A new calculation method for axial load capacity of separated

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A new calculation method for axial load capacity of separated
J. Cent. South Univ. (2013) 20: 1750−1758
DOI: 10.1007/s11771-013-1668-7
A new calculation method for axial load capacity of
separated concrete-filled steel tubes based on limit equilibrium theory
LIU Xia-ping(刘夏平), SUN Zhuo(孙卓), TANG Shu(唐述), HUANG Hai-yun(黄海云), LIU Ai-rong(刘爱荣)
College of Civil Engineering, Guangzhou University, Guangzhou 510006, China
© Central South University Press and Springer-Verlag Berlin Heidelberg 2013
Abstract: A new calculation method for axial load capacity of separated concrete-filled steel tubes based on limit equilibrium theory
was proposed, which took into account the decrease of confinement effect by steel tube and the non-uniform distribution of ultimate
stress in cored concrete. The accuracy of the analytical result is validated through running the numerical result by finite element
method (FEM) and experimental data as well. The influences of the key parameters on the load capacity of the concrete-filled steel
tube (CFST) was studied, including the separation ratio, concrete compressive strength, and steel strength. The results indicate that
the load capacity of the tube increases with concrete strength and steel strength under the separation ratio less than 4%, while
decreases with a higher separation ratio improved.
Key words: concrete-filled steel tube; limit equilibrium theory; axial load capacity
1 Introduction
The use of CFST structure has been widely
accepted in high-rise buildings, bridges and other
structural engineering [1−2]. Because of its advantages
in higher load capacity, smaller cross-section size, better
seismic performance, working status of the CFST can be
categorized in three types: radial extrusion, radial
criticality and radial separation [3−4]. In practice, due to
the unreasonable construction process, the core concrete
with imperfect quality, ambient temperature change, as
well as the shrinkage and creep of the concrete and other
reasons, they often lead to the arch rib separation of
section inside the CFST arch bridge. Even worse, there
exists separation phenomenon inside the entire arch rib,
which is more common failure mode in the bridge
structures [5−6]. The CFST separation not only results in
large deformation in the structure, but also seriously
affects the load capacity of the structure [7−9]. In last
decade, previous research studies have carried out
experimental testing on the mechanical properties of
compression member of the CFST with the separated
core concrete, including component failure mode,
deformation and load capacity and the influence of the
separation ratio, eccentricity, the loading mode and
slenderness ratio and other parameters [10−14]. The
numerical analysis implemented by commercial software
ANSYS is used to evaluate the ultimate strength of
compression members with the separated CFST [14−15].
However, those works focused on general mechanical
behavior without considering non-uniformity of the
constraints of the steel-tube to the concrete due to the
separation, and three dimensional stress constitutive
relations using equal lateral pressure by the concrete. The
structural performance of the separated CFST stress is
complicated, the confinement effect of the steel tube on
core concrete is of non-uniformity, and the concrete is in
three dimensional constraint conditions with non-equal
lateral pressure. Meanwhile, the parameters involved by
the load capacity is more, they interact with each other.
Although the actual performance can be achieved from
the experimental study, it is difficult to implement a
testing on such a large scale. The numerical method is
often used to simulate the stress process of the separated
CFST, but the constitutive relation of the structural
material is hard to define, which makes the modeling
work more difficult.
This problem can be considered by the limit
equilibrium theory by calculating the ultimate load
capacity. Without taking account of the loading history
and deformation process, the load value of the limit state
is calculated by the equilibrium conditions when the
structure is in the limit state.
Foundation item: Projects(51078093, 11272095) supported by the National Natural Science Foundation of China; Projects(2011B010300026,
2012B04032005) supported by Guangdong Science and Technology Project, China; Project(2011Y2-00006) supported by Guangzhou
City Science and Technology Research Project, China; Project(2012CXZD0028) supported by the Science and Technology Innovation
Projects of Department of Education of Guangdong Province, China
Received date: 2012−07−31; Accepted date: 2013−01−10
Corresponding author: LIU Xia-ping, Associate Professor; Tel: +86−13342885552; E-mail: [email protected]
J. Cent. South Univ. (2013) 20: 1750−1758
In Ref. [1], the limit equilibrium theory method has
been used for solving the ultimate load capacity of axial
compressive short column with the CFST. In this work,
the analytical solution of load capacity of the axial
compressive short column with the void CFST is derived
by analyzing the steel tube and the core coagulation
stress state under the axial compressive short column of
the CFST, with considering the non-uniformity of the
confinement effect and using the limit equilibrium
theory. This solution would provide a basis to accurately
estimate the main factors of the load capacity, establish
the simplified calculation method of load capacity and
obtain a way to check the numerical simulation results of
finite element.
2 Axial stress analysis
When the axial compressive member of ordinary
non-separated CFST was in the initial loading phase, the
lateral deformation coefficient of the concrete was less
than Poisson ratio coefficient of steel tube, the squeeze
did not occur between the concrete and steel tube, and
the steel tube and concrete jointly withstood the
longitudinal pressure. With the increase of the load, the
lateral expansion of the concrete exceeded the lateral
expansion of steel tube. As the concrete was restricted by
the steel tube, the concrete had a compressive strength
higher than that under uniaxial compression. If ignoring
steel radial stress, the steel tube was in the longitudinal
compressive-circumferential tensile biaxial stress state.
When the circumferential tensile stress increased, the
axial compressive stress was continuing to reduce with it,
and the longitudinal stress redistribution was produced
between the steel tube and concrete. When the
longitudinal stress sum withstood by both steel tube and
concrete reached the maximum, the CFST reached the
ultimate limit state. So, the steel tube changed from
mainly withstanding the longitudinal compressive stress
into mainly withstanding the circumferential tensile
stress, being in the longitudinal compressivecircumferential tensile biaxial stress state of the nonuniformity and subjected to the flat state yield criterion.
The existing experimental studies have shown that
[10, 12], when the axial compressive member of the
separated CFST was in the late stage of load and the
separation ratio was very small, the concrete at the
separation had been bound because the contact between
the steel tube and the concrete was in three dimensional
constraint state. However, if the separation ratio was
larger, the concrete at the separation was not in contact
with the steel tube, the confining force of steel tube to
the concrete was zero. As the concrete at the
non-separation was confined by the steel tube, there was
a confining force. The farther away from the separation,
1751
the greater the confining force, the core concrete being in
three dimensional stress state under non-equal lateral
pressure.
3 Basic assumption
The separated shape and scope of the separated
CFST members were considered according to the section
for the arched long-slit, using six basic assumptions, in
which there were three basic assumptions according to
the limit equilibrium theory: 1) The load on the member
was quasi-static monotonic loading; 2) The component
deformation prior to the loss of load capacity was very
small which could ignore the change in the geometry of
the static equilibrium method and consider the static
balance according to the component size before the
deformation; 3) As prior to component loss of load
capacity, the steel tube and concrete did not lose stability.
Based on the test results of Refs. [10, 12], the other
three basic assumptions were also added. 1) Similar to
the mechanical analysis of ordinary CFST, the steel tube
radial stress was ignored, the stress analytical model of
the steel tube was simplified as a longitudinal
compressive circumferential tensile biaxial stress state,
and the longitudinal stress of steel tube at one side of the
separation was σ12, circumferential stress was σ22, the
longitudinal stress of steel tube at the another side far
away from the separation was σ11, and the
circumferential stress was σ21, changing gradually in the
middle. In order to simplify the calculation, it was
assumed to change according to the linear law. 2) As the
concrete confinement effect was weakened by the steel
tube after the separation, the restriction of the steel tube
to the concrete was minimum at the separation. However,
at the other side edge away from the separation, the
restriction of the steel tube to the concrete was
maximum, changing gradually in the middle. It was
assumed that the longitudinal stress of core concrete with
the component destruction achieved the ultimate
compressive strength fc without the lateral pressure at the
separation and achieved the compressive strength of
three dimensional compressive concrete at the another
side edge away from the separation, changing according
to the linearity in the middle. 3) It was assumed that the
circumferential stress of core concrete with the
component destruction was 0 at the separation and was p
at the other side edge away from the separation,
changing according to the linearity in the middle.
Accordingly, the steel tube and core concrete stress
diagram is shown in Fig. 1.
4 Formula derivation of ultimate load apacity
According to the limit equilibrium theory, the
J. Cent. South Univ. (2013) 20: 1750−1758
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ultimate load capacity of the component member could
be directly calculated by equilibrium conditions in the
limit state. Figure 1 shows that solving the ultimate load
capacity had altogether seven unknowns, namely the
external load Nu, the longitudinal stress of concrete at the
non-separated side σc1, longitudinal stresses of the steel
tube σ11 and σ12, circumferential stresses of the steel tube
σ21 and σ22, and lateral pressure between steel tube and
concrete contact surface p. Based on basic assumptions
and mechanical analysis of Fig. 2, the mechanical
equations of the seven unknown quantities were
established in order to determine the analytical
expressions of the ultimate load capacity.
4.1 Longitudinal static equilibrium equation
According to the longitudinal static equilibrium
conditions of the component member, the ultimate load
capacity Ns of steel tube pluses the ultimate load capacity
Nc of core concrete considering the confinement effect
equaled the ultimate load capacity Nu of the steel tube,
being able to establish an equation:
Nu  Ns  Nc
(1)
According to the basic assumptions, the ultimate
load capacity of the core concrete was obtained as shown
in Fig. 2(a):
N c  2   c b dy
(2)
where b=rcsin α, dy=rcsin αd α, by the geometric relation,
the concrete stress is
 c  fc 
rc (1  cos  )  
( c1  f c )
2rc  
(3)
After substituting Eq. (3) into Eq. (2), we obtain:
π 

r (1  cos  )  
N c  2  f c  c
( c1  f c ) rc2 sin 2 d 
0
2rc  


f c rc2 ( π   0 
(  f c )rc3
1

sin 2 0 )  c1
2
2rc  
1
2
(π   0  sin 2 0  sin 3  0 ) 
2
3
 ( c1  f c )rc2
1
(π   0  sin 2 0 )
2rc  
2
(4)
where t is steel tube wall thickness; rc is core concrete
radius; δ is core concrete separation height; α0 is the half
value of central angle for the separated part.
Figure 2(b) shows that the ultimate load capacity of
steel tube is
Fig. 1 Simplified model of stress: (a) Three dimensional stress of steel tube; (b) Three dimensional stress of steel tube;
(c) Circumferential stress
Fig. 2 Calculation model: (a) Core concrete; (b) Steel tube
J. Cent. South Univ. (2013) 20: 1750−1758
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N s  ○t s ds
(5)
where ds=rsdα, rs is the steel tube radius. From geometric
relation, the steel tube stress is:
1  cos 
 s   11 
( 12   11 )
2
(6)
After substituting Eq. (6) into Eq. (5), we obtain:
π
1  cos 

N s  2trs   11 
( 12   11 ) d 
0 
2

trs π( 12   11 )
(7)
After substituting Eqs. (4) and (7) into Eq. (1), we
obtain:
N u  f c rc2 ( π   0 
(  f c )rc3
1
sin 2 0 )  c1

2
2rc  
 ( c1  f c )rc2
1
(π   0  sin 2 0 ) 
2rc  
2
trs π( 12   11 )
(8)
4.2 Longitudinal moment equilibrium equation
According to the longitudinal moment equilibrium
condition of component member, longitudinal moment
equilibrium equation is established as
Ms+Mc=0
(9)
where Mc and Ms are longitudinal moments for ultimate
load capacity of concrete and steel tube to the axis,
respectively.
Figure 2(a) shows that:
π 
M c  2   c brc cos dy  2  f c 
0 

rc (1  cos  )  
( c1  f c ) rc3 sin 2  cos d 
2rc  

(  f )r 4 
2
2
f c rc3 sin 3  0  c1 c c ( 0  sin 3  0 
3
2rc  
4 3
2 ( c1  f c )rc3 3
π 1
sin  0
 sin 4 0 ) 
4 16
3(2rc   )
(10)
Figure 2(b) shows that:
1
M s  ○t s rs cosds  trs2 π( 12   11 )
2
 22t   21t 
1
p (2rc   )
2
1
p (2rc   )(rc   )   22 trc   21trc
6
(11)
4.3 Circumferential static and moment equilibrium
equations
According to the circumferential static equilibrium
condition and moment equilibrium condition of the
(12)
(13)
4.4 Calculation formula of core concrete strength
The core concrete strength under the constraint of
steel tube is higher than the uniaxial compressive
strength, and its intensity is closely related with the
lateral pressure, increasing with the increase of lateral
pressure. According to the experimental data, it is
considered that the following linear empirical formula
could be used for the relation between three dimensional
compressive concrete strength σc1 and lateral pressure p :
 c1  f c  Kp
1
2
(π   0  sin 2 0  sin 3  0 ) 
2
3

component member, the equations can be defined as
(14)
where fc is the compressive strength of concrete without
lateral pressure, and K is the coefficient of lateral
pressure determined by the test, generally K is of a range
from 4 to 5.
As the separated core concrete belongs to the
unequal lateral pressure, Eq. (14) is still used taking into
account the unequal lateral pressure of concrete strength
difficult to determine. However, the value of the K
clearly has a relationship with the separation ratio and its
value should be determined by the test. YANG et al [12]
had completed a number of axial compressive tests of
short columns with the separated CFST. According to
their test results, the expression of the value K is
obtained by
K  59.28  3.76
(15)
where β is the separation rate, that is, the division of
separation area and core concrete area.
4.5 Steel tube yield condition
Under the ultimate load Nu, the steel tube is in the
longitudinal compressive-circumferential biaxial stress
yield state. According to the von Mises yield condition,
the tube yield condition equation is established as
2
2
fs2   21
  2111  11
(16)
where fs is steel tube yield strength.
4.6 Computing formula of ultimate load capacity
The expression for the ultimate load Nu of the
variable σ11 is obtained from Eqs. (1, 9, 12−14, 16). The
relational expression is established by the extremum
condition:
dN u
0
d 11
(17)
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From the above equation, we obtain:
2 Af s
 11 
(18)
3 A2  9B 2
where
A  Krc (a 2  a3 )  a1 ;
B  Krc (a 2  a3 ) ;
N u  Ac f c  As f s
a1  πrs2 (4rc   )(2rc   ) 2 ;
3
a 2  2rc3 (rs  2rc  2 ) sin 3  0  rc4 sin 4 0 ;
8
3 2
a3  rc rs (rc   ) sin 2 0  ( π   0 )(rc2  2rc rs  2rs ) .
2
The ultimate bearing capacities of the concrete,
steel tube and separated CFST are obtained respectively
by


N c  f c rc2 y1  (1 

rc
) y1 y 2 
2
y 2 sin 3  0
3
N s  πrs t ( 11   12 )
(19)
(20)
N u  Nc  Ns 
f c rc2 y1  (1 

rc
) y1 y 2 
2
y 2 sin 3  0 
3
πrs t ( 11   12 )
(21)
where
1
sin 2 0 ;
2
(  f c )rc3
;
y 2  c1
2rc  
y1  π   0 
 12   11  x1  x 2 x3  x 4 ;
x1 
x2 
4 f c rc3 sin 3  0
3tπrs2
2( c1  f c )rc4
(2rc   )tπrs2
;
;
2 sin 3  0 sin 4 0

;
4
3
16
4 ( c1  f c )rc3 sin 3  0
;
x4 
3(2rc   )tπrs2
x3 
0  π
wall thickness is much smaller than the steel tube radius
in the actual project, it could be approximately taken
rs=rc. If the separation ratio is smaller, sinα0=α0 and the
effect of high-order small quantity α0 is omitted, Eq. (21)
could be simplified as

where σc1 is the stress of concrete at one side edge away
from the separation:
12 Ktrc f s (3B  A)
 c1  f c 
(2rc   )(4rc   ) 3 A 2  9 B 2
4.7 Simplified calculating formula for ultimate load
capacity
Equation (21) for the ultimate load capacity of the
separated CFST derived from the limit equilibrium
method is more complicated. So, the meaningful
simplified expression to facilitate the application of
engineering practice should be found. As the steel tube
(22)
where As is cross-sectional area of steel tube; Ac is
cross-sectional area of the core concrete excluding the
separation;


3rc2 K (3rc  2 )(3B  A) 
2 A 
;
(2rc   ) 2 (4rc   ) 
3 A 2  9 B 2 
1
A  B  Ac (4rc   )(2rc   ) 2 ;
3
B  Ac Krc2 (3rc  2 ) ;
2
K  59.28  3.76 .
Equation (22) shows that the equation for the
ultimate load capacity of the separated CFST is similar to
the CFST. The effect of separation on the ultimate load
capacity materialized in parameters Ac and λ. Because
separation rate is a comprehensive index about
separation degree, the ultimate load capacity of the
separated CFST depended principally on separation rate,
material strength, and section size.
5 Verification of theoretical value
5.1 Comparison between theoretical calculated value
and experimental one
The test for the axial compressive ultimate load
capacity of two separated CFST specimens (specimens
No.8 and No.9) was carried out, the Q235 welded tube
was adopted for steel tube, the outside diameter was
168 mm, the specimen length was 500 mm and the C40
concrete was poured into the tube. In order to make the
steel pipe and concrete have the common uniform stress,
the specimen was welded all with 20 mm thick end plate
and steel tube at both ends. Steel tube separation was
formed by the padded steel plate. The steel plate was
extracted after casting the concrete for 4 h and the left
section was the arched separated long-slit.
The concrete mixed by the 42.5 ordinary portland
cement, gravel with particle size 0.5−2.0 cm, river sand
and water was used (m(cement):m(sand):m(gravel):
m(water)=1:1.37:2.54:0.45)). The concrete was poured
from the steel tube top, and the vibrating rod was
inserted to conduct the vibration compaction. The
thickness of the concrete layer filled every time was
25−35 cm. Last, the column top was trowelled with the
cement mortar.
The steel strength was given by the uniaxial tensile
test of the standard test strip cut down from the steel tube
J. Cent. South Univ. (2013) 20: 1750−1758
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and the yield strength was 320 MPa. The compressive
strength of the measured concrete cube was 40 MPa.
The specimen was loaded by the YE-500A
hydraulic pressure testing machine. The load was passed
through the knife hinges and 30 mm thick load board
located at both ends of the specimen. The graded loading
system was used for the test. The pressure indicating dial
pointer of the testing machine was used to keep the load
stable or the load of the starting rotation was used as the
ultimate load capacity of the separated CFST.
For the longitudinal strain measurement of the
specimen, two ways were adopted, one was that the
longitudinal adhesive strain gauge was adopted to test in
the middle of the specimen, and the other was that the
dial gauge was adopted to test the specimen top
deformation. The specimen was longitudinally divided
into four sections and three points, the dial gauge was
used to measure the lateral deflection of the specimen
and a pair of opposite dial gauges were used for each
measurement point. The eight strain gauges were
equidistantly pasted along the circumferential direction
in the middle section of the specimen, and the
bidirectional electric resistance strain gage perpendicular
to each other was used.
Figures 3 and 4 are respectively the load-deflection
curve of the specimen, as well as the central
cross-section load-maximum longitudinal strain diagram.
The load capacity tests for a number of axial
compressive short column specimens with the separated
CFST were completed in Ref. [12]. Its test model was
140 mm × 1.6 mm × 420 mm. The steel tube material
was A3 steel and the concrete was the C40. Table 1 lists
the experimental values for ultimate load capacity of
axial compressive test with the separated CFST in
Ref. [12] and this work, as well as the load capacity
values calculated respectively according to Eqs. (21)−
(22). The compressive strength without lateral pressure
of the concrete is calculated according to fc=0.67fcu (fcu is
the compressive strength of 15 cm cube specimen, namely
Fig. 3 Load versus deformation curves
Fig. 4 Load versus maximum longitudinal strain
the strength grade of concrete [1]. From Table 1, it could
be seen that the theoretical results is consistent with the
experimental ones in Eq. (21) or Eq. (22), the maximum
error being less than 4.5%.
5.2 Comparison between theoretical calculated values
and calculated ones of finite element
Large general-purpose finite element analysis
software ANSYS was used to carry out the modeling
Table 1 Comparison between calculated and test values
Specimen Separation Experimental
values, N u /kN
number
ratio/%
Eq. (21)
Eq. (22)
Calculated value, Nu/kN
Error/%
Calculated value, Nu/kN Error/%
1
0.08
1 193
1 159
2.8
1 163
2.5
2
0.14
1 160
1 155
0.4
1 160
0
3
0.30
1 123
1 140
1.5
1 140
1.5
4
0.55
1 100
1 119
1.7
1 120
1.8
5
1.17
1 080
1 069
1.0
1 070
0.9
6
1.94
993
1 011
1.8
1 000
0.7
7
3.28
887
927
4.5
911
2.7
8
0.68
2 050
2 005
2.2
2 030
1.0
9
0.68
1 959
2 005
2.3
2 030
3.6
Experimenter
Ref. [12]
This work
J. Cent. South Univ. (2013) 20: 1750−1758
1756
calculation of above CFST specimen. The Solid 65
element was used to simulate the core concrete; the Solid
45 element was used to simulate the steel tube and rigid
backing plate. The Solid 45 and Solid 65 elements are
both defined by eight nodes having three degrees of
freedom at each node. Solid 45 is used for the 3D
modeling of solid structures,and Solid 65 is used for the
3D modeling of solids with or without reinforcing bars
(rebar).
Three sections of an ideal elastic-plastic constitutive
model were used for the steel tube, and the
one-dimensional two-section expression of the
stress−strain relationship in Ref. [16] was used for the
core concrete constitutive model. Willam-Warnker
five-parameter model was used for Solid 65 concrete
element damage and cracking criteria. For the steel tube
element, the plasticity option-multi-linear kinematic
hardening model (MKIN) in the ANSYS was used to
simulate the stress−strain relationship of steel, applying
the von Mises yield criterion. In the finite element
analysis of the separated CFST, the non-linear contact
element was introduced to consider the interaction
between steel tube and concrete. The “target surface”
of 3D was simulated for Targe170 and the “contact
surface” was simulated for Contact173, taking the
friction coefficient of 0.6. Targe170 is used to represent
various 3D “target” surfaces for the associated contact
elements. The contact elements themselves overlay the
solid elements describing the boundary of a deformable
body and are potentially in contact with the target surface.
This target surface is discretized by a set of target
segment elements and is paired with its associated
contact surface via a shared real constant set. Contact173
is used to represent contact and sliding between 3D
“target” surfaces and a deformable surface, defined by
this element. The element is applicable to 3D structural
and coupled field contact analyses.
The calculation results are shown in Table 2. It
could be seen from Table 2 that the theoretical computed
results corresponded well with finite element computed
ones, with the maximum error less than 4.2%.
6 Parameter analysis
It could be seen from Eq. (22), the load capacity of
axial compressive short column with the separated CFST
is mainly affected by the separation ratio, concrete
strength and steel tube yield strength and other
parameters. The size of the component member was φ
140 mm × 1.6 mm × 420 mm. For its axial compressive
short column of the separated CFST, the theoretical
calculations and parametric analysis of the load capacity
were carried out. The strength of concrete was
respectively elected for the C40, C50, C60 and C70, and
the steel tube material for the Q235, Q345 and Q400, the
separation rate increasing from 0.55% to 3.28%.
6.1 Separation ratio
According to the theoretical calculation of load
capacity in Eq. (22), the load capacity-separation ratio
curve of axial compressive short column with the
separated CFST could be drawn, as shown in Fig. 5.
It could be seen from Fig. 5 that the load capacity
reduced in basic linear law with the increase of the
separation ratio. When the concrete was C40, steel tube
material was Q345 and separation ratio increased from
0.55% to 3.28%, the decreasing amplitude of load
capacity was the largest, reducing from 852 kN to
660 kN, and the load capacity reduced by 22.5%. The
linearly decreased rate was nearly 8.2% with the increase
of separation ratio. In addition, in the case of the same
concrete strength, the higher the steel tube strength, the
more obvious the load capacity of the component
member affected by the separation ratio.
6.2 Concrete strength
From the load capacity−concrete strength curve in
Eq. (22) and Fig. 6, it could be seen that when the
separation ratio and steel tube material remained
unchanged, the load capacity grew linearly with the
increase of concrete strength. When the compressive
strength of concrete increased from 26.8 MPa (C40) to
Table 2 Comparison between calculated and ANSYS values
Specimen
number
Separation height,
δ/mm
Separation
ratio/%
Calculation of load capacity,
Nu/kN
Load capacity by
finite element, N u /kN
Error/%
1
0.8
0.08
1 159
1 205
3.9
2
1.2
0.14
1 155
1 198
3.7
3
2.0
0.30
1 140
1 188
4.2
4
3.0
0.55
1 119
1 164
4.0
5
5.0
1.17
1 069
1 114
4.2
6
7.0
1.94
1 011
1 048
3.7
7
10.0
3.28
927
952
2.7
J. Cent. South Univ. (2013) 20: 1750−1758
1757
Fig. 5 Influence of separation ratio
Fig. 7 Influence of steel yielding strength
Fig. 6 Influence of concrete strength
44.5 MPa (C70), the separation ratio was 3.28% and the
steel tube material was the Q235 component member.
The increasing rate of load capacity was the largest,
increasing from 570 kN to 823 kN and the load capacity
increased by 44%. The linear increasing rate of load
capacity was approximately 2.5% with the increase of
concrete strength. The separation ratio was 0.55% and
the steel tube material was the Q400 component member.
The increasing rate of load capacity was the least,
increasing from 925 kN to 1 184 kN and the load
capacity increased by 28%. The linear increasing rate of
load capacity was approximately 1.6% with the increase
of concrete strength.
Under different parameters, the linear increasing
rate of load capacity with separated CFST was in the
range of about 1.6%−2.5% and the difference was not
obvious, that is to say, the steel tube material and
separation ratio made little impact on the load
capacity-concrete strength curve.
6.3 Yield strength of steel material
Figure 7 is the load capacity-steel yield strength
curve. The load capacity increases linearly with the
increase of the steel strength. When the steel yield
strength increases from 235 MPa to 400 MPa, the
separation ratio is 0.55%. The concrete is the C40
component member, and the increasing rate of carrying
capacity is the largest, increasing from 705 kN to 925 kN
and the load capacity increased by 31.2%. The separation
ratio is 3.28%, and the concrete is the C70 component
member. The increasing rate of load capacity is the least,
increasing from 822 kN to 956 kN and the load capacity
only increased by 16.3%. In addition, the increasing rate
of the load capacity decreased with the increase of steel
yield strength or the separation ratio or the concrete
strength, that is, the load capacity affected by the steel
yield strength gradually reduces with the increase of the
separation ratio or the concrete strength.
7 Conclusions
1) Based on the limit equilibrium theory, the
analytical solution for component load capacity of
compressive short column with the separated concrete is
derived, which consider that the characteristic of the
non-uniformity of the concrete is confined by the steel
tube, the characteristic of the confinement effect
weakened and the mechanical principle for the separation
CFST.
2) Compared with the experimental results and
numerical results by FEM, the reliability and validity of
the analytical solution for the load capacity are studied.
The results of strength capacity show that the error is
below 5%, which is acceptable to meet the needs of
research and engineering applications.
3) The parametric study on the influence of key
parameters shows that within less than 4% of separation
ratio, the load capacity decreases with the increase of
separation ratio and increases linearly with the increase
J. Cent. South Univ. (2013) 20: 1750−1758
1758
of concrete and steel strength. Without changing the
other conditions, the linear changing rate of the
conditions for its load capacity can reach 8.2% with the
change of the separation ratio. This shows that the
separation ratio has a significant effect on the load
capacity.
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(Edited by DENG Lü-xiang)

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