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© Institution of Engineers Australia, 2008 Australian Journal of Structural Engineering Online
* Paper S08-977 submitted 29/02/08; accepted for publication after review and revision 6/05/08.
† Corresponding author Prof Brian Uy can be contacted at b.uy@uws.edu.au.
Design of concrete-filled steel tubular members according to the Australian
Standard AS 5100 model and calibration *
Z Tao University of Western Sydney, Sydney, NSW, Australia
Fuzhou University, Fuzhou, Fujian Province, China
Brian Uy † University of Western Sydney, Sydney, NSW, Australia
L-H Han and S-H He Tsinghua University, Beijing, China
SUMMARY: Procedures given in the Australian bridge design standard AS 5100 (Standards Australia, 2004) for the design of concrete-filled steel tubular (CFST) columns, beams and beam-columns are presented and described briefly in this paper. A wide range of experimental data from two currently available test databases (2194 test results altogether) is used to evaluate the applicability of AS 5100 in calculating the strength of CFST members. Some other existing design codes, such as the Japanese code AIJ (1997), American code AISC (2005), British bridge code BS 5400 (2005), Chinese code DBJ 13-51-2003 (2003) and Eurocode 4 (2004), are also compared with the test results in this paper. From the comparisons, useful information is provided for future possible revision of AS 5100 and for the suggestion that this model be used for building construction.
1 INTRODUCTION
In recent times, concrete-filled steel tubular (CFST)
members have been widely used in civil engineering
in Australia and other countries (Uy, 2000; Han,
2007). Several examples of such engineering practice
in Australia include: the Latitude building and
Market City in Sydney; the Casselden Place and the
Commonwealth Centre in Melbourne; Riverside
Office and Myer Centre in Adelaide; and the Forrest
Centre, Exchange Plaza and Westralia Square in Perth
(Uy & Patil, 2006).
Figure 1 shows the Latitude building in Sydney
during construction. This building was completed
in 2005, and is on George Street on the World Square
Site, directly adjacent to Sydney’s Chinatown at
Haymarket. It is a landmark building, which was
designed by Hyder Consulting and constructed by
Multiplex. The building has a total height of 222 m
over 45 floors and has some very innovative features
in its design. The building uses twin composite
columns on the perimeter frame, using 508 mm
diameter steel tubes filled with 80 MPa concrete.
The building has required the design of 7 m deep
transfer trusses using large diameter steel tubes
filled concrete and large high strength steel boxes
filled with concrete (Chaseling, 2004; Australian Steel
Institute, 2004).
The practical application of CFST construction
is now supported by many well-known national
standards or recommendations, such as the Japanese
code AIJ (1997), American code AISC (American
Institute of Steel Construction, 2005), British bridge
code BS5400 (British Standards Institution, 2005),
Chinese code DBJ 13-51-2003 (2003) and Eurocode 4
(2004). Research and practice of CFST members and
structures has also led to the development of these
design codes.
In 2004, a new version of the Australian bridge
design standard AS 5100 (Standards Australia,
2004) for bridge design was issued, where design
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“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
guidance for composite columns (including CFST
columns) was incorporated. The aim of this paper is
to provide useful information for a future possible
revision of AS 5100 and for the suggestion that this
model be used for building construction. To fulfil this
task, procedures given in AS 5100 for the design of
CFST columns, beams and beam-columns are firstly
presented and described briefly. In order to evaluate
the applicability of AS 5100 in calculating the strength
of CFST members, a wide range of experimental data
from two currently available test databases (2194 test
results altogether) are used for comparison. Effects of
different parameters such as steel strength, concrete
strength and section slenderness on the accuracy of
the strength predictions are discussed. This is to check
the possibility of relaxing the limitations specified in
AS 5100. The above-mentioned existing design codes
are also compared with the test results in this paper.
For simplicity, these codes are to be referred to as
“AIJ”, “AISC”, “BS 5400”, “DBJ 13-51-2003” and
“EC4” in the following.
2 AS 5100 PROVISIONS
2.1 General specifications
The Australian Standard AS 5100 was prepared by
the Standards Australia Committee BD-090, Bridge
Design, to supersede HB 77.6-1996, Australian Bridge
Figure 1: Latitude, Sydney (2005).
Design Code. Seven parts are included in AS 5100
with objectives to provide nationally acceptable
requirements for the design of road, rail, pedestrian
and bicycle-path bridges; the specific application of
concrete, steel and composite construction; and the
assessment of the load capacity of existing bridges.
Part 6 of the standard AS 5100 is concerned with the
design of steel and composite construction, in which
procedures are given for the design of concrete-filled
circular and rectangular hollow steel members,
which take account of the composite action between
the various components forming the cross-section.
The specifications in AS 5100 related to the design of
CFST members are described briefly as follows.
In AS 5100, it is specified that the steel tube should
be fabricated from steel with a maximum yield stress
of 350 MPa. The elastic modulus of steel (E) is given
as 200,000 MPa by AS 5100. The selection of wall
thickness (t) should ensure that the plate element
slenderness (λe) is less than the yield slenderness limit
(λey). The value of λe for rectangular hollow sections
(RHS) is calculated as ( / ) /235yh t f , where h is the
overall height of a RHS, fy is the characteristic yield
strength of the steel. For circular hollow sections
(CHS), the slenderness (λe) is given as (do/t)(fy/235),
where do is the outside diameter of a CHS. The yield
slenderness limit (λey) for CHSs is equal to 82, while
slightly different values of λey (35, 40 and 45) are
specified for RHSs with different fabrication process.
The larger the residual stress remaining in the section,
the smaller the λey resulting. For lightly welded
(longitudinally) tubes or cold formed sections, a
moderate value of 40 is used for λey. It should be
noted that the yield slenderness limit specified in
AS 5100 for CFST members is virtually the same as
those for hollow steel sections, that is, the beneficial
effects from concrete restraint is neglected.
Concrete with normal density and strength is
recommended in AS 5100 to fill the steel tubes. The
characteristic compressive cylinder strengths (fc’) of the standard strength grades of concrete are 25,
32, 40, 50 and 65 MPa, respectively. The maximum
aggregate size is 20 mm. As far as the concrete
modulus of elasticity (Ec) is concerned, a similar
formula presented in AISC is recommended in AS
5100 as follows:
1.5 0.043c cE fρ= × ′ (1)
where ρ is the concrete density taken as not less than
2400 kg/m3 for normal weight concrete.
A steel contribution factor αs is specified in AS 5100
with an allowed range from 0.2 to 0.9, where αs is
defined as the ratio of the contribution of the steel
section (φAsfy) to the total axial capacity (Nus). The
above notation of φ and As, as well as the calculation
method of Nus, will be given in the following
section.
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In AS 5100, it is suggested that reinforcement is not normally required in CFST compression members. Also, almost all currently available tests were carried out without steel reinforcement used. Therefore, the contribution from reinforcement is omitted in the following review of design methods.
2.2 Members subjected to axial compression
2.2.1 Ultimate section capacity
To calculate the section capacity under axial compression, an assumption was used that the steel yields before the concrete reaches its ultimate stress state. Thus, the ultimate section capacity (Nus) for rectangular CFST members can be calculated by summing up the axial load capacities of the tube and the concrete. This leads to:
Nus = φAsfy + φcAc fc’ (2)
where As and Ac are the areas of the steel tube and the core concrete, respectively; and φ and φc are the capacity factors for steel and concrete respectively, given as 0.9 and 0.6 in AS 5100 for section capacity.
For a circular CFST member, the benefits of the increase in concrete strength due to confinement may be taken into account if the relative slenderness of the member (λr) is not greater than 0.5, and the load eccentricity (e) under the greatest design bending moment is not greater than do/10. Otherwise, Nus should be calculated using equation (2). If the benefits of confinement are taken into account, Nus may be calculated as follows:
1
2 ' 1'
yus s y c c c
o c
tfN A f A f
d f
ηφ η φ
⎛ ⎞= + +⎜ ⎟
⎝ ⎠ (3)
in which, η1 and η
2 are coefficients used to reflect
the confinement benefit that are dependent on the relative slenderness (λr) and load eccentricity (e). The coefficient of η
2 is used to account for the strength
reduction of the steel because of the circumferential tensile strains in the steel induced by confining the concrete, while the coefficient of η
1 is used for the
concrete to reflect the strength increase from the tube confinement. The calculation formulae for η
1 and η
2
are given in Clause 10.6.2.2 of AS 5100: Part 6.
From the above introduction, it can be seen that the formula for calculating the ultimate section capacities is virtually the same as those suggested in EC4, except different values have been used for the capacity factors.
2.2.2 Ultimate member capacity
Like many other codes, a slenderness reduction factor αc is introduced in AS 5100 to reflect the basic relationship between strength and stability for an axially loaded column, as follows:
290
1 1cα ξξλ
⎡ ⎤⎛ ⎞⎢ ⎥= − −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
(4)
where ξ and λ are coefficients related to the relative
slenderness (λr). λr is defined herein as /s cN N r , in
which Ns is determined according to equation (2) or (3),
with φ and φc taken as 1.0, and Ncr is the elastic critical
load. The expression for Ncr is given as equation (5),
where (EI)e is the effective flexural stiffness determined
according to equation (6), and Le is the effective length
of a composite compression member.
2
2
( )ecr
e
EIN
Lπ
=
(5)
(EI)e = φEIs + φcEcIc (6)
In equation (6), Is and Ic are the second moment of
areas of the steel section and the uncracked concrete
section, respectively, and φ and φc herein are also
taken as 1.0.
After the slenderness reduction factor αc is determined
from equation (4), the member capacity of a composite
column can be expressed as:
Nuc = αcNus ≤ Nus (7)
2.3 Members under combined compression and bending
In AS 5100, strengths of CFST beams and beam-
columns should be calculated on the basis of
rectangular stress blocks, assuming that the maximum
concrete compressive stress is (φc fc’) and the maximum
steel stress is (φfy). An interaction curve based on the
plastic resistance analysis can be obtained as shown
in figure 2(a). It should be noted that both φ and φc
are taken as 0.9 for a composite member subjected
to combined axial and flexural actions.
To verify the resistance of a beam-column subjected
to compression and uniaxial bending, the following
criterion should be satisfied:
Mx* ≤ 0.9Mrx (8a)
My* ≤ 0.9Mry (8b)
where Mx* and My* are the design bending moments
about the principal major x-axis and minor y-axis,
respectively; Mrx and Mry are the section moment
capacities reduced by the effect of axial compression,
slenderness and imperfection (see figure 2(a)).
In figure 2(a), Mdx and Mdy are the total moment
capacities of the section when the design axial force
N* is acting on the section; αn is a factor for the
interaction curve, given by αc(1 + βm)/4; βm is the ratio
of the smaller to the larger end bending moments
taken as positive when the member is bent in reverse
curvature.
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In order to simplify the design process, the full interaction curve shown in figure 2(a) may be approximated by the polygon joining the five points A, B, C, D and E, as shown in figure 2(b). These points are determined as follows:
1. Point A is defined by the nominal axial capacity (Nus) of the member without bending.
2. Point B is defined by the nominal section moment capacity (Msx or Msy) of the member.
3. Point C is determined by moving the neutral axis determined for point B to a new position equidistant from the centroid, but on the other side of the centroid, and parallel with its previous position. Therefore, the stresses in the section with the neutral axis in this position will create a moment equal to that derived from point B, ie. Msx or Msy, but with a compression load equal to the axial load in that part of the section between the neutral axis positions for points B and C.
4. Point D is determined by placing the neutral axis at the centroid of the section. At this location, the axial load in the section is half that for point C, and the moment is a maximum.
5. Point E is any point approximately mid-way between points A and C, determined with the neutral axis approximately mid-way between its location for point C and the edge of the section, which is in tension when determining point C.
In determining the value of Mrx or Mry, the second order moment Mp due to imperfections (imperfection moment) of the column can be determined using the simplified interaction curve shown in figure 2(b). By reading off the horizontal distance representing the imperfection moment as shown in figure 2(a), the moment resistance of the composite column under combined compression and bending may then be evaluated.
It should be noted that the benefits of the confining stresses on the concrete may be considered to
determine the plastic compressive stress for circular
members in accordance with section 2.2.1. It should
also be noted that the above methodology generally
follows that presented in the last version of Eurocode
4 (1994). To simplify the design process, point E in
figure 2(b) has been removed in the new version of
Eurocode 4 (2004).
Due to page limitations, the design procedures
given in other standards is not presented herein.
More details and limitation provisions for them can
be found in Chung & Matsui (2005) and Zhang et
al (2007).
3 COMPARISONS BETWEEN TEST AND PREDICTED CAPACITIES
3.1 Brief introduction to test databases
Over the last few decades, numerous tests have
been carried out on CFST members. A database was
established by Goode (2006) recently, in which 1792
test results from 92 references were included. These
test results can be accessed via the website http://
web.ukonline.co.uk/asccs2 (ASCCS, 2007). In this
paper, 1575 test results from Goode’s database,
including 918 for circular specimens and 657 for
rectangular specimens (square sections mainly), are
used to perform the code comparisons. The other test
results in this database have been discarded because
they are not relevant to this study.
Apart from the test results in Goode’s database,
another database developed by Wu (2006) contains
1514 experimental results from 104 references, where
some of them have not been included in Goode’s
database, especially for 81 tests on beams. No test
results on beams are available in Goode’s database.
After merging the two databases, 1232 and 962 test
results (2194 altogether) from 130 references on
circular and rectangular specimens, respectively, are
used in this paper. The ranges of the test properties
are given in table 1. It should be noted that in some
Msx (or Msy)o
Interaction curve for the cross-section
N
M
Nus A
E
C
D
B
Msx (or Msy)
o
Interaction curve for the cross-section
N
M
Nus
Mdx (or Mdy)
Nuc(= cNus)
N*
nNus
Mrx or Mry
Figure 2: Interaction curve for CFST members subjected to combined compression and bending.
(a) (b)
13“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Australian Journal of Structural Engineering Online
references no concrete cylinder strength (fc’) was available. Instead, a compressive strength (fcu) of 150 mm cubes was reported. In general, fc’ can be taken as 0.8fcu for normal strength concrete, but this relationship is not quite applicable for high-strength concrete (Chen et al, 1996; Mansur & Islam, 2002). Therefore, equivalent cylinder strengths (fc’) were determined according to Chen et al (1996), where a table demonstrating the approximate relationship of two types of concrete strengths can be found in Yu et al (2008). This relationship is quite close to that given by Mansur & Islam (2002).
3.2 Strength comparison
When comparing design calculations with the tests, the material partial safety factors specified in all design codes have been taken as unity. At the same time, all code limitations are ignored with a purpose to check the feasibility of those design codes in predicting the load-carrying capacities of the test specimens. In the following sections, “stub column” is defined as a short member (Le/do or Le/b ≤ 4; b is the section width of a rectangular tube) under axial compression to determine section capacity, while “column” is defined as a long one (Le/do or Le/b > 4) under axial compression, where the slenderness
effect is expected to be considered. “Beam-column”
is defined as a member subjected to the combined
action of compression and flexure. It is worth noting
that, the classification standards for short and long
columns in different codes are quite different. Some
of them are very complex to follow and, in some
codes, a slenderness reduction factor is applicable
even for a very short column. Therefore, the above
rather simple criterion used by Goode (2006) is also
adopted in this paper.
In order to better reflect the deviations of code
predictions from the experimental results, the –15%
and +15% error bounds are depicted in figures
presented in the following sub-sections. It is worth
noting that this is not a criterion used to assess the
acceptability of prediction accuracy. Generally, a
reliability analysis should be performed based on a
regional reliability standard to accomplish this task
(Han, 2007).
3.2.1 Section capacity under axial compression
Currently available test results are 484 and 445 for
circular and rectangular stub columns, respectively.
Figure 3 shows the comparison between experimental
ultimate strength Nue and predicted strength Nuc
Section type Member typedo(h)
(mm)λe
fy (MPa)
fc’ (MPa)
No. of tests
No. of references
Circular
Stub column 48-1020 13-237 186-853 10-110 484 39
Column 25-500 9-192 178-682 10-96 420 28
Beam-column 76-200 17-198 186-433 18-114 304 19
Beam 34-300 23-196 262-436 23-82 24 4
Rectangular
Stub column 60-400 13-181 192-835 12-103 445 34
Column 60-360 19-163 217-550 10-94 234 25
Beam-column 76-323 18-94 205-761 18-103 226 20
Beam 100-306 22-115 194-750 19-88 57 7
Table 1: Summary of test properties.
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
5000 12000 19000 26000 33000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
Figure 3: Comparison between test results and predictions using AS 5100 (circular stub column).
(a) (b)
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“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
using AS 5100 for circular stub columns. Table
2 also shows both the mean value (μ) and the
standard deviation (σ) of the ratio of Nue/Nuc for all
the strength predictions. As can be seen, generally
good agreement is achieved with an average value
(μ) of 1.037 and a standard deviation (σ) of 0.139. In
the test databases, some tests were performed on
specimens with a rather large diameter. In order to
illustrate more clearly, those tests are compared in
figure 3(b), which demonstrates that AS 5100 is also
applicable in this circumstances without apparent
size effect observed.
Comparison results from other design codes are
given in figure 4 and table 2, which clearly show
that AISC is quite conservative in its prediction
and BS 5400 gives slightly (3.4%) higher capacities
on average than the test results. For clarity, the test
results for those specimens with large diameters are
not given in figure 4. The agreement of the measured
and predicted strengths is generally good.
Figure 5 compares the test strength (Nue) with the
calculated strength (Nuc) using different design
codes for rectangular stub columns. All codes give
accurate predictions except that AISC and BS 5400
underestimates the strength by as much as 15% on
average (table 2). At the same time, all predictions
have smaller variations compared to those for
circular stub columns. This may be attributed to the
fact that a lot of circular specimens did not show
strain softening behaviour, thus different definitions
of ultimate strength have been applied by different
authors.
3.2.2 Column member capacity
Figures 6 and 7 show the comparisons between
test results (Nue) and code predictions (Nuc) for
circular and rectangular columns, respectively.
It appears that AISC and BS 5400 give the most
conservative prediction results. As far as AS 5100 is concerned, its predictions are generally accurate, but it underestimates the load-bearing capacity of circular columns (16% lower on average). The same trend is found for the predicted results from EC4. The reason is attributed to the fact that no confinement effect is considered for columns with a relative slenderness λr greater than 0.5. In fact, the apparent concrete confinement can still be expected even for a very slender circular column (Han, 2000).
Figure 8 compares the calculated strength of column members based on different code provisions. Test results reported by Matsui et al (1995) are shown as dots in this figure. Parameters for the circular specimens are as follows: do =165.2 mm, t = 4.08 mm, fy = 353 MPa, fc’ = 40.9 MPa; while those for the square ones are: b = 149.8 mm, t = 4.27 mm, fy = 412 MPa, fc’ =31.9 MPa. From the comparisons, it seems that all curves are close and generally agree with the test results, except that BS 5400 gives an obvious conservative prediction for square columns. Also, there are apparent discrepancies amongst predictions for circular columns when the relative slenderness λr is less than 0.5.
3.2.3 Beam-column member capacity
The comparisons between predicted load-bearing capacities (Nuc) and test results (Nue) are illustrated in figures 9 and 10 for circular and rectangular beam-columns, respectively. It has been demonstrated that AISC gives the most conservative results for circular beam-columns (μ = 1.385, σ = 0.467), and BS 5400 does that for rectangular beam-columns (μ = 1.300, σ = 0.278). All codes except BS 5400 give less conservative predictions for rectangular members than for circular ones. The predictions from AS 5100 are quite close to those from EC4, which demonstrates that they are quite accurate in predicting load-bearing capacities for circular
Section type
Member type
AS 5100 AIJ AISC BS 5400DBJ
13-51-2003EC4
μ σ μ σ μ σ μ σ μ σ μ σ
Circular
Stub column
1.037 0.139 1.097 0.154 1.275 0.199 0.966 0.150 1.155 0.149 1.048 0.139
Column 1.163 0.170 1.115 0.177 1.195 0.172 1.130 0.302 1.080 0.189 1.133 0.162
Beam-column
0.997 0.146 1.138 0.211 1.385 0.467 1.185 0.234 1.078 0.161 1.004 0.160
Beam 1.194 0.151 1.422 0.323 1.422 0.323 1.236 0.281 1.204 0.213 1.194 0.151
Rectangular
Stub column
1.062 0.123 1.061 0.123 1.150 0.138 1.169 0.147 1.037 0.125 1.061 0.123
Column 1.049 0.120 1.036 0.127 1.130 0.133 1.195 0.161 1.092 0.161 1.030 0.124
Beam-column
0.952 0.134 1.041 0.138 1.278 0.305 1.300 0.278 1.076 0.192 0.966 0.138
Beam 1.141 0.146 1.306 0.196 1.306 0.196 1.188 0.158 1.164 0.160 1.141 0.146
Table 2: Comparison results of code predictions with test results.
15“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Australian Journal of Structural Engineering Online
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
15%
15%
Figure 4: Comparison between test results and predictions using other codes (circular stub columns) – (a) AIJ, (b) AISC, (c) BS 5400, (d) DBJ 13-51-2003, and (e) EC4.
beam-columns, but overestimate those of rectangular
beam-columns (4-5% on average). It seems that the
assumed rectangular stress blocks are less valid for
rectangular beam-columns.
To illustrate the differences among the code
predictions more clearly, the predicted axial load
(N) versus moment (M) interaction curves using
different methods are compared in figure 11, with the
test results of circular members obtained by Matsui
et al (1995). The section properties are the same as
those of the columns given before (figure 8 (a)). As
can be seen from figure 11, there are considerable
discrepancies among predictions from different
codes. For shorter members, AS 5100 and EC4 give
accurate predictions. As the slenderness increases,
they tend to overestimate the strength compared
(a) (b)
(c) (d)
(e)
16
Australian Journal of Structural Engineering Online
“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
Figure 5: Comparison between test results and code predictions (rectangular stub columns) – (a) AS 5100, (b) AIJ (EC4), (c) AISC, (d) BS 5400, and (e) DBJ 13-51-2003.
to the test results reported by Matsui et al (1995).
Overall, DBJ 13-51-2003 gives the best prediction in
this comparison.
3.2.4 Beam moment capacity
The moment capacities (Muc) predicted using the
six design codes are compared with test results
(Mue) shown in figures 12 and 13 for circular and
rectangular beams, respectively. The ratios of Mue/Muc
for all codes are presented in table 2. As can be seen,
all predicted results are conservative overall. AIJ and
AISC give the most conservative predictions due to
ignoring the concrete contribution. AS 5100, EC4 and
DBJ give the best predictions for both circular and
rectangular beams.
(a) (b)
(c) (d)
(e)
17“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Australian Journal of Structural Engineering Online
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
Figure 6: Comparison between test results and code predictions (circular columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4.
3.3 Discussion
For design purposes, all codes have provided
some limitations on material strengths and section
slenderness. However, many tests have been
conducted to date beyond those limitations, which
makes it possible to check the possibility of relaxing
those limitations. The following sections discuss this
topic for AS 5100.
3.3.1 Effect of steel strength
Figure 14 shows the effect of steel strength (fy) on
the prediction accuracy of AS 5100. Table 3 provides
the mean values (μ) and the standard deviations (σ)
of measured to calculated strength ratios for test
specimens with fy larger than 350 MPa. From the
comparisons, it can be seen that there is a decrease
of 2-3% in μ except circular beam-columns with a
(a) (b)
(c) (d)
(e) (f)
18
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0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 1000 2000 3000 4000 5000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
Figure 7: Comparison between test results and code predictions (rectangular columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4.
0
500
1000
1500
2000
2500
0 0.5 1 1.5 2 2.5
Relative slenderness r
Ulti
mat
e st
reng
th (k
N)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
0
400
800
1200
1600
2000
0 0.5 1 1.5 2 2.5
Relative slenderness r
Ulti
mat
e st
reng
th (k
N)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
Figure 8: Column strength based on different code provisions – (a) circular section, and (b) square section.
(a) (b)
(c) (d)
(e) (f)
(a) (b)
19“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Australian Journal of Structural Engineering Online
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
15%
15%
15%
15%
Figure 9: Comparison between test results and code predictions (circular beam-columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4.
(a) (b)
(c) (d)
(e) (f)
decrease of 5% and circular beams with an increase
trend. But all mean values are still above unity except
those for beam-columns.
3.3.2 Effect of concrete strength
The effect of concrete strength (fc’) on the prediction
accuracy of AS 5100 is shown in figure 15. For test
specimens with fc’ larger than 65 MPa, the mean
values (μ) and the standard deviations (σ) of
measured to calculated strength ratios are presented
in table 3. From figure 15 and table 3, it seems that
the effect of concrete strength on circular specimens
is different from that on rectangular specimens. For
circular specimens, a decrease of 3-6% in the mean
value μ is found. In the case of rectangular specimens,
only a decrease of 4% is found for stub columns while
an increase of 3-4% is found for columns, beam-
20
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0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
0
0.5
1
1.5
2
0 600 1200 1800 2400 3000Test strength N ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Nue
/Nuc
15%
15%
15%
15%
Figure 10: Comparisons between test results and code predictions (rectangular beam-columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4.
(a) (b)
(c) (d)
(e) (f)
columns or beams. Once again, all mean values of
measured to calculated strength ratios are above or
near unity except those for beam-columns.
3.3.3 Effect of section slenderness
Figure 16 illustrates the effect of section slenderness
(λe) on the prediction accuracy of AS 5100. Table
3 provides the mean values (μ) and the standard
deviations (σ) of measured to calculated strength
ratios for test specimens with section slenderness
beyond the allowed values given in AS 5100. Though
different yield slenderness limits have been specified
for RHSs, only the middle value of 40 is used herein
to analyse the data for simplicity considerations. It
can be seen from figure 16 that there is a declining
trend of the measured to calculated strength ratios
as λe increases. For circular specimens, a decrease of
21“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Australian Journal of Structural Engineering Online
0
500
1000
1500
2000
2500
0 15 30 45 60
Moment M (kN m)
Axi
al lo
ad N
(kN
)Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
0
500
1000
1500
2000
2500
0 15 30 45 60
Moment M (kN m)
Axi
al lo
ad N
(kN
)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
0
500
1000
1500
2000
2500
0 15 30 45 60
Moment M (kN m)
Axi
al lo
ad N
(kN
)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
0
500
1000
1500
2000
2500
0 15 30 45 60
Moment M (kN m)
Axi
al lo
ad N
(kN
)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
0
300
600
900
1200
1500
0 15 30 45 60
Moment M (kN m)
Axi
al lo
ad N
(kN
)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
0
200
400
600
800
1000
0 15 30 45 60
Moment M (kN m)
Axi
al lo
ad N
(kN
)
Test resultsAS 5100AIJAISCBS 5400DBJ 13-51-2003EC4
Figure 11: Comparison of predicted interaction curves with test results by Matsui et al (1995) – (a) λr = 0.18, (b) λr = 0.35, (c) λr = 0.51, (d) λr = 0.80, (e) λr = 1.22, and (f) λr = 1.82.
(a) (b)
(c) (d)
(e) (f)
about 5% in the mean value μ is found when λe is
larger than 82. However, only 1-2% in the mean value
μ is found for rectangular members when λe is larger
than 40. It can also be seen from table 3 that all mean
values of measured to calculated strength ratios are
above or near unity except those for beam-columns.
This demonstrates the fact that there is a tendency to
relax the limitation of section slenderness.
4 CONCLUSIONS
In this paper, the AS 5100 approach to the design of
CFST members has been described briefly. 2194 test
results from two currently available test databases
are used to evaluate the design approach of AS 5100.
Some other existing design codes are also compared
with the test results. The following conclusions may
be made within the present scope of investigation:
Moment M (kN m)
22
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0
0.5
1
1.5
2
0 100 200 300 400Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Mue
/Muc
0
0.5
1
1.5
2
0 100 200 300 400Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Mue
/Muc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 100 200 300 400Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Mue
/Muc
0
0.5
1
1.5
2
0 100 200 300 400Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Mue
/Muc
15%
15%
15%
15%
Figure 12: Comparison between test results and code predictions (circular beams) – (a) AS 5100 (EC4), (b) AIJ (AISC), (c) BS 5400, and (d) DBJ 13-51-2003.
(a) (b)
(c) (d)
0
0.5
1
1.5
2
0 60 120 180 240 300Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Mue
/Muc
0
0.5
1
1.5
2
0 60 120 180 240 300Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stren
gth
Mue
/Muc
15%
15%
15%
15%
0
0.5
1
1.5
2
0 60 120 180 240 300Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Mue
/Muc
0
0.5
1
1.5
2
0 60 120 180 240 300Test strength M ue (kN)
Nor
mal
ized
cal
cula
ted
stre
ngth
Mue
/Muc
15%
15%
15%
15%
Figure 13: Comparison between test results and code predictions (rectangular beams) – (a) AS 5100 (EC4), (b) AIJ (AISC), (c) BS 5400, and (d) DBJ 13-51-2003.
(a) (b)
(c) (d)
23“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Australian Journal of Structural Engineering Online
0
0.5
1
1.5
2
180 360 540 720 900Steel yield strength f y (MPa)
Nor
mal
ized
cal
cula
ted
stre
ngth
Stub column ColumnBeam-column Beam
0
0.5
1
1.5
2
180 360 540 720 900Steel yield strength f y (MPa)
Nor
mal
ized
cal
cula
ted
stre
ngth
Stub column ColumnBeam-column Beam
15%
15%
fy=350 MPa
15%
15%
fy=350 MPa
Figure 14: Effect of steel strength on the prediction accuracy of AS 5100 – (a) circular section, and (b) square section.
0
0.5
1
1.5
2
0 30 60 90 120Concrete cylinder strength f c (MPa)
Nor
mal
ized
cal
cula
ted
stre
ngth
Stub column ColumnBeam-column Beam
0
0.5
1
1.5
2
0 30 60 90 120Concrete cylinder strength f c (MPa)
Nor
mal
ized
cal
cula
ted
stre
ngth
Stub column ColumnBeam-column Beam
15%
15%
fc =65 MPa
15%
15%
fc =65 MPa
Figure 15: Effect of concrete strength on the prediction accuracy of AS 5100 – (a) circular section, and (b) square section.
0
0.5
1
1.5
2
0 44 88 132 176 220Section slenderness e
Nor
mal
ized
cal
cula
ted
stre
ngth
Stub column ColumnBeam-column Beam
0
0.5
1
1.5
2
0 40 80 120 160 200Section slenderness
Nor
mal
ized
cal
cula
ted
stre
ngth
Stub column ColumnBeam-column Beam
15%
15%
e=40
15%
15%
e=82
Figure 16: Effect of section slenderness on the prediction accuracy of AS 5100 – (a) circular section, and (b) square section.
(a) (b)
(a) (b)
(a) (b)
1. The approach in AS 5100 gives generally
accurate predictions, thus it is also possible to
be used for building construction. However,
it should be noted that it overestimates the
strength of rectangular beam-columns by 5% on
average.
2. After ignoring all code limitations and taking
material partial safety factors as unity, there are
considerable differences among different code
predictions. The predicted results using AS 5100
are quite close to those from EC4.
3. All three factors of steel strength, concrete
strength and section slenderness slightly affect
the prediction accuracy, but the comparisons
still indicate a tendency to relax the limitations
24
Australian Journal of Structural Engineering Online
“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
Section type
Member type
fy > 350 MPa fc’ > 65 MPaλe > 82 (circular)
or λe > 40 (rectangular)
No. of tests
μ σ No. of tests
μ σ No. of tests
μ σ
Circular
Stub column
213 1.024 0.130 153 0.994 0.115 161 0.996 0.105
Column 141 1.137 0.135 13 1.102 0.081 58 1.085 0.151
Beam-column
45 0.947 0.100 55 0.944 0.112 31 0.957 0.072
Beam 2 1.320 0.058 4 1.383 0.088 10 1.322 0.083
Rectangular
Stub column
166 1.038 0.104 64 1.020 0.088 237 1.044 0.124
Column 65 1.011 0.118 36 1.093 0.146 141 1.039 0.125
Beam-column
82 0.929 0.140 55 0.988 0.115 113 0.951 0.129
Beam 28 1.121 0.088 4 1.172 0.092 2 1.021 0.045
Table 3: Comparison results for tests beyond the limitations of AS 5100.
of AS 5100. This relaxation will allow a designer
to use higher strength materials and to design
composite members with larger section
slenderness.
4. Additional concrete confinement at higher
slenderness ratios can be expected for circular
columns. This beneficial effect may be
considered in a column design.
ACKNOWLEDGEMENTS
This research work has been partially supported
by the International Research Initiatives Scheme
provided by the University of Western Sydney.
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26
Australian Journal of Structural Engineering Online
“Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He
ZHONG TAO
Zhong Tao is Professor of Structural Engineering at Fuzhou University, China, and is currently visiting the University of Western Sydney. He received his MS and PhD degrees from the Harbin Institute of Technology, China. His main research interests are steel-concrete composite structures and FRP-confined concrete. Zhong has published more than 80 journal papers, and recently published a Chinese book about innovative composite columns. He has played an important role in drafting five Chinese design codes on steel-concrete composite structures, including DBJ13-61-2004, DBJ13-51-2003 and GJB4142-2000. He was awarded three patents by the Chinese National Bureau of Knowledge Property Rights since 2005. He is currently on the Editorial Board of the international journal of Steel & Composite Structures.
BRIAN UY
Brian Uy is Professor of Structural Engineering and Head of the School of Engineering at The University of Western Sydney. He has been involved in research in steel and steel-concrete composite structures for over 15 years and published more than 300 articles. Much of his research has been underpinned by competitive grant research funding from the Australian Research Council (ARC) and industry. He is currently a member of the ARC College of Experts, providing advice to the federal government on peer reviewed research in civil and structural engineering. Brian currently serves on the Australian Standards Committee for Composite Structures (BD 32), the AISC Task Committee 5 on Composite Construction, ASCE Technical Committee on Composite Construction, and the IABSE Working Commission 2 for Steel, Timber and Composite Structures. He also holds roles on the Editorial Board for seven major international journals in steel and composite structures, including being the Chief Editorial Asia-Pacific of Steel & Composite Structures. Brian is a chartered civil and structural engineer in Australia, the UK and the USA.
LIN-HAI HAN
Lin-Hai Han is Professor of Structural Engineering at Tsinghua University, China. He has published 60 refereed international journal papers and 40 refereed international conference papers. He has received several excellence awards from the Chinese government since 1995 in recognition of his contributions to the research and application of steel-concrete composite construction. He is one of the outstanding young researchers awarded by the National Natural Science Foundation of China. He holds roles on the Editorial Board for several international and national journals. Lin-Hai has consulted industry and government authorities on a wide range of structural engineering projects. He has played an important role in drafting several design codes on steel-concrete composite structures in China. His current research interests include steel-concrete composite and hybrid structures under different kinds of loadings, such as static, dynamic and fire.
SHAN-HU HE
Shan-Hu He is a PhD candidate at Tsinghua University and her supervisor is Professor Lin-Hai Han. She received her bachelor’s degree from Tsinghua University in 2007 and is currently working in the field of concrete-filled steel tubular columns.
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