Large Scale Fire Tests of a 4-Story Type Car Park
Part 2: Analysis of the thermal stresses and deflections
T.HIRASHIMA, Y.WANG and H.UESUGI
Department of Architectural Engineering, Faculty of Engineering, Chiba University
1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
[email protected]
T.KITANO
Sankensetsubi Corporation
1-1-3, Chuo, Chuo-ku, Chiba 260-0013, Japan
T.AVE
Structural Engineering Research Center, Tokyo Institute of Technology
4259, Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan
ABSTRACT
The Large-scale fire test is carried out in a 4-story type car park at the deepest part of
the ground floor. This experimental results indicate that car fire spreads one after another,
the steel temperature of the beam located above the combusted vehicle reaches near to
700℃ and the frame stability is maintained [1].
This paper presents the two-dimensional structural analysis of the thermal stresses and
deflections about this experiment.
KEYWORDS: car park, steel structure, numerical analysis, frame stability, fire
INTRODUCTION
Previous reports indicate that there is a little risk in an open car park building exposed
to developed fire, because the fire is likely to be constrained to the burning car or at most
be spread to one or two adjacent cars and the temperature of steel members without fire
protection reaches less than 400℃ [2-4]. In Japan, a 4-story type car park of steel
structure with 4000m2 area per floor is allowed without fire protection. In the case of a
fire at the deepest part of 4000m2 area, it is considered a high-temperature gas layer is
accumulated under a ceiling. Then, naked steel members are subjected to severe heating.
This frame receives the large thermal stress, thermal deflection and the decrease of the
strength. In consequence of these phenomena, this frame stability is possible not to be
maintained. Therefore, the large-scale fire test is carried out in a 4-story type car park at
the deepest part of the ground floor. This experimental results indicate that car fire
spreads one after another, the steel temperature of a beam located above the combusted
vehicles reaches near to 700℃, frame stability is maintained during developed fire and
FIRE SAFETY SCIENCE--PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM, pp. 655-666
Copyright © International Association for Fire Safety Science
655
the residual deformation is not observed after the fire [1].
Following to the report Part 1 [1], this paper presents the two-dimensional structural
analysis of the thermal stresses and deflections about this experiment. The followings are
the conceivable factors as the reason which this structure is not damaged. One is that the
service load is very low for the strength of structural members designed against seismic
load. Another is that the column bases of the frame are not restraint by footings because
they could not be connected to the ground beam in this experiment. It is considered that
the thermal stress is relieved by this weak restraint conditions. The analysis of thermal
stresses and deflections are carried out, therefore, assuming four kinds of support
conditions about the column bases in this paper.
LARGE SCALE FIRE TEST
Fig.1 shows the external view of the experimental structure and the view of the
spreading car fire during the experiment. Fig.2 shows the plan of the ground floor. This
experiment is performed by starting a fire at the deepest part of the thermally insulated
corner on the ground floor. The structural members are covered with no fire protection.
The maximum allowed floor area for prefabricated parking structure is 4000m2 by a floor
in Japanese specification. If the area is square, the dimensions are 63m x 63m. A fire
started in the center of the floor is thought as the most violent type possible. In order to
achieve the fire conditions described above, a thermally insulated structure is used to
form a combustion space. This space is surrounded by the ceiling (floor of the second
story) and walls on ⑤-line and E-line. Combustion progress is considered more severely
because of heat radiated from the floor and walls to cars in the insulated space. Therefore,
the corner side fire exhibits faster combustion and spreads wider than the open side fire.
The purpose of the experiment is to understand the behavior of car combustion and
structural frames under this extreme condition.
Table 1 shows the passage of fire spreading. As shown in Fig.2, the No.102 car is set
on fire and car fire spreads to adjacent cars one after another.
FIGURE 1. The external view of the experimental structure and the view of the
spreading car fire during the experiment
656
A
+-0
+-0
7.500
B
7.500
30.000
Ignition car (102)
C
7.500
104
110
103
109
7.500
着火車両
102
D
108
101
107
1200
+-0
+-0
Auto-craved aerated concrete wall
1800
昇降設備
5.000
5.000
5
4
E
1800
5.000
5.500
20.500
3
2
1
FIGURE 2. Plan of the ground floor
TABLE 1. Passage of fire spreading
TIME RECORD
Date: 26 January 1999
Time of starting test:
10:54 a.m.
00’00”
08’30”
19’15”
Weather: Fine
23’45”
25’30"
Temperature: 5℃
Direction and velocity 25’45”
of wind:
43’00”
NNW 2-3m/sec
43’45”
Start of ignition (No.102)
Fire spread to left side car (No.101)
Fire spread to right side car (No.103)
Fire spread to tail side car (No.108)
Fire spread to No.108’s right side car (No.109)
Fire spread to No.108’s left side car (No.107)
Fire spread to cars (No.110 and No.104)
Start of fire fighting
657
59 kN
2.0 kN/m
59 kN
2.0 kN/m
59 kN
2.0 kN/m
F
E
90 kN
3.2 kN/m
H
C
B
D
A
G
①
②
5,000
③
5,500
2FL
1FL
Free Condition
Roller Condition
Pin Condition
Fixed Condition
⑤
④
5,000
3FL
2,900
59 kN
2.0 kN/m
RFL
4,350
59 kN
2.0 kN/m
59 kN
2.0 kN/m
2,900
59 kN
2.0 kN/m
2,900
59 kN
2.0 kN/m
59 kN
2.0 kN/m
2,900
ANALYSIS OF THE THERMAL STRESSES AND DEFLECTIONS
The Frame
Fig.3 shows side elevation of analytical frame (E-frame). As shown in Fig.2, E-frame
is subjected to severe fire because columns and beams at the ground floor are located
between burning cars and auto-craved aerated concrete wall. In this experiment, the sets
of two wide flange shapes with small section are put on the each line of ①-⑤ instead of
footings which cannot be located in the ground. And the partial inner columns are
connected to these wide flange shapes by high-tension bolts. Therefore, this analysis is
conducted under the four kinds of support conditions of the column base as shown in
Fig.3. At first, it is assumed that the point of ④line’s column base, which move little in
horizontal direction in this experiment, is fixed for horizontal movement. In case1, ⑤
line’s column base is not supported at all and other ones are in roller bearing except ④
line’s column base, named “Free Condition” in this paper. In case2, all column bases are
in roller bearing except ④line’s column base, named “Roller Condition”. In case3, all
column bases are in pin bearing, named “Pin Condition”. In case4, all column bases are
fixed on the ground, named “Fixed Condition”. Free Condition and Roller Condition
simulate roughly this experiment. Pin Condition and Fixed Condition simulate a general
car park building structure.
5,000
1F Column：□-200×200×6 (①), □-300×300×12 (②-⑤)
2F・3F Column：□-300×300×9 (②-⑤)
Beam：H-300×150×6.5×9 (①)，H-400×200×8×13 (②-⑤)
FIGURE 3.
Side elevation of analytical frame (E-frame)
658
Steel Temperatures
Fig.4 shows the distribution of structural steel temperatures in this analysis.
Temperatures of members for axial direction are given as uniform distribution and for
sectional direction are given as variable distributions on the bases of experimental results.
In this test, fire fighting is started at 44 minutes after ignition.
Stress-Strain Curves
Fig.5 shows stress-strain curves of the steel column at elevated temperature. The
stress-strain curves of the steel beam are approximately as same as column’s one. The
analytical model of SS-curve is based on the tension tests of these materials.
The Method of Analysis
Elasto-plastic analysis of the frame is based on a non linear direct stiffness formulation
coupled with a time step integration [5,6].
Room퉷
Temp.
‰· “x ‚U
Temp.6
‰· “x ‚P ‚P
Temp.11
2FL
‰· “x ‚X
Temp.9
‰· “x ‚P ‚Q
‰· “x ‚P ‚R
Temp.12
Temp.13
‰· “x ‚Q
Temp.2
‰· “x ‚P ‚O
Temp.10
‚R
400
Temp.6
Temp.7
Temp.8
Temp.11
Temp.12
Temp.13
600
500
300
200
100
‰· “x ‚T
Temp.5
1FL
‰· “x ‚S
Temp.4
‚T
Beam Temperature
Column Temperature
500
‰· “x ‚R
Temp.3
‰· “x ‚W
Temp.8
‚S
Temp.2
Temp.3
Temp.4
Temp.5
Temp.9
Temp.10
600
‰· “x ‚V
Temp.7
400
300
200
100
0
0
0
10
20
30
40
50
60
70
80
0
Time
Time(minute)
minite
10
20
30
40
50
Time
Time(minute)
minite
FIGURE 4. Structural steel temperatures
659
60
70
80
500
300℃
200℃
RT
100℃
2
St r ess ( N/ mm )
400
400℃
300
Experiment
―
- Analitical models
500℃
○
200
600℃
100
700℃
800℃
0
0
1
2
3
St r ai n ( %)
4
5
FIGURE 5. Stress-strain curves of the steel column
Deflection
Fig.6 shows thermal deformation of the frame. In this picture, frame displacement lines
are drawn by 5 minutes during a heating phase. Fig.7 shows thermal deflection of outer
column and beam exposed to fire. In Fig.7, the experimental results are compared with
calculated ones. The symbols A, C, D and H denote the points as shown in Fig.3.
At first, the frame doesn’t collapse as same as the experiment. In the case of Free
Condition, ⑤line’s column is lifted up according to fire development time as shown in
Fig.6 (a). About the vertical displacement at the end of beam as shown in Fig.7 (c), the
calculated values approximately agree with the experimental values during a heating
phase. As shown in Fig.6 (a) and (b), in the case of Free Condition and Roller Condition,
outer column is pushed out due to the thermal elongation of the beam exposed to fire.
About the horizontal displacement at the outer column base as shown in Fig.7 (a), the
calculated values are somewhat larger than the experimental values. As shown in Fig.6
(c) and (d), in the case of Pin Condition and Fixed Condition, large bending deflections
are developed at the top of outer column due to the thermal elongation of the beam and
the restraint of column base displacement for horizontal direction. About the horizontal
displacement at the top of column as shown in Fig.7 (b), the calculated values agree with
the experimental values. As shown in Fig.7 (d), vertical displacement at center of beam
exposed to fire is yielded downward in the experiment, but this displacement is yielded
upward in the analysis. It is considered that the deflection of beam is influenced largely
by the three-dimensional factors due to the behavior of the fire exposed slab and beam
meeting at right angles. It is difficult to describe the experimental deflection of the beam
exposed to fire by two-dimensional analysis.
660
15
30
45
45
15
①
②
③
④
(a) Free Condition
30
⑤
①
②
③
④
(c) Pin Condition
⑤
15
30
45
15
①
②
30
45
③
④
⑤
(b) Roller Condition
①
②
③
④
(d) Fixed Condition
⑤
FIGURE 6. Thermal deformation of the frame
Exp.
Free
Roller
P in
Fixed
100
80
60
40
20
50
40
H-p oint
30
20
10
0
0
0
10 20
30
40 50
60 70
T ime（ minute)
(a) Horizontal displacement at outer column base
Exp.
Free
Ro ller
P in
Fix ed
40
80
0
10
20
30
40
50
60
70
80
T ime（ minute)
(b) Horizontal displacement at top of outer column
Ex p .
Free
Ro ller
P in
Fix ed
20
C-p oint
15
Displacement (mm)
50
Displacement (mm)
Exp.
Free
Roller
P in
Fixed
60
A-p oint
Displacement (mm)
Displacement (mm)
120
30
20
10
0
10
D -p oint
5
0
-5
-10
-15
-20
0
10
20
30
40
50
60
70
80
0
10
20
30
40
50
60
70
T ime（ minute)
(d) Vertical displacement at center of beam
T ime（ minute)
(c) Vertical displacement at end of beam
FIGURE 7. Thermal deflection of outer column and beam exposed to fire
661
80
90
90
75
75
Time (minute)
Time (minute)
Curvature
The curvatures of fire exposed column and beam are shown in Fig.8. The symbols from A
to G denote the points as shown in Fig.3. As shown in Fig.8 (a) and (b), in the case of Free
Condition and Roller Condition, the value of beam’s curvature at the inside end reaches 2.5
times of the room temperature’s yielding curvature at 45 minutes after ignition and remains
near to 2 times at 80 minutes after ignition. As shown in Fig.8 (d), in the case of Fixed
Condition, the value of the outer column’s curvature reaches 5.5 times of the room
temperature’s yielding curvature at 45 minutes after ignition and remains 4.5 times at 80
minutes after ignition. When the column bases of a frame are restrained for the horizontal
displacement by footings, large curvatures are developed at the top of outer columns due to
the thermal elongation of the beam exposed to fire, and they remain after a fire.
60
45
30
15
0
60
45
30
15
0
-6 -5 -4 -3 -2 -1 0
κκt /κ
t y κy
1
2
3
4
-6 -5 -4 -3 -2 -1 0
κκt /κ
t y κy
2
3
4
2
3
4
(b) Roller Condition
90
90
75
75
Time (minute)
Time (minute)
(a) Free Condition
1
60
45
30
15
60
45
30
15
0
0
-6 -5 -4 -3 -2 -1 0
κκ
t y κy
t /κ
1
2
3
-6 -5 -4 -3 -2 -1 0
4
κκt t/κyκy
(c) Pin Condition
1
(d) Fixed Condition
κt : Curvature at Elevated Temperature ,κy : Yielding Curvature at Room Temperature
:outer column base (A), ▲:top of outer column (B), ■:outside end of beam (C), +:center of beam (D),
×:inside end of beam (E), ○:top of inner column (F), ●:inner column base (G)
FIGURE 8. Curvatures of fire exposed column and beam
662
Thermal Stress
Fig.9 shows moment distribution of the frame at 45 minutes after ignition. Fig.10 shows
development of the thermal stresses resultant in steel members. The symbols B, D and E
denote the points as shown in Fig.3. As shown in Fig.9 (a) and (b), in the case of Free
Condition and Roller Condition, development of the bending moment is remarkable at
the inside end of the fire exposed beam between ④ and ⑤. It is considered that this
part supports the service load between ④ and ⑤. As shown in Fig.10 (b), bending
moment at the inside end of beam (E-point) increases according as axial force at the top
of outer column (B-point) decreases during a heating phase. The reverse phenomenon
occurs during a cooling phase and the value of bending moment at the end of beam is less
than the value before ignition. So, it is indicated that the value of bending moment at
center of beam increase before ignition as shown in Fig.10 (a) and (b). In the case of Pin
Condition, development of the bending moment is remarkable at the top of ground floor’s
column and at the top and bottom of the upper floor’s column as shown in Fig.9 (c). In
the case of Fixed Condition, development of the bending moment is remarkable at the top
and bottom of most columns as shown in Fig.9 (d). This bending moment is developed
due to the thermal elongation of the beam exposed to fire. As shown in Fig.10 (c) and (d),
bending moment at the top of outer column (B-point) increases according as axial force
of beam increases during a heating phase. The reverse phenomenon occurs during a
cooling phase and the value of bending moment at the top of outer column is the same
value before ignition. As shown in Fig.9 and Fig.10, development of the negative bending
moment is remarkable at the beam exposed to fire. It is considered that this negative
bending moment is developed due to the restraint of around members against the
deflection of the fire exposed beam which has different temperature between the upper
flange and the under flange.
663
①
②
③
④
⑤
①
②
③
④
⑤
②
③
④
⑤
④
⑤
(a) Free Condition
①
②
③
④
⑤
①
(b) Roller Condition
①
②
③
④
⑤
①
②
③
(c) Pin Condition
①
②
③
④
⑤
①
②
③
④
(d) Fixed Condition
FIGURE 9. Moment distribution
(Left: Column, Right: Beam, unit: t･m)
664
⑤
m,n
Top of outer column (B)
1.5
1
0.5
○
×
m
：
n
：
m,n
Inside end of beam (E)
1.5
m
○：
n
×：
1
0.5
m,n
Center of beam (D)
1.5
0
0
-0.5
-0.5
-0.5
-1
0 15 30 45 60 75 90
T ime (minute)
×
0.5
0
-1
：m
：n
○
1
-1
0 15 30 45 60 75 90
0 15 30 45 60 75 90
Time (minute)
Time (minute)
(a) Free Condition
m,n Top of outer column (B)
m,n Inside end of beam (E)
m,n
1.5
1.5
1.5
1
0.5
m
○：
n
×：
m
○：
n
×：
1
0.5
0.5
0
0
0
-0.5
-0.5
-1
0 15 30 45 60 75 90
-1
0 15 30 45 60 75 90
Time (minute)
Top of outer column (B)
1.5
1
0.5
○
×
m
：
n
：
0 15 30 45 60 75 90
Time (minute)
(b) Roller Condition
m,n
m,n
1.5
Inside end of beam (E)
○
1
×
0.5
：m
：n
Time (minute)
m,n
1.5
0
-0.5
-0.5
-0.5
-1
-1
m,n
Top of outer column (B)
1.5
1
0.5
m
：
n
：
○
×
0 15 30 45 60 75 90
Time (minute)
(c) Pin Condition
Inside end of beam (E)
1.5
：m
：n
○
1
×
0.5
Time (minute)
m,n
0
-0.5
-0.5
Time (minute)
×
0.5
-0.5
-1
○
1
0
0 15 30 45 60 75 90
Center of beam (D)
1.5
0
-1
×
-1
0 15 30 45 60 75 90
m,n
：m
：n
○
0.5
0
Time (minute)
Center of beam (D)
1
0
0 15 30 45 60 75 90
：m
n
×：
○
1
-0.5
-1
Center of beam (D)
：m
：n
-1
0 15 30 45 60 75 90
Time (minute)
0 15 30 45 60 75 90
Time (minute)
(d) Fixed Condition
m=bending moment as resultant of thermal stress / yielding moment at room temperature
n=axial force as resultant of thermal stress / yielding axial force at room temperature
FIGURE 10. Development of the thermal stresses resultant
665
CONCLUSIONS
The following results are obtained by the numerical analysis of the large-scale fire test.
(1) The frame does not collapse as same as the experiment. It is considered that a steel
frame exposed to a cars fire without fire protection is stable in case of members
connected rigidly and designed against seismic load in Japan.
(2) But when the column bases of a frame are restrained for the horizontal displacement
by footings, large curvature is developed at the top and bottom of outer columns due
to the thermal elongation of the fire exposed beam and it remains after a fire.
(3) The calculated values of the displacements of frame approximately agreed with the
experimental values.
ACKNOWLEDGEMENTS
The experiment in this study is performed with the full support of the Prefabricated
Parking Lot Industrial Association of Japan. The authors thank everyone involved in the
study.
REFERENCES
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buildings”, Fire Note No.10.HMSO, London, 1968.
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666