. The complete penetration butt welds can be designed in accordance with the tension member
rule in AS 4100-1998 with a capacity factor (φ) of 0.9. The nominal capacity of a tension member is
governed by the lesser of fyA and 0.85fuA, where A is the cross-section area, fy is the yield stress and fu
is the ultimate tensile strength. For grade C350 RHS sections, fyA is less than 0.85fuA. For grade C450
RHS sections, 0.85fuA is less than fyA.
22
6.2
Transverse Fillet Welds
The actual weld sizes (leg lengths) in the test specimens less than 3.0 mm thick were found to be
oversized. This finding agrees with the trend found in the international test series (Pham and Bennetts
(1983)) as shown in Figure 18, ie. welds are slightly oversized when the nominated size is small and
are slightly undersized when the nominated size is large. Weld failure (shear across the weld throat)
was observed in tests where transverse fillet welds were not applied to the full perimeter of an RHS
section. The full strengths of RHS sections were achieved if the full perimeter was welded using
transverse fillet welds.
2.0
International Test Series
Current Test Series
Actual / Nominal ( Mean )
1.5
1.0
0.5
0
4
8
12
Nominal Throat Thickness (mm)
Fig. 18 Variation of Actual Throat Thickness
The design rules for transverse fillet welds and those for longitudinal fillet welds are the same in AS
4100-1998, ie φ0.6XuaL where φ is the capacity factor, Xu is the weld metal strength, a is the weld
throat thickness and L is the weld length. The predictions in AS 4100-1998 were found conservative
for design of transverse fillet welds. The design strength of transverse fillet welds in the American
Institute of Steel Construction Specification (AISC (1993)) has now been increased from φ0.6XuaL to
1.5 x φ0.6XuaL where the capacity factor is 0.75. However, for simplicity no changes have been made
to the existing design rules for transverse fillet welds in AS 4100-1998.
6.3
Longitudinal Fillet Welds
A schematic view of longitudinal fillet welds is shown in Fig. 19. The failure mode observed in the
tests without end return welds was tube failure at the end of the weld adjacent to the end of the plate
as shown in Fig.19. The failure may be due to the stress concentration in the area between the weld
and the end of the plate. The failure mode observed in tests where end return welds were applied was
tube failure in the heat-affected zone adjacent to the end return weld as shown in Fig. 19. The shift of
the failure position is most likely due to the fact that the end return weld formed a continuous path of
load transfer along the end of the plate.
The variation of the weld strength with respect to the ratio of weld length to wall thickness derived by
Pek`z and McGuire (1981) and that with respect to the ratio of weld length to plate width derived by
Stark and Soetens (1980) were not confirmed in the current tests. This may be because these two
formulae were based on regression analysis of tests on lap-joint fillet welds in sheet steel, while Tjoint fillet welds in RHS sections were used in the current tests.
23
The strength of the longitudinal fillet welds ranges from 68% to 81% of the strength of the transverse
fillet welds, and the corresponding deformation of the longitudinal fillet welds ranges from 1.3 to 2.1
times larger than that of the transverse fillet welds. The variation in values of strength and
deformation in different tests is mainly due to the differences in orientation of RHS sections, the weld
length, and the inclusion or exclusion of the end return welds.
10 mm
10 mm
Plate
Plate
RHS
RHS
Tube
Tube
failure
failure
(a) Without End Return
(b) With End Return
Fig. 19 Longitudinal Fillet Welds – Typical Failure Positions
The existing design rule for longitudinal fillet welds in AS 4100-1998 is φ0.6XuaL where φ is the
capacity factor (0.8), Xu is the weld metal strength, a is the weld throat thickness and L is the weld
length. The predictions in AS 4100-1990 were found to produce an inadequate reliability index for
design of longitudinal fillet welds in RHS sections less than 3mm thick. Two options can be used to
produce adequate reliability index (Zhao and Hancock (1994)).
Option No.1: Keep the same design rule, but specify the need for end return welds as a requirement in
AS 4100.
Option No.2: Change the capacity factor from 0.8 to 0.7 without specifying the end return welds as a
requirement in AS 4100.
The second option has been adopted in AS 4100-1998.
7.
BOLTED CONNECTIONS
Moment end plate connections joining I-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.
24
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. 20. 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 governed 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
u
(a) Mode 1
(b) Mode 2
(c) Mode 3
Fig. 20 Yield Line Mechanisms for Bolted Moment End Plate Connection
8. PLASTIC DESIGN OF PORTAL FRAMES
8.1 Introduction
Plastic design of statically indeterminate frames, can lead to higher ultimate loads with associated
higher deformations compared to traditional elastic design methods. As some point in the frame
reaches its plastic moment (Mp), a plastic zone is created. The zone forms a hinge and rotates further,
maintaining Mp, while redistributing additional load to other parts of the structure. The hinge process
is repeated as other hinges form, until there is a sufficient number of hinges to create a plastic collapse
mechanism for the whole structure or part of the structure. All hinges, particularly those which form
early, must be able to rotate sufficiently for this mechanism to form.
There are specific requirements for the suitability of sections for plastic design. A Compact or Class 1
section is deemed suitable for plastic design. The flanges and webs of the RHS must be sufficiently
stocky to avoid local buckling before large plastic rotations occur. Beam tests have examined the
appropriate slenderness limits for cold-formed RHS (Wilkinson and Hancock (1998)) as described in
Section 1.4. The rotation capacity of knee joints has also been examined (Wilkinson and Hancock
(2000), since plastic hinges often form at the connections of portal frames.
25
Due to the large strains occurring in plastic hinges, material ductility requirements are imposed by
design standards. Most cold-formed RHS do not satisfy the requirements of Clause 3.2.2.2 of
Eurocode 3 or Clause 4.5.2 of Australian Standard AS 4100-1998. The AISC-US Specification
(AISC, 1993) permits plastic design of frames composed of cold-formed RHS.
This section briefly describes tests on portal frames manufactured from cold-formed RHS. The aims
of the test series included: (1) investigation of the ultimate load capacity of RHS frames; (2) whether a
plastic collapse mechanism can form in such a frame; (3) a study of rotation capacity requirements for
portal frames.
8.2 Test Frame Layout
Three frames were tested under simulated combined gravity and transverse wind loads. The ratio of
vertical load (V) to horizontal load (H) is summarised in Table 1. The general layout of each frame is
shown in Figure 21. Each frame spanned 7 metres, with an eaves height of 3 metres, and a total
height of 4 metres. There was a collar tie which joined the midpoint of each rafter. The frames were
constructed from RHS, and the collar tie was made from a pair of channel sections.
The RHS were manufactured by BHP Structural and Pipeline Products. Two strength grades were
selected, Grade C350L0 and C450L0 (nominal yield stress fyn of 350 MPa and 450 MPa respectively),
manufactured to Australian Standard AS 1163. The Grade C450 specimens are called DuraGal,
produced using a unique cold-forming and in-line galvanising process.
SOUTH
NORTH
Points of lateral restraint
Bolted end
plate
Internal sleeve
knee joint
1000
Roller bearing supported
by auxiliary frame
(not shown)
Collar tie (channel)
(Restraint for
Frames 2 & 3 only)
Pinned base
Strong
Floor
MTS actuator
1000
2000
Horizontal load
cradle
Gravity load
simulator
7000
Fig. 21 Portal Frame Test Arrangement
8.3 Connections
The welded internal sleeve joint (Wilkinson and Hancock (2000)), as shown in Fig. 22, was selected
for the knee joints of the portal frame. A welded box section, cut in an open •V• shape (to match the
angle of the portal frame knee), was fabricated from 10 mm Grade 250 plate. The sleeve was sized to
fit tightly inside the RHS. The sleeve extended 300 mm into both the column and the rafter of each
knee joint and required a sledge hammer to insert the sleeve in place. The sleeve connection forces
the plastic hinge at the knee to form away from the connection centreline.
26
A moment resisting bolted end plate connection was used at the apex of the frame. A 10 mm plate
was butt welded to the end of each rafter, and the two plates were bolted together with eight high
strength fully-tensioned M16 bolts positioned symmetrically about the x-axis of the RHS.
A common connection for portal frames is the bolted base plate connection to a concrete footing. To
simulate the column base plate, a pinned connection was used. The webs of the RHS were stiffened
locally by a steel plate, and a 30 mm diameter high strength steel pin was inserted through the neutral
axis of the RHS. A thick steel base plate supported the pin. The base plate was securely fastened to
the strong floor of the laboratory. The pin connection was greased to reduce friction.
Limit of
sleeve
B
Fillet
weld
RHS
300
Sleeve
B
Full penetration
butt weld
C
300
C
Groove cut
for RHS
seam weld
RHS wall
Sleeve
(i) Column – rafter joint
(ii) Section B-B
(iii) Section C-C
Fig. 22 Internal sleeve knee joint connection
8.4 Loading Method
A combination of vertical gravity and transverse wind loads was selected for the test series. In a
prototype portal frame, gravity and wind loads are transferred to the frame from the sheeting via
purlins and girts, similar to a distributed load. It is difficult to replicate distributed loads in a
laboratory, and hence the loads were applied as point loads.
The vertical load was applied at the midpoint of the collar tie. Large in-plane sway displacements
were anticipated and it was essential that the downwards loads remained vertical to simulate true
gravity loading. A hydraulic jack was required to achieve the large vertical load. However, a jack
connected directly to the strong floor of the laboratory would produce a non-vertical load as the frame
swayed horizontally. A gravity load simulator was attached to the strong floor of the laboratory as
shown in Fig. 21. The simulator had two inclined members, pinned together by a rigid triangular unit,
and pinned at the other end to the base. The jack was bolted to the top of another vertical member,
which was pinned to the base of the triangular section.
8.5 Results
The ultimate loads are given in Table 1 and compared with the results of a first order plastic analysis
using program PRFSA (CASE, 1997). The first order plastic analysis of the frames does not include
second order effects and the reduction of plastic moment to account for interaction with axial force.
27
Specimen
Frame 1
150 × 50 × 4.0 C350
Load
ratio
V/H
40
Frame 2
150 × 50 × 4.0 C450
40
71.5
1.87
0.98
Frame 3
150 × 50 × 4.0 C450
3.3
45.7
13.8
0.91
Note:
Cut from
section
Load at ultimate (kN)
Vertical
Horizontal
Ultimate vertical load
Plastic analysis load
68.2
1.75
1.00
1
(1) Plastic analysis load based on measured properties
Table 1 Results of Tests and Analyses
In particular, the ultimate load for Frame 3, is low compared with the first order plastic analysis.
However, preliminary advanced analysis has shown that the second order effects are substantial and
reduce the ultimate load of Frame 3 by approximately 10%. Results of the advanced analysis are
available in Wilkinson and Hancock (1999).
8.6 Discussion of Portal Frame Tests
The following important points can be derived from the results:
C
Plastic collapse mechanisms were formed in all three frames. Large curvatures (hinges)
occurred in (or very close to) the locations predicted by the computer analysis.
C
The ultimate loads were similar to or smaller than those predicted by the first order plastic
analysis.
C
There was no significant difference in the behaviour of the Grade C350 and Grade C450
frames (Frame 1 and Frame 2).
C
There was no failure due to insufficient material ductility.
C
The welded internal sleeve knee joints performed without any signs of distress.
C
The lateral restraints performed adequately and the frame did not buckle out-of-plane.
C
Frames with large sway deflections (Frame 3) require a second order elastic analysis to predict
the ultimate load.
9. CONCLUSIONS
The paper has described a substantial research program based mainly on testing of cold-formed square
and rectangular hollow sections produced to the Australian Standard AS 1163 Structural Steel Hollow
Sections but including some finite element analyses. The purpose of the research was to understand
the behaviour of cold-formed hollow sections in order to produce design rules for use in structural
steel design standards, especially the Australian Steel Structures Standard AS 4100.
Design rules for plate slenderness, long columns, beams in bearing, beam-columns and welded
connections less than 3 mm thick have been produced and incorporated in AS 4100–1998. Design
rules have also been produced for lateral buckling but not yet incorporated in AS 4100. Ongoing
research on plastic design includes plastic bending of sections in combined compression and bending
and fracture in welded steel connections.
28
The research has allowed cold-formed tubular members to be safely designed to the Australian Steel
Structures Standard AS 4100. Future and ongoing research will enhance the capability of AS 4100
when applied to cold-formed tubular members and connections.
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31
APPENDIX 1
Fig. A1 Olympic Stadium Australia (under construction)
Fig. A2 Olympic Aquatic Centre, Homebush Bay, Sydney (under construction)
32