-
FIRE RESISTANCE OF CONCRETE FILLED SQUARE STEEL TUBE COLUMNS
SUBJECTED TO ECCENTRIC AXIAL LOAD
Chung, Kyung-Soo1, Park, Su-Hee2, Choi, Sung-Mo3
1 Structural Engineering Research Center, Tokyo Institute of
Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan,
E-mail: [email protected]
2, 3Department of Architectural Engineering, University of
Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul, 130-743, Korea,
E-mail: [email protected], [email protected]
Abstract. The fire resistance of concrete filled square steel
tube columns (CFT columns) without fire protection under constant
axial load has been examined. The purpose of this study is to
investigate the fire resistance of CFT columns subjected to
combined loads. In the first step, this paper presents a nonlinear
thermal stress analysis method for predicting the mechanical
behaviour and fire resistance of these columns under eccentric
axial load (axial load and flexure moment). This method is based on
the stress-strain characteristics of materials at high temperatures
and the mechanics of column deflection curves. From the results of
the developed computational technique, it was demonstrated that as
the yield stress and rigidity of the steel tube decreased rapidly
for about 30 minutes, the decrease of flexure moment capacity
became much smaller than that of the axial load capacity. In
addition, as the eccentricity increased, the fire resistance time
drastically decreased. However, the time of maximum expansion under
eccentric axial load did not depend on the eccentricity of the
load.
Abstract: Fire Resistance, Concrete-Filled Steel Tube Column,
Eccentric Compression Loads
1. Introduction
Concrete-filled square steel tube (CFT) columns provide improved
strength and strain characteristics because of the interactions
between steel tube and concrete. The columns also can obtain a high
fire resistance without fire protection due to the heat storage of
the concrete filling inside the steel tube.
Because column size can be reduced by the no fire protection,
materials can be simplified and the number of works can be reduced.
For these reasons, various experiments and numerical analyses on
the fire resistance of CFT columns have been conducted (e.g. Kodur
and Lie 1996; Poh and Bennetts 1995; Saito et al. 2004; Yin et al.
2006; Zha 2003). However, there have not been enough studies about
beam-column subjected to combined loads consisting of axial loads
and moments, which would demonstrate the behavior of actual
structures in fire (Han 2001; Ichinohe et al. 2001; Kimura et al.
1990).
The purpose of this study is to investigatethe fire resistance
of CFT columns subjected to combined loads consisting of axial
loads and moments. Axial load-moment correlations, moment-strain
relations and axial strain behaviors in fire were demonstrated by
numerical analysis. Consequently, the mechanical behavior and fire
resistance of these columns subjected to both a constant axial load
and a constant moment due to eccentric axial load were
evaluated.
2. Numerical Analysis Method
2.1 Objectives According to the fire resistance experiment
to
perform for CFT columns under concentric axial loads
(Kim et al. 2005), steel tube and concrete were shown to have
rigidities of 363Mpa and 27.5Mpa, respectively. The length, width
and thickness of concrete-filled steel tubes were 3000mm, 350mm and
9mm, respectively.
2.2 Construction of cross section In order to compute the
temperature, strain and stress
of concrete-filled steel tubes, the cross sections of the tubes
were constructed, as shown in Figure 1.
Fig 1. Arrangement of elements
2.3 Thermal stress analysis In order to predict the temperature
of the elements in
two dimensions, the relation between temperature changes in tiny
elements and the amount of heat inflow is given as follows.
2 2
2 2 ,T T T Q
a at x y c c
= + + = (1)
Here, a = Thermal diffusivity
c = Specific heat
= Density
X-AXIS
Y-AXIS
Element of steel
Element of concrete
o
-
= Thermal conductivity
Based on the formula, finite calculus was used for the
temperature of the cross section. In other words, formula (2) was
derived from formula (1) using the Crank-Nicolson method.
1, ,
1 1 1 1 1 11, , 1, , 1 , , 1
2 2
1, , 1, , 1 , , 12 2
2 22
2 2
k ki j i j
k k k k k ki j i j i j i j i j i j
k k k k k ki j i j i j i j i j i j
T Tt
T T T T T Tax y
T T T T T T Qx y c
+
+ + + + + ++ +
+ +
+ += + + ++ + +
(2)
In order to predict the temperature of each element, formula (3)
was obtained by modifiying formula (2).
( ) [ ( )( )
( ) ]
1,
1 11, 1, 1, 1,
1 1, 1 , 1 , 1 , 1
,
12 1
2 1 2
ki j
k k k kx i j i j i j i j
x y
k k k ky i j i j i j i j
kx y i j q
T
c T T T Tc c
c T T T T
c c T c Q
+
+ ++ +
+ ++ +
= + + ++ ++ + + ++ +
(3)
Here, Cx 2
a t
x
= , Cy
2a t
y=
, Cq tc =
The amount of heat inflow acting as a boundary condition is
given as follows.
( ),s fQ l q T T= (4)
Here,
l = Distance between element i & element j q = Rate of heat
inflow per unit area Ts = Temperature of steel tube surface Tf =
Furnace temperature
Assuming thermal convection and thermal radiation, the rate of
heat inflow was obtained as follows.
( ) ( )4 4f s f sq A T T V = + (5a)
11 1 1
f s
=+
(5b)
Here,
A = Thermal convection coefficient (23W/m2K) V = Radiation angle
coefficient (1.0) = Stefan-Boltzman constant (5.67 10-8W/m2K4) f =
Thermal radiation rate of furnace (0.9) f = Absolute temperature of
furnace s = Thermal radiation rate of steel tube (0.8) s = Absolute
temperature of steel tube surface
With respect to the temperature rise of the column section in
fire, a standard fire resistance curve based on KSF 2257 was
constructed, as shown in figure 2.
0
300
600
900
1200
0 30 60 90 120 150
KSF 2257ISO 834ASTM E119JIS A 1304
ISO 834
Time (min)
Temperature (oC)
Figure 2. Standard fire resistance curve
Thermal characteristic formula of EUROCODE (Eurocode 4, 2003)
was employed to obtain the thermal characteristics of the steel
tube and concrete. Figure 3 shows the specific heats, thermal
conductivities and densities of the steel tube and concrete.
Steel tube Concrete (a) Specific heat
Steel tube Concrete (b) Thermal conductivity
Steel tube Concrete (c) Density
Figure 3. Thermal characteristics of steel tube &
concrete
0
500
1000
1500
2000
0 200 400 600 800 1000 1200
TEMP.()
Specific heat (J/kgK)
0
500
1000
1500
2000
0 200 400 600 800 1000 1200
TEMP.()
Specific heat
(J/kgK)
0
20
40
60
80
0 200 400 600 800 1000 1200
TEMP.(
)
Thermal Conductivity
(W/mK)
0
0.5
1
1.5
2
2.5
0 200 400 600 800 1000 1200
TEMP.()
Thermal Conductivity
(W/mK)
0
2500
5000
7500
10000
0 200 400 600 800 1000 1200
TEMP.(
)
Density of material
(kg/m3)
0
600
1200
1800
2400
3000
0 200 400 600 800 1000 1200
TEMP.(
)
Density
(kg/m3)
-
2.4 Stress analysis method In order to predict the fire
resistance of a concrete-
filled steel tube subjected to an eccentric load, 3 numerical
analyses were conducted based on the surface temperature obtained
from the results of thermal stress analysis as follows.
2.4.1 Correlation between axial load & moment Based on the
ultimate rigidities of the steel tube and
concrete against temperature, the correlation between axial load
and moment was computed. For this, the ultimate rigidities of the
materials against temperature provided by EUROCODE (Eurocode 4,
2003) were used, as shown in figure 4. The rigidities of the steel
tube and concrete were 363MPa and 27.5MPa, respectively. And, the
correlation between axial load and moment is as follows.
,
( , ) ( , )n
i jN F i j dA i j= (6)
( ),
( , ) ( , ) ,n
i jM F i j dA i j x i j= (7)
Here,
F(i,j) = Ultimate rigidity of element x(i,j) = Distance between
the center of cross
section and that of each element dA(i,j) = Size of cross
sectional area of element
Figure 4. Ultimate rigidity of steel tube and concrete against
the temperature
2.4.2 Moment-Curvature relation
In the relation between moment and curvature, it was assumed
that the plane status would be maintained, as in the case of normal
temperature. Based on the ever-changing stress-strain relation
along with temperature increase, the analysis under constant axial
load was computed at intervals of 1 minute (Figure 5). Following
formula demonstrates the degree of strain for the steel tube and
concrete.
( ) ( ),th T T x = + + (8)
Here,
= Total degree of strain = Stress
T = Temperature th
= Thermal expansion degree of strain
= Degree of strain corresponding to stress against
temperature
= Curvature X = Distance between the center of cross section and
that of
each element Local buckling at steel tube and fracture at
concrete were
ignored. Steps for analysis are as follows.
a) Renew surface temperature according to time. b) Compute
thermal expansion degrees of strain
for steel tube and concrete. c) Input axial load and curvature.
d) Based on the condition for force equilibrium,
condition for appropriateness and the relation between stress
& degree of strain against temperature on the assumption of
plane status, obtain the moment and degree of strain at the center
of cross section.
e) Increase curvature, return to step d) and repeat until the
curvature for computing the moment is obtained.
Figure 5. Analysis model and analysis condition
(a) Steel tube (b) Concrete
Figure 6. Stress-Strain relations at steel tube and concrete
against the temperature
Figure 7. Thermal expansion coefficients for steel tube and
concrete
2.4.3 Axial strain behavior along with time passage Unlike the
case in which the CFT column is under
concentric axial force, the computed axial strain of the CFT
column subjected to eccentric axial load in the event
0
100
200
300
400
500
0 200 400 600 800 1000 1200
TEMP.()
Fy (MPa)
0
10
20
30
40
50
0 200 400 600 800 1000 1200
TEMP.(
)
Fc (MPa)
0
5
10
15
20
25
30
35
0 0.005 0.01 0.015 0.02 0.025 0.03
20 100200
300400
500
600
700
800
(MPa)
0
100
200
300
400
500
0 0.005 0.01 0.015 0.02 0.025 0.03
20,100
200
300
500
600
700800
(MPa)
400
0.E+00
5.E-06
1.E-05
2.E-05
2.E-05
3.E-05
0 200 400 600 800 1000 1200
Steel tubeConcrete
TEMP. ()
s (1/)
-
of a fire requires that flexure strain caused by a moment be
taken into consideration. For an axial strain under an eccentric
axial load, the central axial force and moment were computed and
accumulated. Since each material under an eccentric axial load
presents a constant moment, flexure strain was obtained from the
following formula on the assumption that it would be parabolic when
boundary condition is taken into consideration.
2 2
_
8,
3 8h
v h hl
l = = (9)
Here, l= Length of material
Finally, axial strain was obtained as follows with the degree of
axial strain due to the axial force taken into consideration at the
center of a materials cross section.
_v v h c l = + (10)
Here, c= Degree of axial strain at the center of materials cross
section
Figure 8. Analysis condition
3. Comparison between the Findings of Thermal Stress Analysis
and Experiment
To prove the thermal stress analysis method, the results from
this method were compared with the result of a previously conducted
experiment (Kim et al. 2005). As shown in figure 9, the findings of
the thermal stress analysis and the experiment were identical.
(a) 300x9 (b) 350x9 Figure 9. Comparison between the findings of
analysis and
experiment
4. Review of Stress Analysis Result
4.1 Relation between axial load & moment
Figure 10 shows axial load-moment correlation curves with the
evolution of fire. At 30 minutes after ignition, the temperature of
steel tube rose to over 600 degrees and the ultimate rigidity of
the tube decreased by approximately 50% (Figure 9, 6 & 4).
Accordingly, the axial load capacity and moment strength decreased.
Because the concrete temperature did not rise very much after that
point in time, axial load capacity and moment strength did not
decrease severely, as they did in the 30 minute period from
ignition.
Figure 10. Correlation between axial load & moment with
time
Non-dimensional interpretation of the maximum axial load and
moment to the axial load and the moment at normal temperature is
shown in figure 11.
Figure 11. Non-dimensional interpretation of axial load and
moment against time passage
As shown in the figure, the longer the distance from the center,
the greater the strength decrease caused by temperature rise.
Therefore, moment decrease was more severe than axial load decrease
with time after ignition.
4.2 Moment-Curvature relation
Figure 12 shows the relation between moment and curvature with
time. Curvature up to 1.2X10-4(1/mm) was included in the analysis.
And, 0.2 of the strength of CFT column was used as the axial load
ratio. At normal temperature, the influence of the steel tube was
dominating and the increase of the curvature did not decrease the
strength significantly. After 30 minutes from ignition, the steel
tube temperature rose rapidly and the rigidity of the steel tube
decreased. Consequently, the influence of concrete became
dominating and the increase
( )_ 2
4 hh y y l yl
=
0
300
600
900
1200
0 30 60 90 120 150
Prediction EXP.-SAL2 EXP.-SAH1
Time (min)
Temperature (oC)
Centre
D/4
Surface
0
300
600
900
1200
0 30 60 90 120 150Prediction EXP.-SBL1 EXP.-SBL2
EXP.-SBH1 EXP.-SBH2
Time (min)
Temperature (oC)
Centre
D/4
Surface
-5000
-2500
0
2500
5000
7500
10000
0 200 400 600 800 1000
N (kN)
M (kN-m)
0 min
30 min
-1000
0
1000
2000
3000
4000
0 50 100 150 200 250
N (kN)
M (kN-m)
30 min
60 min
120 min180 min
0.01
0.1
10 30 60 90 120 150 180 210
LOADMOMENT
N/N_0, M/M_0
Time(min)
-5000
-2500
0
2500
5000
7500
10000
0 200 400 600 800 1000
N (kN)
M (kN-m)
0 min
30 min
-1000
0
1000
2000
3000
4000
0 50 100 150 200 250
N (kN)
M (kN-m)
30 min
60 min
120 min180 min
-
of the curvature accompanied the increase of the moment. When
the curvature increased to a certain limit, strength of the steel
tube decreased, and the initial stiffness and ultimate moment
decreased with after ignition. Temperature was not constant at the
cross sectional area. Because of the relation between stress and
degree of strain, the ultimate moment was conservative in
comparison with the moment computed from the correlation curve
between the axial force and moment.
Figure 12. Relation between moment and curvature against time
passage
4.3 Axial strain behavior against time
Figure 13 shows the comparison of concrete-filled steel tube
columns (width of cross section 1/10 (e=35mm), 1/20 (e=17.5mm)
subjected to eccentric axial load with those subjected to
concentric axial force.
Figure 13. Axial strain behavior under concentric axial force
and eccentric axial load
The time it took the concrete-filled steel tube columns
subjected to eccentric axial load to reach maximum expansion point
did not differ greatly with that subjected to concentric axial
force. However, the time it took them to present axial strain of
more than 1/100 of the material length was much shorter than that
subjected to concentric axial force when eccentric force was
greater. In other words, the time it took the columns (1/10)
subjected to eccentric axial load to reach failure was
approximately half of that of the columns subjected to concentric
axial force. And, the section where the axial strain behavior
stopped was shorter under the eccentric axial load than under the
concentric axial force.
5. Conclusion
This study was conducted to investigate the fire resistance of
concrete-filled steel tube columns subjected to combined loads
consisting of an axial force and moment. The mechanical behavior
and fire resistance of these columns subjected to constant axial
load and constant moment due to an eccentric axial load were
evaluated based on numerical analyses. Consequently, a correlation
between axial load and moment, a relation between moment and
strain, and the axial strain behavior were demonstrated. The
findings are as follows
1) With regard to the correlation between axial force and
moment, 30 minutes after ignition, the temperature of the steel
tube rose to over 600 degrees, and its strength decreased, so the
ultimate moment decreased more than the ultimate axial force. Then,
the temperature of concrete did not increase greatly, and the
strength decreased less than it did during the 30 minute period
after ignition.
2) With regard to the relation between moment and curvature,
moment was influenced by the extent of strength that was maintained
in the part far from the center. Accordingly, at normal temperature
where the influence of steel tube was dominant, the strength
decrease due to the increase of the curvature was not observed.
However, after the ignition of fire, temperature-rise decreased the
rigidity of the steel tube. Due to the influence of concrete, whose
temperature was less vulnerable to fire, the strength decreased
after the curvature reached a certain limit. And, compared with the
correlation between axial force and moment, the relation between
ultimate moments against axial force was found to be conservative.
This may be because of the difference in the period of time taken
to reach the ultimate stress in the relation between stress and
degree of strain influenced by the temperature difference of the
cross sectional area.
3) With regards to how long it took for the steel tube to reach
the maximum expansion point, there was no significant difference
between the columns subjected to the eccentric axial load and those
subjected to the concentric axial force. However, the greater the
eccentric force imposed, the much shorter time it took the column
to present the axial strain of 1/100.
This study was based on numerical analysis to evaluate the fire
resistance of concrete-filled steel tube columns subjected to an
eccentric axial load. We strongly urge that the numerical analysis
method be confirmed by experiments.
Acknowledgement
This research was supported by a grant(06 Construction
Consequence D07) from Construction Technology Innovation Program
funded by Ministry of Construction & Transportation of Korean
government.
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0
200
400
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800
0 0.5 1 1.5
30 min
0 min
(x10-4/mm)
M (kN-m)
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-10
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