Investigation of concrete-filled steel composite (CFSC) stub columns with bar stiffeners.
Bahrami, Alireza ; Badaruzzaman, Wan Hamidon Wan ; Osman, Siti Aminah 等
Reference to this paper should be made as follows: Bahrami, A.; Wan
Badaruzzaman, W. H.; Osman, S. A. 2013. Investigation of concrete-filled
steel composite (CFSC) stub columns with bar stiffeners, Journal of
Civil Engineering and Management 19(3): 433-446.
Introduction
Steel columns have the benefits of high ductility and tensile
strength; on the other hand, reinforced concrete columns possess the
benefits of large stiffness and compressive strength. Composite columns
which comprise steel and concrete also have the structural advantages of
the two materials. Concrete-filled steel composite (CFSC) columns are an
alternative to steel and reinforced concrete columns in modern civil
projects worldwide. The steel consumption in the CFSC columns is less
than the steel columns which leads to cost saving. Also, the CFSC
columns not only have structural benefits such as high strength, large
stiffness and high ductility but also possess ecological benefits over
reinforced concrete columns: reinforcement and formwork are not utilised
in the CFSC columns which result in a clean construction site; when the
building is demolished, high-strength concrete which is without
reinforcement in the CFSC columns can be easily crushed and reused as
aggregates. Also, the steel wall which peels from the concrete core can
be used again. A number of theoretical and experimental research works
have been done during the past years on the CFSC columns. Shakir-Khalil
and Mouli (1990) tested nine 3 m long composite columns of
concrete-filled rectangular hollow sections and studied experimentally
12 short specimens under axial compression to establish the squash load
of the stub columns. Effects of different materials and geometric
properties on the strength and ductility of concrete-filled steel box
columns were investigated by Uy (1998). Lakshmi and Shanmugam (2002)
presented a semi-analytical method to predict the behaviour of in-filled
steel-concrete composite columns. Twelve high-strength rectangular
concrete-filled steel hollow section columns were tested under pure
bending by Gho and Liu (2004). Liu (2005) evaluated experimentally 22
high-strength rectangular concrete-filled steel hollow section columns
in order to investigate three parameters including material strength,
cross sectional aspect ratio and volumetric steel-to-concrete ratio.
Tests on concrete-filled steel tubular stub columns with inner and outer
welded longitudinal stiffeners were reported by Tao et al. (2005) under
axial compression. Guo et al. (2007) conducted tests on 24 bare steel
and concrete-filled tubes to study the occurrence of local buckling.
Reasons of the complex stress state appearance and behaviour of hollow
concrete-filled steel tubular element components in various load stages
of compressed stub structural member were analysed by Kuranovas and
Kvedaras (2007). Han et al. (2008) performed 46 tests on thin-walled
steel tube confined concrete stub columns subjected to axial compression
to assess effects of sectional type, local compression area ratio and
steel tube width-to-wall thickness ratio on the behaviour of the
columns. Experimental investigation of stiffened thin-walled hollow
steel structural stub columns filled with concrete was carried out by
Tao et al. (2008) to uncover strength and ductility of such columns.
Load carrying capacity of thin-walled box-section stub columns
fabricated by high-strength steel was experimentally evaluated by Gao et
al. (2009) under uniaxial compression. Several types of concrete-filled
steel columns were tested by Kuranovas et al. (2009) to determine their
load-carrying capacities. Petrus et al. (2010) presented effects of tab
stiffeners on the bond and compressive strengths of concrete-filled
thin-walled steel tubes. Goode et al. (2010) analysed the experimental
data of concrete-filled steel tubes. Circular and rectangular hollow
section stub and long columns fully with concrete were investigated with
and without applied moments at the ends of the specimen. de Oliveira et
al. (2010) assessed experimentally passive confinement effect of the
steel tube in concrete-filled steel tubular columns. A series of tests
were performed on short and slender concrete-filled stainless steel
tubular columns by Uy et al. (2011) to illustrate their performance
under axial compression and combined action of axial force and bending
moment. Twenty-eight concrete-filled steel tubular stub columns
subjected to eccentric partial compression were tested by Yang and Han
(2011) to study effects of parameters such as section type, load
eccentricity ratio and shape of the loading bearing plate. Bahrami et
al. (2011a) studied structural behaviour of CFSC slender columns to
investigate and develop different shapes (V, T, L, Line &
Triangular) and number (1 on side & 2 on side) of longitudinal
cold-formed steel sheeting stiffeners and also evaluate their effects on
the behaviour of the columns. However, it seems that limited researches
have been conducted on the behaviour of the CFSC stub columns with bar
stiffeners.
This paper presents the investigation of the CFSC stub columns with
bar stiffeners. To establish the accuracy of the modelling in this
study, the experimental test result reported by Tao et al. (2005) is
used to compare with the proposed three-dimensional (3D) finite element
modelling. A special arrangement of bar stiffeners in the columns with
various number, spacing and diameters of the bar stiffeners are
developed using the non-linear finite element method. The investigation
of the CFSC stub columns is further carried out by considering different
variables in the non-linear finite element analyses. The main variables
are such as number of bar stiffeners (2, 3 and 4), spacing of bar
stiffeners (from 50 to 150 mm), diameter of bar stiffeners (from 8 to 12
mm), steel wall thicknesses (from 2 to 3 mm), concrete compressive
strengths (from 30 to 50.1 MPa) and steel yield stresses (from 234.3 to
450 MPa). Effects of various number and spacing of the bar stiffeners
and also steel wall thicknesses on the ultimate axial load capacity and
ductility of the columns are evaluated. Also, effects of different
diameters of the bar stiffeners, concrete compressive strengths and
steel yield stresses on the ultimate axial load capacity of the columns
are assessed. The obtained ultimate axial load capacities from the
non-linear finite element analyses are compared with the predicted
capacities by the design code Eurocode 4 (2004) and recommended
equations by Baig et al. (2006) and Bahrami et al. (2011b).
1. Description of non-linear finite element modelling
The experimental test of a CFSC stub column performed by Tao et al.
(2005) has been chosen for the non-linear modelling using the finite
element software LUSAS herein. Figure 1 shows the cross section and
elevation of the column. The steel wall thickness of the column was 2.5
mm. In the experimental test, concrete was vertically poured in the
steel box in layers. Each layer was vibrated using a poker vibrator. The
column was then located upright to air until testing. The environmental
average temperature and relative humidity were about 15[degrees]C and
80%, respectively. The column was tested to failure under axial
compression using a 5000 kN capacity testing machine after 28 days of
curing in the laboratory. The test of the column was conducted with a
loading rate of 0.2 mm/min before the ultimate load capacity was
reached. The loading rate was thereafter changed to 0.5 mm/min.
[FIGURE 1 OMITTED]
1.1. Material properties and constitutive models
The steel wall, steel bar stiffener and concrete are the materials
used in the numerical analysis of this study. The material properties
and their constitutive models are presented as follows.
1.1.1. Steel wall
The steel wall has been modelled as an elasticperfectly plastic
material in both tension and compression. Figure 2 illustrates the
stress-strain curve used for the steel wall. The yield stress, modulus
of elasticity and Poisson's ratio of the steel wall have been
adopted identical to those of the corresponding experimental test done
by Tao et al. (2005), respectively as 234.3 MPa, 208,000 MPa and 0.247.
Von Mises yield criterion, an associated flow rule, and isotropic
hardening have been employed in the nonlinear material model.
1.1.2. Steel bar stiffener
The uniaxial behaviour of the steel bar stiffener is similar to
that of the steel wall. Accordingly, it can be simulated by the
elastic-perfectly plastic material model (Fig. 2). The yield stress and
modulus of elasticity of the steel bar stiffener have been taken as 400
MPa and 200,000 MPa, respectively.
[FIGURE 2 OMITTED]
1.1.3. Concrete
The compressive strength and modulus of elasticity of concrete have
been taken identical to those of the corresponding experimental test
done by Tao et al. (2005), respectively as 50.1 MPa and 35,100 MPa.
Figure 3 indicates the equivalent uniaxial stress-strain curves utilised
for concrete (Ellobody, Young 2006a, b). The unconfined concrete
cylinder compressive strength [f.sub.c] is equal to 0.8[f.sub.cu] in
which [f.sub.cu] is the unconfined concrete cube compressive strength.
The corresponding unconfined strain [[epsilon].sub.c] is usually around
the range of 0.002-0.003, as recommended by Hu et al. (2005). The
[[epsilon].sub.c] was considered as 0.002 in their study. The same value
for [[epsilon].sub.c] has been also adopted in the analyses of this
study. When concrete is under laterally confining pressure, the confined
compressive strength [f.sub.cc] and the corresponding confined strain
[[epsilon].sub.cc] are much higher than those of unconfined concrete.
Eqns (1) and (2) have been respectively used to determine the
confined concrete compressive strength [f.sub.cc] and the corresponding
confined stain [[epsilon].sub.c] (Mander et al. 1988):
[f.sub.cc] = [f.sub.c] + [k.sub.1][f.sub.1]; (1)
[[epsilon].sub.cc] = [[epsilon].sub.c](1 +
[k.sub.2][[f.sub.1]/[f.sub.c]]), (2)
where: [f.sub.1] is the lateral confining pressure provided by the
steel wall for the concrete core. The approximate value of [f.sub.1] can
be obtained from the interpolation of the values presented by Hu et al.
(2003). The factors of [k.sub.1] and [k.sub.2] have been considered as
4.1 and 20.5, respectively (Richart et al. 1928). Because [f.sub.1],
[k.sub.1] and [k.sub.2] are known [f.sub.cc] and [[epsilon].sub.cc] can
be determined using Eqns (1) and (2).
The equivalent uniaxial stress-strain curve for confined concrete
(Fig. 3) is consisted of three parts which should be defined. The first
part comprises the initially assumed elastic range to the proportional
limit stress. The value of the proportional limit stress has been
considered as 0.5[f.sub.cc] (Hu et al. 2003). The empirical Eqn (3) has
been used to obtain the initial Young's modulus of confined
concrete [E.sub.cc] (ACI 31899 1999). The Poisson's ratio
[[upsilon].sub.cc] of confined concrete has been chosen as 0.2:
[E.sub.cc] = 4700[square root of [E.sub.cc]] MPa. (3)
The second part is the non-linear portion which starts from the
proportional limit stress 0.5[f.sub.cc] to the confined concrete
strength [f.sub.cc]. The common Eqn (4) can be used to obtain this part
(Saenz 1964). The values of uniaxial stress f and strain [epsilon] are
the unknowns of the equation that define this part of the curve. The
strain value o has been adopted between the proportional strain
(0.5[f.sub.cc]/[E.sub.cc]), and the confined strain [[epsilon].sub.cc]
which corresponds to the confined concrete strength. By assuming the
strain values [epsilon], Eqn (4) can be used to calculate the stress
values f:
f = [E.sub.cc][epsilon]/[1 + (R + [R.sub.E] -
2)([epsilon][[epsilon].sub.cc]) - (2R -
1)[([epsilon]/[[epsilon].sub.cc]).sup.2] +
R[([epsilon]/[[epsilon].sub.cc]).sup.3]], (4)
where:
[R.sub.E] = [E.sub.cc][[epsilon].sub.cc]/[f.sub.cc]; (5)
R = [[R.sub.E]([R.sub.[sigma]] - 1)/[([R.sub.[epsilon]] -
1).sup.2]] - [1/[R.sub.[epsilon]]]. (6)
The constants [R.sub.[epsilon]] and [R.sub.[sigma]] have been
considered as 4 in this study (Hu, Schnobrich 1989). The third part of
the curve consists of the descending part that is between [f.sub.cc] and
r[k.sub.3][f.sub.cc] with the corresponding strain of
11[[epsilon].sub.cc]. The reduction factor [k.sub.3] depends on the H/t
ratio and the steel wall yield stress [f.sub.y]. Empirical equations
given by Hu et al. (2003) can be used to determine the approximate value
of [k.sub.3]. To take into account the effect of different concrete
strengths, the reduction factor r was introduced by Ellobody et al.
(2006) on the basis of the experimental study performed by Giakoumelis
and Lam (2004). The value of r has been considered as 1.0 for concrete
with cube strength [f.sub.cu] of 30 MPa and as 0.5 for concrete with
[f.sub.cu] greater than or equal to 100 MPa (Mursi, Uy 2003). The value
of r for concrete cube strength between 30 and 100 MPa has been
interpolated in this study. A linear Drucker-Prager yield criterion G
(Fig. 4) has been used to model the yielding part of the curve which is
the part after the proportional limit stress (Ellobody, Young 2006a, b;
Hu et al. 2005). This criterion has been utilised to define yield
surface and flow potential parameters for concrete under triaxial
compressive stresses. Also, this criterion has been used with associated
flow and isotropic rule. The criterion is expressed as Eqn (7):
G = t - p tan [beta] - d = 0, (7)
in which t, p and d are obtained from the following equations:
t = [[square root of 3[J.sub.2]]/2][1 + [1/k] - (1 -
[1/k])[(r/[square root of 3[J.sub.2]]).sup.3]]; (8)
r = [[[9/2]([S.sup.3.sub.1] + [S.sup.2.sub.3] +
[S.sup.3.sub.3])].sup.1/3]; (9)
P = -([[sigma].sub.1] + [[sigma].sub.2] + [[sigma].sub.3])/3; (10)
d = (1 - [tan [beta]/3])[f'.sub.cc]. (11)
[S.sub.1], [S.sub.2] and [S.sub.3] are principal stress deviators,
[[sigma].sub.1], [[sigma].sub.2] and [[sigma].sub.3] are the principle
stresses and [J.sub.2] is the second stress invariant of the stress
deviator tensor. The ratio of flow stress in triaxial tension to that in
compression K and the material angle of friction [beta] have been chosen
as 0.8 and 20[degrees], respectively (Hu et al. 2003).
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
1.2. Finite element type and mesh
Element types for the steel wall and concrete core of the columns
were chosen from the element library of the finite element software
LUSAS (2006) in this study. The 6-noded triangular shell element, TSL6,
was utilised to model the steel wall. This is a thin, doubly-curved,
isoparametric element that can be used to model 3D structures. It has
six degrees of freedom per node and provides accurate solution to most
applications. This element can accommodate generally curved geometry
with varying thickness and anisotropic and composite material
properties. The element formulation considers both membrane and flexural
deformations. The steel bar stiffeners were modelled by the 3-noded bar
element type BRS3. This is an isoparametric bar element in 3D which can
accommodate varying cross sectional area. This element is suitable to
model stiffening reinforcement with continuum elements. The 10-noded
tetrahedral element, TH10, was used for modelling of the concrete core.
This element is a 3D isoparametric solid continuum element capable of
modelling curved boundaries. This is a standard volume element of the
LUSAS software (2006). The elements can be employed for linear and
complex non-linear analyses involving contact, plasticity and large
deformations.
Different finite element mesh sizes were examined to find a
reasonable mesh size which can achieve accurate results. As a result,
the mesh size corresponding to 7713 elements was revealed to obtain
exact results. A typical finite element mesh used in this study is
illustrated in Figure 5.
1.3. Boundary conditions and load application
The pin-pin boundary conditions have been considered in the 3D
finite element modelling in this study. Therefore, the rotations of the
top and bottom surfaces of the columns in the X, Y and Z directions were
considered to be free. Also, the displacements of the bottom and top
surfaces in the X and Z directions were restrained. On the other hand,
the displacement of the bottom surface in the Y direction was restrained
while that of the top surface, in the direction of the applied load and
where the load is applied, was set to be free.
[FIGURE 5 OMITTED]
The load application on the column in the modelling was on the
basis of the loading arrangement in the corresponding experimental test
of the column. The axial load of the experimental test was exactly
modelled by incremental displacement load with an initial increment of 1
mm in the negative Y direction acting axially to the top surface of the
column. Increment is a step in a non-linear analysis where a portion of
the total load is applied. The increment change was 0.1 mm in the
analysis. Iteration is a step within a load increment where the analysis
solver attempts to converge to an acceptable solution. The iterations
per increment were 10 in the analysis. Incremental loading adds
displacements to a previous increment (LUSAS 2006). Each step in the
non-linear analysis was a small amount of the displacement of the column
and it was continued up to the failure of the column.
1.4. Modelling of concrete-steel interface
The contact between the concrete core and the steel wall was
simulated by slide-lines. The slide-lines attributes can be used to
model contact surfaces in the finite element software LUSAS (2006). The
slideline contact facility is non-linear. Slave and master surfaces
should be selected correctly to provide the contact between two
surfaces, steel and concrete. If a smaller surface is in contact with a
larger surface, the smaller surface can be best selected as the slave
surface. If it is not possible to distinguish this point, the body which
has higher stiffness should be selected as the master surface. It needs
to be mentioned that the stiffness of the structure should be taken into
account and not just the material. Although, the steel material is
stiffer than the concrete material, the steel wall may have less
stiffness than the volume of the concrete core in this study.
Consequently, the concrete core and steel wall surfaces were
respectively selected as the master and slave surfaces. Dabaon et al.
(2009) has also presented this process of choosing master and slave
surfaces. The slide-lines have the capability of defining properties
such as friction coefficient. The friction between two surfaces, the
steel wall and concrete core, is considered so that they can remain in
contact. The Coulomb friction coefficient in slidelines was selected as
0.25. The slide-lines allow the concrete core and steel wall to separate
or slide but not to penetrate each other.
1.5. Accuracy of modelling
The finite element modelling result was compared with the
experimental test result reported by Tao et al. (2005) to reveal the
accuracy of the 3D modelling in this study. According to Figure 6, the
curves obtained from the modelling and corresponding experimental test
agree well with each other. The difference between the ultimate axial
load capacity obtained from the modelling 3325 kN, and that from the
experimental test 3230 kN is only 2.9%. This small difference
demonstrates the accuracy of the finite element modelling. As a result,
the accurate prediction of the behaviour of the columns is absolutely
possible by the proposed 3D finite element modelling in this study.
[FIGURE 6 OMITTED]
2. Numerical analysis
Since the proposed 3D finite element modelling of this study was
demonstrated to be accurate, the method was utilised for the non-linear
analysis of stub columns of same size and cross section as that of Tao
et al. (2005) but with bar stiffeners. The previously explained
modelling specifications were exactly employed for simulating each of
the CFSC stub columns. Details of the stiffened CFSC stub columns which
were analysed by the use of the non-linear finite element method are
illustrated in Figure 7. Figure 7a indicates the arrangement of the bar
stiffeners in the columns. Different number (2, 3 and 4) and spacing of
the bar stiffeners (50, 100 and 150 mm) are considered in the analyses
in which two typical elevations are shown in Figure 7b and c. Moreover,
typical finite element meshes of the columns are illustrated in Figure
8.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
3. Results and discussion
Features and obtained ultimate axial load capacities of the CFSC
stub columns are listed in Table 1. The C in the column labels
represents the columns and the first four numbers following C
respectively designate the steel wall thickness t (mm), diameter of bar
stiffener D (mm), steel wall yield stress [f.sub.y](MPa) and concrete
compressive strength [f.sub.c](MPa). Also, the number before the
parentheses is the number of bar stiffeners and the number in the
parentheses presents the centre-to-centre spacing (mm) between the bar
stiffeners. Effects of different variables on the behaviour of the
columns are also discussed in the following sections.
3.1. Effect of number of bar stiffeners on ultimate axial load
capacity
To study the effect of number of bar stiffeners on the behaviour of
the CFSC stub columns, the varied number of bar stiffeners (2, 3 and 4)
(Fig. 7a) were considered in the analyses. Figure 9 shows these effects
on the ultimate axial load capacity of the columns. Also, Table 1 lists
the corresponding ultimate axial load capacity values of the curves.
According to the figure and table, the ultimate axial load capacity of
the unstiffened CFSC stub column is improved by the use of the bar
stiffeners. For instance, the use of four bar stiffeners
(C-2.5-10-234-50-4(50)) increases the ultimate axial load capacity of
the unstiffened column from 3325 to 3700 kN, an enhancement of 11.3%.
Also, increasing the number of bar stiffeners enhances the ultimate
axial load capacity of the columns. For example, as the number of bar
stiffeners is enhanced from 2 (C-2.5-10-234-50-2(150)) to 4
(C-2.5-10-234-50-4(150)) for the same bar spacing of 150 mm, the
ultimate axial load capacity is increased from 3353 to 3557 kN, an
improvement of 6.1%.
3.2. Effect of spacing of bar stiffeners on ultimate axial load
capacity
Three various bar spacing of 50, 100 and 150 mm were adopted in the
analyses to examine the effect of spacing of bar stiffeners on the
behaviour of the CFSC stub columns. This effect on the ultimate axial
load capacity of the columns is illustrated in Figure 10. As can be seen
from the figure and Table 1, the decrease of spacing of the bar
stiffeners enhances the ultimate axial load capacity. As an example, the
ultimate axial load capacity increases from 3456
(C-2.5-10-234-50-3(150)) to 3606 kN (C-2.5-10-234-50-3(50)) if spacing
of the bar stiffeners decreases from 150 to 50 mm with the same number
of bar stiffeners, an enhancement of 4.3%.
3.3. Effect of steel wall thickness on ultimate axial load capacity
The effect of steel wall thickness on the behaviour of the CFSC
stub columns was evaluated by considering three different steel wall
thicknesses of 2, 2.5 and 3 mm in the analyses. Figure 11 shows the
results. In accordance with the figure and Table 1, as the steel wall
thickness enhances the ultimate axial load capacity increases. For
instance, the increase of the steel wall thickness from 2
(C-2-10-234-50-4(50)) to 3 mm (C-3-10-234-50-4(50)) with the same number
and spacing of the bar stiffeners improves the ultimate axial load
capacity of the columns from 3544 to 3856 kN, an increase of 8.8%.
[FIGURE 9 OMITTED]
3.4. Effect of diameter of bar stiffeners on ultimate axial load
capacity
To investigate the effect of diameter of bar stiffeners on the
ultimate axial load capacity of the CFSC stub columns, three various
diameters of the bar stiffeners (8, 10 and 12 mm) were utilised in the
analyses. The results are indicated in Figure 12. According to the
figure and Table 1, higher ultimate axial load capacity can be obtained
by larger diameter of the bar stiffeners. For example, as the diameter
of the bar stiffeners increases from 8 (C-2.5-8-234-50-3(50)) to 12 mm
(C-2.5-12-234-50-3(50)) for the same number and spacing of the bar
stiffeners, the ultimate axial load capacity enhances from 3560 to 3648
kN, an enhancement of 2.5% and not much appreciable.
[FIGURE 10 OMITTED]
3.5. Effects of number and spacing of bar stiffeners on ductility
The ductility of the columns is assessed by the use of a ductility
index (DI) as following (Lin, Tsai 2001):
DI = [[epsilon].sub.85%]/[[epsilon].sub.y], (12)
in which [[epsilon].sub.85%] is the nominal axial shortening (D/L)
corresponding to the load which falls to its 85% of the ultimate axial
load capacity and [[epsilon].sub.y] is [[epsilon].sub.75%]/0.75 where
[[epsilon].sub.75%] is the nominal axial shortening corresponding to the
load that obtains 75% of the ultimate axial load capacity. The values of
[[epsilon].sub.85%] and [[epsilon].sub.y] can be taken from Figure 9.
Figure 13 illustrates effects of number and spacing of bar stiffeners on
the ductility of the columns.
[FIGURE 11 OMITTED]
The increase of the number of bar stiffeners enhances the ductility
of the columns (Fig. 13). For instance, the ductility of the columns is
increased from 3.112 (C-2.5-10-234-50-2(50)) to 3.363
(C-2.5-10-234-50-4(50)) by the enhancement of the number of bar
stiffeners from 2 to 4 for the same bar stiffeners spacing of 50 mm, an
increase of 8.1%.
In addition, the reduction of spacing of the bar stiffeners leads
to increase of the ductility. As an example, if the bar stiffeners
spacing is reduced from 150 (C-2.5-10-234-50-4(150)) to 50 mm
(C-2.5-10-234-50-4(50)), the ductility of the columns is enhanced from
3.150 to 3.363, an improvement of 6.8%.
3.6. Effect of thickness of steel wall on ductility
The ductility index, Eqn (12), is also used to study the effect of
steel wall thickness on the ductility of the columns. This effect on the
ductility of the columns is shown in Figure 14. The thicker steel wall
results in the greater ductility (Fig. 14). For example, increasing the
steel wall thickness from 2 (C-2-10-234-50-2(50)) to 3 mm
(C-3-10-234-50-2(50)) improves the ductility from 2.984 to 3.245, an
improvement of 8.7%.
[FIGURE 12 OMITTED]
[FIGURE 13 OMITTED]
[FIGURE 14 OMITTED]
3.7. Effect of concrete compressive strength on ultimate axial load
capacity
Different concrete compressive strengths (30, 40 and 50.1 MPa) have
been considered in the analyses to assess their effect on the ultimate
axial load capacity of the columns (Fig. 15). It can be seen from the
figure and Table 1 that the increase of the concrete compressive
strength enhances the ultimate axial load capacity of the columns. As an
example, the ultimate axial load capacity is increased from 2490 to 3700
kN as the concrete compressive strength is enhanced from 30
(C-2.5-10-234-30-4(50)) to 50.1 MPa (C-2.5-10-234-50-4(50)), an
improvement of 48.6%.
[FIGURE 15 OMITTED]
3.8. Effect of steel yield stress on ultimate axial load capacity
The effect of different steel yield stresses (234.3, 350 and 450
MPa) on the ultimate axial load capacity of the columns is shown in
Figure 16. As can be seen from the figure and Table 1, the higher steel
yield stress leads to larger ultimate axial load capacity of the
columns. For instance, the ultimate axial load capacity is increased
from 3700 to 4322 kN respectively for the steel yield stresses of 234.3
(C-2.5-10-234-50-4(50)) and 450 MPa (C-2.5-10-450-50-4(50)), an
enhancement of 16.8%.
[FIGURE 16 OMITTED]
3.9. Failure modes of stiffened CFSC stub columns
Figures 17 and 18 show the typical failure modes of the columns in
the cross section and elevation respectively. According to Figure 18,
the failure modes of the columns were characterised as concrete crushing
about their mid-height where the steel wall buckled locally. Also, the
inward buckling of the steel wall was prevented by the in-filled
concrete.
It can be also mentioned that the enhancement of the ultimate axial
load capacity and ductility of the columns owing to the use of the bar
stiffeners, increase of the number of bar stiffeners, decrease of
spacing of the bar stiffeners, increase of the steel wall thickness, or
enhancement of diameter of the bar stiffeners can be
becauseoftheincreaseofthe confinementeffectprovided by the steel wall on
the concrete core. As the confinement effect is enhanced the local
buckling of the steel wall is delayed, which results in the improvement
of the ultimate axial load capacity and ductility of the columns.
[FIGURE 17 OMITTED]
[FIGURE 18 OMITTED]
3.10. Comparison of obtained ultimate axial load capacity with
predictions
The ultimate axial load capacity of a square or rectangular CFSC
stub column can be predicted from Eqns (13), (14) and (15),
respectively, based on Eurocode 4 (2004), Baig et al. (2006) and Bahrami
et al. (2011b):
[N.sub.EC4] = [A.sub.c][f.sub.c] + [A.sub.s][f.sub.y]; (13)
[N.sub.N] = 1.10[A.sub.c][f.sub.c] + [A.sub.s][f.sub.y]; (14)
[N.sub.B] = 1.05[A.sub.c][f.sub.c] + [A.sub.s][f.sub.y], (15)
in which [A.sub.c] and [A.sub.s] are areas of concrete and steel
cross section respectively, and also [f.sub.c] and [f.sub.y] are
compressive strength of the concrete core and yield stress of the steel
wall, respectively. Table 2 summarises the predicted ultimate axial load
capacities based on the mentioned equations and their comparisons with
the values obtained from the non-linear analyses of the columns,
[N.sub.u]. Standard deviation and coefficient of variation are denoted
as SD and COV in Table 2, respectively. A mean ratio
([N.sub.EC4]/[N.sub.u]) of 0.956 is achieved with a COV of 0.031 which
reveals that Eurocode 4 (2004) underestimates the ultimate axial load
capacity of the columns by 4.4%. Also, a mean of 1.038 is obtained for
[N.sub.N]/[N.sub.u] with a COV of 0.034 which shows that Eqn (14) gives
the ultimate axial load capacity of the columns by 3.8% higher than
those from the non-linear analyses. Moreover, a mean ratio
([N.sub.B]/[N.sub.u]) of 0.999 is achieved with a COV of 0.032 which
uncovers that Eqn (15) underestimates the ultimate axial load capacity
by only 0.1%. Consequently, the proposed equation by Bahrami et al.
(2011b), Eqn (15), can predict the ultimate axial load capacity of the
columns with a very good accuracy.
Conclusions
CFSC stub columns with bar stiffeners have been investigated in
this paper. The finite element software LUSAS was used to perform the
non-linear analyses. Comparison of the modelling result with the
existing experimental test result uncovered the accuracy of the proposed
3D finite element modelling. It was revealed that the proposed modelling
can predict the behaviour of the columns with a reasonable accuracy. A
special arrangement of bar stiffeners in the columns with various
number, spacing and diameters of bar stiffeners were developed using the
non-linear finite element method. Effects of different variables such as
various number, spacing and diameters of the bar stiffeners, steel wall
thicknesses, concrete compressive strengths, and steel yield stresses on
the structural behaviour of the columns were investigated in this study.
It was demonstrated that these variables are effective on the behaviour
of the columns. The ultimate axial load capacity and ductility of the
columns are improved by the use of the bar stiffeners. The enhancement
of the number of bar stiffeners and/or steel wall thickness increases
the ultimate axial load capacity and ductility of the columns. As the
diameter of the bar stiffeners enhances the ultimate axial load capacity
increases. The reduction of spacing of the bar stiffeners increases the
ultimate axial load capacity and ductility. Also, the higher concrete
compressive strength results in larger ultimate axial load capacity.
Moreover, the increase of the steel yield stress enhances the ultimate
axial load capacity. Meanwhile, the failure modes of the columns were
dominated by concrete crushing about their mid-height, where the local
buckling of the steel wall was induced. The in-filled concrete prevented
the steel wall from the buckling inward. In addition, the ultimate axial
load capacities of the columns were predicted based on Eurocode 4 (2004)
and the equations recommended by Baig et al. (2006) and Bahrami et al.
(2011b), and also compared with those obtained values from the
non-linear analyses. These comparisons showed that Eurocode 4 (2004) and
equations of Baig et al. (2006) and Bahrami et al. (2011b),
respectively, predicted the ultimate axial load capacities with 4.4%
underestimation (a COV of 0.031), 3.8% overestimation (a COV of 0.034),
and 0.1% underestimation (a COV of 0.032). Therefore, the proposed
equation by Bahrami et al. (2011b) could predict the ultimate axial load
capacities of the columns with a very good accuracy.
doi: 10.3846/13923730.2013.768545
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Alireza BAHRAMI, Wan Hamidon WAN BADARUZZAMAN, Siti Aminah OSMAN
Department of Civil and Structural Engineering, Universiti
Kebangsaan Malaysia, Bangi, Selangor, Malaysia
Received 1 Aug. 2011; accepted 19 Oct. 2011
Corresponding author. Alireza Bahrami
E-mail:
[email protected]
Alireza BAHRAMI. PhD student in the Department of Civil and
Structural Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi,
Selangor, Malaysia since 2009 to date. BE in Civil Engineering from
Bushehr Islamic Azad University in 1998. MSc in Civil and Structural
Engineering with an excellent grade from Universiti Kebangsaan Malaysia
(UKM) in 2009. Fourteen years of industrial experience in Civil
Engineering. A lecturer at some universities in Iran. Research
interests: steel-concrete composite structural elements and their
behaviour and also engineering software for structural elements
analysis.
Wan Hamidon WAN BADARUZZAMAN. Professor in the Department of Civil
and Structural Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi,
Selangor, Malaysia. PhD in Structural Engineering from the University of
Wales, Cardiff, UK in 1994. Twenty-six years of vast teaching, training,
research, publication, administration, accreditation and consultancy
experiences. On secondment, was the Chief Executive Officer of the UKM
Perunding Kejuruteraan & Arkitek Sdn. Bhd., a university
professional consultancy company. Research interests: steel-concrete
composite structural elements, light weight, cold-formed composite
structures and their behaviour.
Siti Aminah OSMAN. Dr, Senior lecturer in the Department of Civil
and Structural Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi,
Selangor, Malaysia. A member of Board of Engineers Malaysia (BEM).
Graduated from Universiti Teknologi Malaysia in 1992 with BE (Hons), MSc
in Structural Engineering from University of Bradford, UK in 1995 and
PhD in Civil and Structural Engineering from Universiti Kebangsaan
Malaysia (UKM) in 2006. After undergraduate studies, started teaching as
a lecturer at Universiti Kebangsaan Malaysia (UKM). Research interests:
structural engineering, wind engineering and industrial building system
(IBS) construction.
Table 1. Features and obtained ultimate axial load capacities
([N.sub.u]) of the columns
No. Column label Steel Bar Steel wall,
wall, stiffener [f.sub.y]
t (mm) D (mm) (MPa)
1 C-2.5-10-234-50-4(50) 2.5 10 234.3
2 C-2.5-10-234-50-3(50) 2.5 10 234.3
3 C-2.5-10-234-50-2(50) 2.5 10 234.3
4 C-2.5-10-234-50-4(100) 2.5 10 234.3
5 C-2.5-10-234-50-3(100) 2.5 10 234.3
6 C-2.5-10-234-50-2(100) 2.5 10 234.3
7 C-2.5-10-234-50-4(150) 2.5 10 234.3
8 C-2.5-10-234-50-3(150) 2.5 10 234.3
9 C-2.5-10-234-50-2(150) 2.5 10 234.3
10 C-3-10-234-50-4(50) 3 10 234.3
11 C-2-10-234-50-4(50) 2 10 234.3
12 C-3-10-234-50-3(50) 3 10 234.3
13 C-2-10-234-50-3(50) 2 10 234.3
14 C-3-10-234-50-2(50) 3 10 234.3
15 C-2-10-234-50-2(50) 2 10 234.3
16 C-2.5-12-234-50-4(50) 2.5 12 234.3
17 C-2.5-8-234-50-4(50) 2.5 8 234.3
18 C-2.5-12-234-50-3(50) 2.5 12 234.3
19 C-2.5-8-234-50-3(50) 2.5 8 234.3
20 C-2.5-12-234-50-2(50) 2.5 12 234.3
21 C-2.5-8-234-50-2(50) 2.5 8 234.3
22 C-2.5-10-234-40-4(50) 2.5 10 234.3
23 C-2.5-10-234-30-4(50) 2.5 10 234.3
24 C-2.5-10-234-40-3(50) 2.5 10 234.3
25 C-2.5-10-234-30-3(50) 2.5 10 234.3
26 C-2.5-10-234-40-2(50) 2.5 10 234.3
27 C-2.5-10-234-30-2(50) 2.5 10 234.3
28 C-2.5-10-450-50-4(50) 2.5 10 450
29 C-2.5-10-350-50-4(50) 2.5 10 350
30 C-2.5-10-450-50-3(50) 2.5 10 450
31 C-2.5-10-350-50-3(50) 2.5 10 350
32 C-2.5-10-450-50-2(50) 2.5 10 450
33 C-2.5-10-350-50-2(50) 2.5 10 350
No. Column label Concrete, [N.sub.u]
[f.sub.c] (kN)
(MPa)
1 C-2.5-10-234-50-4(50) 50.1 3700
2 C-2.5-10-234-50-3(50) 50.1 3606
3 C-2.5-10-234-50-2(50) 50.1 3486
4 C-2.5-10-234-50-4(100) 50.1 3611
5 C-2.5-10-234-50-3(100) 50.1 3516
6 C-2.5-10-234-50-2(100) 50.1 3410
7 C-2.5-10-234-50-4(150) 50.1 3557
8 C-2.5-10-234-50-3(150) 50.1 3456
9 C-2.5-10-234-50-2(150) 50.1 3353
10 C-3-10-234-50-4(50) 50.1 3856
11 C-2-10-234-50-4(50) 50.1 3544
12 C-3-10-234-50-3(50) 50.1 3741
13 C-2-10-234-50-3(50) 50.1 3469
14 C-3-10-234-50-2(50) 50.1 3635
15 C-2-10-234-50-2(50) 50.1 3334
16 C-2.5-12-234-50-4(50) 50.1 3735
17 C-2.5-8-234-50-4(50) 50.1 3658
18 C-2.5-12-234-50-3(50) 50.1 3648
19 C-2.5-8-234-50-3(50) 50.1 3560
20 C-2.5-12-234-50-2(50) 50.1 3504
21 C-2.5-8-234-50-2(50) 50.1 3461
22 C-2.5-10-234-40-4(50) 40 3093
23 C-2.5-10-234-30-4(50) 30 2490
24 C-2.5-10-234-40-3(50) 40 3010
25 C-2.5-10-234-30-3(50) 30 2404
26 C-2.5-10-234-40-2(50) 40 2915
27 C-2.5-10-234-30-2(50) 30 2325
28 C-2.5-10-450-50-4(50) 50.1 4322
29 C-2.5-10-350-50-4(50) 50.1 4052
30 C-2.5-10-450-50-3(50) 50.1 4165
31 C-2.5-10-350-50-3(50) 50.1 3925
32 C-2.5-10-450-50-2(50) 50.1 4034
33 C-2.5-10-350-50-2(50) 50.1 3819
Table 2. Comparison of obtained ultimate axial load capacity
([N.sub.u]) with [N.sub.EC4], [N.sub.N] and [N.sub.B]
No. Column label [N.sub.u] [N.sub.EC4] [N.sub.EC4]/
(kN) (kN) [N.sub.u]
1 C-2.5-10-234-50-4(50) 3700 3409 0.921
2 C-2.5-10-234-50-3(50) 3606 3409 0.945
3 C-2.5-10-234-50-2(50) 3486 3409 0.978
4 C-2.5-10-234-50-4(100) 3611 3409 0.944
5 C-2.5-10-234-50-3(100) 3516 3409 0.970
6 C-2.5-10-234-50-2000) 3410 3409 1.000
7 C-2.5-10-234-50-4(150) 3557 3409 0.958
8 C-2.5-10-234-50-3(150) 3456 3409 0.986
9 C-2.5-10-234-50-2(150) 3353 3409 1.017
10 C-3-10-234-50-4(50) 3856 3499 0.907
11 C-2-10-234-50-4(50) 3544 3380 0.954
12 C-3-10-234-50-3(50) 3741 3499 0.935
13 C-2-10-234-50-3(50) 3469 3380 0.974
14 C-3-10-234-50-2(50) 3635 3499 0.963
15 C-2-10-234-50-2(50) 3334 3380 1.014
16 C-2.5-12-234-50-4(50) 3735 3409 0.913
17 C-2.5-8-234-50-4(50) 3658 3409 0.932
18 C-2.5-12-234-50-3(50) 3648 3409 0.934
19 C-2.5-8-234-50-3(50) 3560 3409 0.958
20 C-2.5-12-234-50-2(50) 3504 3409 0.973
21 C-2.5-8-234-50-2(50) 3461 3409 0.985
22 C-2.5-10-234-40-4(50) 3093 2860 0.925
23 C-2.5-10-234-30-4(50) 2490 2285 0.918
24 C-2.5-10-234-40-3(50) 3010 2860 0.950
25 C-2.5-10-234-30-3(50) 2404 2285 0.950
26 C-2.5-10-234-40-2(50) 2915 2860 0.981
27 C-2.5-10-234-30-2(50) 2325 2285 0.983
28 C-2.5-10-450-50-4(50) 4322 3957 0.916
29 C-2.5-10-350-50-4(50) 4052 3717 0.917
30 C-2.5-10-450-50-3(50) 4165 3957 0.950
31 C-2.5-10-350-50-3(50) 3925 3717 0.947
32 C-2.5-10-450-50-2(50) 4034 3957 0.981
33 C-2.5-10-350-50-2(50) 3819 3717 0.973
Mean 0.956
SD 0.029
COV 0.031
No. Column label [N.sub.N] [N.sub.N]/
(kN) [N.sub.u]
1 C-2.5-10-234-50-4(50) 3728 1.008
2 C-2.5-10-234-50-3(50) 3728 1.034
3 C-2.5-10-234-50-2(50) 3728 1.069
4 C-2.5-10-234-50-4(100) 3728 1.032
5 C-2.5-10-234-50-3(100) 3728 1.060
6 C-2.5-10-234-50-2000) 3728 1.093
7 C-2.5-10-234-50-4(150) 3728 1.048
8 C-2.5-10-234-50-3(150) 3728 1.079
9 C-2.5-10-234-50-2(150) 3728 1.112
10 C-3-10-234-50-4(50) 3782 0.981
11 C-2-10-234-50-4(50) 3672 1.036
12 C-3-10-234-50-3(50) 3782 1.011
13 C-2-10-234-50-3(50) 3672 1.059
14 C-3-10-234-50-2(50) 3782 1.040
15 C-2-10-234-50-2(50) 3672 1.102
16 C-2.5-12-234-50-4(50) 3728 0.998
17 C-2.5-8-234-50-4(50) 3728 1.019
18 C-2.5-12-234-50-3(50) 3728 1.022
19 C-2.5-8-234-50-3(50) 3728 1.047
20 C-2.5-12-234-50-2(50) 3728 1.064
21 C-2.5-8-234-50-2(50) 3728 1.077
22 C-2.5-10-234-40-4(50) 3090 0.999
23 C-2.5-10-234-30-4(50) 2458 0.987
24 C-2.5-10-234-40-3(50) 3090 1.026
25 C-2.5-10-234-30-3(50) 2458 1.022
26 C-2.5-10-234-40-2(50) 3090 1.060
27 C-2.5-10-234-30-2(50) 2458 1.057
28 C-2.5-10-450-50-4(50) 4245 0.982
29 C-2.5-10-350-50-4(50) 4005 0.988
30 C-2.5-10-450-50-3(50) 4245 1.019
31 C-2.5-10-350-50-3(50) 4005 1.020
32 C-2.5-10-450-50-2(50) 4245 1.052
33 C-2.5-10-350-50-2(50) 4005 1.049
Mean 1.038
SD 0.035
COV 0.034
No. Column label [N.sub.B] [N.sub.B]/
(kN) [N.sub.u]
1 C-2.5-10-234-50-4(50) 3584 0.969
2 C-2.5-10-234-50-3(50) 3584 0.994
3 C-2.5-10-234-50-2(50) 3584 1.028
4 C-2.5-10-234-50-4(100) 3584 0.993
5 C-2.5-10-234-50-3(100) 3584 1.019
6 C-2.5-10-234-50-2000) 3584 1.051
7 C-2.5-10-234-50-4(150) 3584 1.008
8 C-2.5-10-234-50-3(150) 3584 1.037
9 C-2.5-10-234-50-2(150) 3584 1.069
10 C-3-10-234-50-4(50) 3641 0.944
11 C-2-10-234-50-4(50) 3526 0.995
12 C-3-10-234-50-3(50) 3641 0.973
13 C-2-10-234-50-3(50) 3526 1.016
14 C-3-10-234-50-2(50) 3641 1.002
15 C-2-10-234-50-2(50) 3526 1.058
16 C-2.5-12-234-50-4(50) 3584 0.960
17 C-2.5-8-234-50-4(50) 3584 0.980
18 C-2.5-12-234-50-3(50) 3584 0.982
19 C-2.5-8-234-50-3(50) 3584 1.007
20 C-2.5-12-234-50-2(50) 3584 1.023
21 C-2.5-8-234-50-2(50) 3584 1.036
22 C-2.5-10-234-40-4(50) 2975 0.962
23 C-2.5-10-234-30-4(50) 2371 0.952
24 C-2.5-10-234-40-3(50) 2975 0.988
25 C-2.5-10-234-30-3(50) 2371 0.986
26 C-2.5-10-234-40-2(50) 2975 1.020
27 C-2.5-10-234-30-2(50) 2371 1.020
28 C-2.5-10-450-50-4(50) 4101 0.949
29 C-2.5-10-350-50-4(50) 3861 0.953
30 C-2.5-10-450-50-3(50) 4101 0.985
31 C-2.5-10-350-50-3(50) 3861 0.984
32 C-2.5-10-450-50-2(50) 4101 1.017
33 C-2.5-10-350-50-2(50) 3861 1.011
Mean 0.999
SD 0.032
COV 0.032
