Analysis of the behavior of concrete-filled steel tubular columns with axial
loading under fire condition
Te-Wei Fan
Department of Civil Engineering and Engineering Informatics
Chung Hua University
707, Sec.2, WuFu Rd., Hsinchu, Taiwan 30012, R.O.C.
Tel.: +886-3-518-6711
Fax.: +886-3-5372188
E-mail:dfan@chu.edu.tw
Abstract
CFT, concrete-filled steel tubular columns, are often used as the main supporting columns for high-rise
buildings, whose fire resistance – how long they can actually support under load without collapsing in the high
temperature at the fire scene – has become a topic of academic concern in recent years; the past domestic
research about CFT focused more on its ultimate strength and mechanical behavior of connections. Many
discussions on the fire resistance of CFT are based on fire endurance time. The experiment method was more
used in the past studies engaged, which is usually expensive and time-consuming. Other research methods
include combining experimental data with appropriate theory to design or calculate the fire resistance, and these
methods tend to have a conservative assessment of the results. Therefore, some researches have been developing
finite element model to simulate and analyze the fire resistance of CFT and its component behavior. In this paper,
finite element analysis is used as the main analytical method to explore the fire resistance of CFT. Study found
that the fire endurance limitation time for CFT columns obtained by finite element analysis can achieve good
accuracy compared with the results obtained by the experiment, and in the mean time the mechanical behavior of
CFT columns in the temperature curve at the fire scene can be observed and recorded.
Keywords: concrete-filled tubular column, fire behavior, finite-element method.
resistance of steel structure and RC structure, the
1. Introduction
CFT is often used as the lower column of
more belong to exploring the structural behavior of
ultra-high-rise buildings for its good mechanical
the newly developed fire-resistant steel. Many
properties such as strength, stiffness and toughness, as
discussions on the fire resistance of CFT are based on
well as the advantage of easy construction and
the fire endurance time without fire-resist coating
cost-effectiveness, whose fire resistance – how long it
[13-15], and experiment method was more used in the
can actually support under load without collapsing in
past studies engaged. Among some experiments for
the high temperature of fire scene – has become a
CFT column or beam-column, there were situations
topic of academic concern in recent years[1-12]; the
such as sometimes that due to limited space for
past domestic studies on CFT focused more on its
experimental equipments or limited loading capacity,
ultimate
of
there are certain limitations in planning CFT
connections; and with regard to studies on the fire
experimental scale, or unable to load with maximum;
strength
and
mechanical
behavior
or that the plastic deformation is unable to be
is that concrete, after coated with steel pipe, is more
measured because the deformation is too large during
likely to be prevented from crushing at the scene of
experiment. Basically, it is usually expensive and
the fire. The important design criteria of CFT columns
time-consuming to use experimental method to
consider fire resistance performance in addition to
analyze the fire resistance of CFT, and sometimes its
bearing capacity and serviceability. If the CFT
results could hardly apply to different fire scene
columns in high-rise buildings are designed as having
conditions.
include
high load bearing capacity, it is more difficult for
combining the experimental data and theoretical
them to achieve the desired fire endurance time.
relevance to design or calculate the fire resistance, and
Therefore, with consideration of economic factors,
these methods tend to have a conservative assessment
how to get the maximal structural efficiency for CFT
of the results. Therefore, some researches have been
column,
developing finite element analysis model to simulate
material to reach ideal fire-resistant property should
the fire resistance of CFT and component behavior,
be the important topic to review design criteria in the
for examples, Ge and Usami [16] used MARC to
future. And FEM is actually a very appropriate tool to
analyze the ultimate strength of CFT short columns;
simulate the above-stated process and effect. In
Schneider [17] used ABAQUS to analyze the
addition, based on the reasons that it has been
behavior that CFT short column is undermined by
accumulated quite experience on analysis of CFT
axial compression. In aspect of fire-resistance, Zha
components using FEM, and the feasibility is quite
[18] used DYNA3D to analyze the fire resistant
high for FEM to analyze relevant data such as
properties of the circular CFT; Lie and Kodur [19-20]
temperature distribution, thermal strain, etc., this
used numerical analysis method to analyze the fire
study will use FEM as main analysis method to
resistance of, respectively, steel reinforced CFT and
explore the fire resistance property of CFT column.
Other
research
methods
and
simultaneously
use
fire-resistance
steel fiber filled CFT; mainland scholar Han Lin-Hai
[21] used numerical methods to analyze the fire
resistance capacity of CFT beam and column.
2. The theoretical base of thermal analysis
Theoretical basis for analysis include: thermal
The biggest advantage of using Finite Element
Method(FEM) to analyze mechanic behavior of CFT
convection,
coupling analysis of heat transfer
-mechanics, and material stress-strain relation.
is that it is not subject to space limitation, not subject
Transient heat transfer analysis should obtain
to load limitation, easy to carry out detailed
temperature history of the heat current during heating,
observation as well as quite rapid in parameter
the main model in the analysis should include a heat
changes; with FEM architected over theory and
source for fire scene, whose basis will be further
numerical methods, coupled with rapid development
described in the next section. In addition, it should be
of computer technology, the current development of
set up the temperature-dependent material properties
hardware and software have had the ability to carry
such as thermal conductivity, elastic modulus and
out
for
coefficient of thermal expansion, and convection
thermal-mechanical couple analysis of CFT fire
conditions between material surface and atmospheric
resistance.
environment.
more
accurate
simulation
than
past
The materials in consideration in this analysis
The reason that the fire-resistant property of CFT
include steel pipe, concrete and fire-resist coating.
column is better than that of conventional RC column
Since the temperature loading curve is changing
continually with time, the analysis belongs to transient
heat transfer analysis in which system temperature,
heat flow rate, thermal boundary condition and system
internal energy, all are time-varying, whose heat
conduction formula takes the coordinate system
suitable for square CFT, that is, x-y coordinate system,
and the matrix form of which is as follows:
   C e  e0 
Where [C] denotes material constant matrix, {e0}
denotes thermal strain. From the equation[K]{U}={F},
where [K] denotes stiffness matrix, {F} denotes the
vector of nodal load as a result of temperature changes,
the nodal displacement vector can be derived, which
is then substituted into the former two equations to

CT   K T  Q
 
obtain strains and their corresponding thermal stresses
for all the nodes.
Where [C] denotes specific heat and density
matrix, used to convey the increase of system internal
energy; [K] denotes thermal conductivity matrix,
including thermal conductivity coefficient, thermal
convection coefficient and shape function; {T}
denotes temperature vector of the node; {Q} denotes
heat flow rate vector of the node. In addition, because
this article also takes into account that the thermal
properties and boundary conditions vary with the time,
the thermal equilibrium formula becomes a non-linear
3. Finite element model
If the CFT columns in high-rise buildings are
designed as having high load bearing ratio, it is more
difficult for them to achieve the desired fire endurance.
Therefore, how to get the maximal structural
efficiency for CFT column, and simultaneously use
fire-resist coating to reach ideal fire-resistant property
should be the important topic to review design criteria
in the future. In addition, based on the reasons that it
thermal analysis matrix equation as follows:
has been accumulated quite experience on analysis of

CFT components using FEM, and the feasibility is
 
quite high for FEM to analyze relevant data such as
CTT   K TT  Q T
temperature distribution, thermal strain, etc., as well
With regard to the transient thermal-mechanical
as there is already an applicable temperature
analysis, the transient thermal-conductivity analytical
dependent stress-strain relation model, this study will
results are introduced and conducted non-linear
use nonlinear FEM software ANSYS as main
analysis in order to obtain thermal-stress results.
analytical tool to conduct analysis of the fire
According to FEM, the strain component can be
resistance properties of CFT columns with various
expressed
specifications, and aggregate analytical result. The
as
a
matrix
equation
with
nodal
displacement as follows:
finite element mesh and deformation analyzed in the
article are shown in Figure 1.
e  Bu
Where {e} denotes strain vector, [B] denotes
stress-strain matrix, {u} denotes the displacement
vector for the node.
In addition, thermal-stress matrix equation can be
derived from stress-strain relationship as follows:
f (T ,0.001) 
(50  0.004T )  {1  exp[( 30  0.03T ) 0.001]}  6.9
f [T ,  i   p  0.001)] 
(50  0.04T )  {1  exp[( 30  0.03T )  i   p  0.001]}  6.9
Due to the confinement effect, for the concrete
in CFT, it should be considered the stress-strain
relation of tri-axial force, and due to different shape of
cross section, basically the stress-strain relation in
Figure 1. Finite element model of concrete-filled
steel tubular column
high temperature is similar to that in ambient
temperature, except that some parameters vary with
3.1 Parameters and geometry conditions
the time such that temperature effect is introduced, as
With regard to the relevant parameters of the fire
follows, respectively:
resistance for CFT, according to Kodur’s research
[22],
the
parameters
impacting
fire
resistant
performance include: load size, dimension of cross
section, filled concrete type, effective length, concrete
strength, type of aggregate, thickness of steel tube. In
Stress-strain relation for square/rectangular CFT
when  c   0
 c   0 [ A( c /  0 )  B( c /  0 ) 2 ]
when  c   0
 c   0 ( c /  0 ) /[  ( c /  0  1)  ( c /  0 )]
this article, the main purpose is to use FEM to verify
where
the fire resistance of CFT, and then more extensive
 0  f ck (T )[1.194  0.25(1  T / 1000) 9.55 (13 / f ck ) 0.45 
parametric study can be conducted further in the
(0.07485 2  0.5789 )]
future. Listed in Table 1 are the experimental data the
f ck (T )  f ck /[1  1.986(T  20) 3.21  10 9 ]
paper uses to conduct verification, which refers to the
 0   cc (T )  0.95  [1400  800
experimental results published by Han Linhai in 2003.
The fire endurance time obtained and temperature
results calculated by finite element analysis in this
( f ck  20) 0.2
] 
20
(1.03  3.6  10  4 T  4.22  10 6 T 2 )
(  )
 cc (T )  (1.03  3.6  10  4 T  4.22  10 6 T 2 ) 
(1300  14.93 f ck )
(  )
paper will be listed as follows.
3.2 Stress-strain relation
3.3 Axial load and the temperature curve
Steel stress-strain relation under high temperature
The standard model of flame temperature curve is
may refer to the literature [23] which can be expressed
defined in all main specifications. In this paper, the
as follows:
temperature-ascending curve of ISO-834[24] will be
adopted as follows:
when    p
i 
f (T ,0.001)
i
0.001
when    p
T  T0  345 log10 (8t  1)
Where T0 is initial ambient temperature, t is the
f (T ,0.001)
i 
 p  f [T , ( i   p  0.001)]  f (T ,0.001)
0.001
fire duration (min).
The heating is more fierce at the initial heating
stage(0~25 min, ambient temperature~80℃) in which
where
 p  4  10 f y
6
the time step should be set shorter to get more
accurate results; the subsequent stages of the
conductivity coefficient (unit W/m ℃ ), thermal
temperature curve is relatively flat, in which the time
expansion coefficient (unit m/m℃), specific heat, and
step can be set for a longer period of time to increase
density.
efficiency. Among which ISO-834 heating curve is
4. Results
shown as Figure 2.
In this paper, the analysis contains two parts: the
ISO-834升溫曲線
temperature(C)
ISO-834 Temperature curve
first, it will be based on the experimental specimen
1200
1000
800
and geometry conditions and experimental results in
the literature to verify the accuracy of analytical
model. Secondly, observe the mechanical behavior of
600
400
200
0
CFT columns in the fire scene temperature curve, and
simultaneously
0
100
200
300
time(min)
select
the
parameters’
variation
condition to analyze, and not only show FEA
application capability on CFT column’s fire resistance,
but also the parameter discussion of the fire
resistance.
Figure 2. ISO-834 heating curve
4.1 Finite element model and verification
3.4 Thermal properties
The heat conductivity coefficient of different steel
varies with its carbon content, thus it is different for
different steel, and however as far as structure-use
steel as concerned, such impact can be neglected.
There are three factors impacting on concrete heat
conductivity, specific heat and density, including
aggregate type, water content and grading. Among
which the most important factor affecting heat
conductivity coefficient is water content, whose
reason is that the water of concrete will evaporate
when
temperature
increases,
therefore
after
temperature is greater than 100℃, the impact of water
In this paper, in order to verify the foregoing
analysis programs and model accuracy, the results of
analysis and verification carried out are as follows:
Figure 3 is the axial compression-strain relation
from FEA results for rectangular CFT, which also
includes the experiment results of the related literature,
as well as the result from FEA for the material under
high temperature. In the figure, under ambient
temperature, the maximum compressive strength of
the column, obtained by FEA, is 2351.28kN, and
compared with the experiment data of 2424kN, the
error is 3%; only the strain incurred is still different –
the maximum compressive strength in the experiment
content on heat conductivity coefficient is smaller and
smaller, and because the temperature reaches hundred
degree ℃
within very short time in previous
temperature curve of fire scene, the impact of water
content on heat conductivity coefficient can be
neglected in this analysis. In addition, the impact of
the above-stated three factors on specific heat and
density is not too great. This study assembled thermal
properties of, respectively, steel, concrete, fire coating
at
various
temperatures,
including:
thermal
is about to occur at the strain of 0.4%, whereas it is
about the strain of 0.6% for FEA. In addition, under
high temperature, the maximum compressive strength
obtained by FEA is 1696.8kN, reduced about 27.8%
compared with the ambient temperature, which occurs
at the strain of 0.4%, then the strength of CFT column
decreased dramatically and then increased slowly due
to steel plate buckling. The deformation of steel plate
buckling is shown as Figure 5.
Axial Load(kN)
3000
Nexp
2500
N,FEM
2000
N,FEM,
TEMP
experimental data for round CFT
Table 1. Verification of axial compression strength
with the experimental data for CFT column FEA
B/t,
D/t
1500
Circular
50.4
CFT
Rectang
101.5
CFT
1000
500
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
σsy
'
(Mpa) f c ( MPa )
Nexp
(kN)
NFEM
(kN)
Error(%)
308
25.4
941
918
2.4
279
25.4
2,382
2,358
1.0
3.5
Axial Strain(%)
The results showed that it can be indeed up to a
Figure 3. Comparison of FEM result and
experimental data for rectangular CFT
satisfactory extent if the aforementioned ANSYS
Figure 4 is the axial load-axial strain relation from
FEA results for circular CFT, which also include the
model and material properties are set to analyze the
strength of CFT column.
experiment result from the literature, and material
FEA result under high temperature. In the figure,
under room temperature, the maximum compressive
strength of the column obtained by FEA is 3244.2kN,
with the error of 1% compared with the experiment
data of 3277kN. Only the strain incurred is still
different: the maximum compressive strength in
experiment is about to occur at the strain of 0.4%,
whereas it is about to occur at the strain of 0.6% for
FEA. In addition, the maximum compressive strength
obtained by FEA under high temperature is 2556.1kN,
which is reduced about 21.2% compared with that
Figure 5. Deformation of steel plate buckling of FEM
of CFT under pressure
under ambient temperature, but the strength occurs at
From verification of the aforementioned analysis
the strain of 3.0%. However, when the strain is
result, discussion is as follows: First, the fire
between 0.4%~0.5%, the strength of CFT column
endurance time of experiment and that obtained by
ever decreased dramatically then increased slowly due
FEA are basically in line, but the result from FEA
to steel plate buckling, therefore if the maximum
tends to be conservative, whose reason might lie in
compressive strength prior to buckling, that is
that the thermal transfer efficiency in FEA is higher
2293.9kN, is considered, the reduction of compressive
than that in practice. Second, the analysis result is
strength caused by high temperature is 29%. The
greatly subjected to material model, so it is worthy of
analysis result is shown as Table 1.
further discussion for the analytical difference which
might be caused by the stress-strain relation under
3500
Axial Load(kN)
3000
different temperature for steel tube and concrete.
2500
Third, FEA can observe the mechanical behavior
2000
Nexp
1500
caused by different thermal deformation between steel
N,FEM
1000
N,FEM,
TEMP
500
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Axial Strain(%)
Figure 4. Comparison of FEM analysis result and
tube and concrete when CFT column is affected by
the temperature, such as the contact condition
between steel tube and concrete during temperature
ascending, and the change of behavior under axial
loading caused by different axial deformation for steel
the length of the column gradually reduces over
tube and concrete during temperature ascending,
change of time and temperature. The final state is
which of this topic will be discussed in the next
such that the column reduces rapidly due to failure of
section.
concrete load, at this time it can be obtained the fire
5.2 The mechanical behavior and the effect of steel
plate thickness in the fire temperature curve
It can be observed the following situation by time
endurance time of the CFT column and its relevant
data, and at this stage the numerical analysis often has
issue of being difficult to converge.
history of temperature distribution during analysis and
In addition, in order to assess the impact of the
by the history of the reaction force for material:
thickness of steel tube on the fire resistance of CFT
during
the
column, this paper takes specimen SP-2 as an example,
temperature is first conducted to steel tube; therefore
changing its thickness in order to measure the analysis
steel tube produces earlier thermal expansion of axial
results at different thickness of steel tube. The
and lateral than concrete. In addition, in Figure 6 -
supposed thicknesses of steel tube are 6.2mm, 7.7mm
reaction force-time relation, it can be seen that the
and 9.5mm, among which 7.7mm is the original
axial reaction on steel tube is gradually increasing
thickness of steel tube of specimen SP-2. The analysis
during this stage, which causes that the axial thermal
result is shown as Figure 7. The figure shows the main
stress produced in column due to axial constraint of
effect of larger thickness of steel tube under the same
both ends of column is mainly bore by steel tube.
temperature ascending condition, including: 1. Large
During the first stage, except that the axial load by
increment of axial deformation at the
steel tube gradually increases over the temperature
temperature ascending, 2. Shorter fire endurance time.
and time, its stiffness of material decreases with
It can be seen from the Figure that , in relation to the
temperature increase, finally steel plate local buckling
change rate of thickness of steel tube, increment of
occurs, which causes that the axial loading begins to
axial deformation and fire endurance time in the
transfer to core concrete. Therefore the axial loading
analysis result are not very significant, whose reason
bore by core concrete begins to reverse and increase,
should lie in that steel has higher heat conduction
and the axial load for steel tube also begins to reverse
efficiency, and after the temperature is transferred to
and decrease, in the mean time, because the stiffness
concrete, the heat conduction rate reduces, therefore
of the two material reduces due to temperature effect,
concrete has a role of heat sink during heat conduction,
therefore it is observed that the axial length of the
therefore under circumstance that the size of core
column as a whole is no longer increasing over the
concrete does not change, the thickness of steel tube
temperature and instead tends to reverse and decrease.
does not have significant effect on fire resistance.
the
initial
temperature
ascending,
initial
Third, after local buckling occurred in steel tube, the
axial load by the column is continuously transferred to
concrete, and afterwards, the main task of steel tube
should confine core concrete, during which the
mechanical behavior of member is mainly subject to
soften material due to high temperature because steel
tube and concrete both reach high temperature status.
This phenomenon can be observed that although the
axial load keeps fixed value during analysis process,
Figure 6. The variation of axial reaction force over
time for steel tube and concrete
With regard to parametric analysis of fire resistance,
this paper first takes thickness of steel tube as control
Axial deformation(mm)
10
t=9.5
t=7.7
t=6.2
5
0
parameter, compares the analysis result and finds that
thickness of steel tube does not have significant
impact on fire endurance time, and in the future the
numerical analysis program built according to the
-5
paper can conduct more extensive parameter analysis,
-10
including the impact and degree of impact of
-15
cross-section size of the CFT column, thickness of fire
coating, the centrifugal axial compression, etc., on fire
-20
0
50
100
150
endurance time, all of which can be used as discussion
Time(min)
criteria for current design specifications.
Figure 7. Impact of thickness of steel tube on
fire-resistance of CFT column
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6. Conclusion
modeling of the standard fire behavior of loaded
In practice, the experiment about fire-resistance of
construction
component
is
expensive
and
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fire
temperature
variation
of
design
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