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Computer simulation of the thermal fire resistance of building materials and structural elements
Construction and Building Materials, Vol. 10, No. 2, pp. 131-140, 1996
Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 095&0618/96 $15.00+0.00 ELSEVIER
Computer simulation of the thermal fire resistance of building materials and structural elements W. K. Chow and Y. Y. Chan Department Hong Kong
of Building Services Engineering,
Received 3 September
The Hong Kong Polytechnic
University,
1994; revised 26 May 1995; accepted 2 June 1995
Prediction of the thermal fire resistance of building materials using a microcomputer based finite element analysis program is further reported in this paper. The thermal behaviour of three samples of commonly used materials including aluminium, hardwood and cement mortar were studied with one side exposed to an electric furnace. A small electric furnace was built with the transient variation of the furnace air temperature following the standard fire curve of British Standard BS476. Thermocouples were put inside the materials for monitoring the increase in temperature. Computer simulations with the finite element package was performed to study the temperature change inside the materials when they were exposed to fire. Results were compared with the experimental measurement on the transient temperature. Sensitivity analysis on the effect of element size was performed to check the results. Good agreement was found in the case of aluminium, but not so good in the cases of the other two building materials where other changes occurred at the same time - moisture evaporation from the cement mortar, and burning of the material of hardwood. Lastly, demonstrations in using the technique to study the thermal fire resistance of steel sheet, wooden doors and concrete beams were reported. Keywords:
fire; resistance; computer
simulations
for testing doors is being planned. Therefore, computer simulation is proposed for assessing the fire resistance of structures and new building products. Analysis of fire resistance for the non-combustible materials can be described as a thermal conduction problem. Usually, numerical methods are employed to predict the thermal fire resistance for those materials3-7. Once the failure criteria like the critical temperature for steel are specified, the model can be applied to predict the thermal fire resistance. In this paper, the use of finite element methods to study the thermal fire resistance of materials is reported. Results are verified by carrying out tests using a small electric furnace which gave exactly the BS476 standard fire curve’. Three samples of aluminium, hardwood and cement mortar were studied. Effects of the element size on the predicted temperature were investigated. Lastly, the method was used to study the thermal resistance of structural elements including steel sheet, wooden doors and concrete beams.
The term ‘fire resistance’ is associated’s2 with the ability of a building element to perform its usual function when exposed to fire. Fire resistance periods are specified for different building elements to denote how long they can stand without loss in function as loadbearing or prevention of fire spreading. Therefore, studying the thermal fire resistance of building structures and elements is essential, and standard tests such as the BS476 part 20’ are needed for evaluating the fire resistance of structures and building components. Either an oil furnace or a gas fuel furnace is used to heat up the structure for testing its stability, integrity and insulation. Stability is the ability for the element to carry the load without collapsing. Integrity is the ability to prevent the formation of cracks or perforations so that smoke and flame cannot spread from one side to the other side of the element. Insulation is the ability to prevent the passage of heat through the element. It is true that the test is deficient in a number of respects. However, the test is required for many applications including doors, beams, columns etc. and those products must be assessed according to this test. Carrying out such a test is very expensive and time-consuming. There is no laboratory in Hong Kong equipped with such a furnace for testing the fire resistance, although construction of a furnace
The physical problem In determining the fire resistance of a building element, one side of the element is exposed to a fire furnace with a standard temperature time curve. Studying the ther-
131
Computer
132
simulation
of fire resistance: W. K. Chow and Y. Y. Chan 6.7cm
ma1 fire resistance of in the material itself is a thermal conduction* problem and so the following equation can be used for describing the temperature T of the material at time t after starting the fire if there is no combustion or phase transition such as evaporation: aT
__=(r
ar
8T + 8T + d2T h2 dy2 az’ 1
(1) Height
w 1.
h (Ta- To>
,
7
In the above equation, X, y and z are the spatial coordinates inside the material, a is the thermal diffusivity of the material expressed in terms of its density p, specific heat capacity c and thermal conductivity k as klpc. The following boundary condition can be used at the surfaces exposed to fire and the other sides: q =
_,’ _
27cm
(2)
where h is the heat transfer coefficient, T, is the surrounding medium temperature and To is the surface temperature of the material. Finite element methodsY can be used to solve Equations (1) and (2). The material isdivided into a set of elements with certain geometric shapes at some nodal points. At each node, a heat balance equation is set up by equating the rate of heat input to the heat stored in the element and the amount of heat transferred to the adjacent elements. Many computer packages for studying the thermal problem by finite element method are available in the market and some of them can be executed on an IBM-286 or above personal computer. There are also three-dimensional versions for these heat transfer models. The finite element heat transfer program, LIBRA” is one of the many personal computer based packages for solving heat transfer problems available in the literature. This had been applied to study the thermal fire resistance of building materials” with verification reports on the thermal behaviour on metal using a smaller furnace. It is used in this paper as the simulation tool. Experiments on thermal fire resistance An electric furnace made of brick was built to verify the predicted results. Cement mortar was used for joining the bricks. The furnace was of length 46 cm, width 46 cm and height 27 cm with an opening of length 25.8 cm and width 6.7 cm at the top as shown in Figure 1. Fireclay brick was used because it has a lower value of thermal conductivity and so only a small amount of heat would be lost to the surroundings. Also the small furnace can be moved easily because of its light weight. An electric furnace was used because it is cleaner, safer and easier to control its temperature compared with a gas furnace. Heating coils of 3 kW were mounted at the bottom of the furnace. Type J and K thermocouples were adhered to the fire and free surfaces of the materials. The furnace temperatures was controlled by varying the input voltage of a transformer to the heating coils.
Figure 1
Furnace
This was calibrated by measuring the transient temperature in the furnace. The input voltage was changed to give a standard temperature/time curve similar to that described in BS476: Part 20’: T = 345 log (8t + 1) + 20
(3)
A comparison between the above temperature/time curve and the measured furnace air temperature is shown in Figure 2. Very good agreement is found. Three materials, aluminium, hardwood and cement mortar, were selected for studying their thermal fire resistance. A summary of their physical properties and dimensions is listed in Tuble I. In the fire tests, one side of the specimen was exposed to fire while the other side was exposed to the atmos-
loo0 1 ,u -. cl” z $
x El Y .!: a
800
600
400
s
2
c4
x Furnace -BBS 476
200
20
10
30
Timet/min Figure 2 Comparison standard fire curve
of
furnace
air
temperature
with
BS476
Computer
simulation
Table 1
Physical properties for materials in the fire test
Material
Physical dimensions length (mm) x width (mm) x height (mm)
Aluminium Hardwood Cement mortar Steel
60 94 70 30
x x x x
255 250 255 2000
x x x x
of fire resistance:
19 45 50 1000
phere. Type K thermocouples were used to measure the furnace air temperature and the temperatures at different positions of the specimens for comparing with the numerical results. Small holes of 1 mm in diameter were drilled along the width of the aluminium and hardwood specimens to accommodate the thermocouples. For the cement mortar, the thermocouples were inserted while mixing the raw materials. The temperature readings were recorded at time intervals of 30 s by a personal computer through the data acquisition unit. To minimize heat loss, the sidewalls of the specimens were covered by fireclay bricks.
Computer simulations One-dimensional simulations were performed first with one side of the materials exposed to fire and the other to ambient. Each sample of the material was subdivided into 18 elements running for the full width of the specimen with four nodal points, giving a total number of 18 nodal points as shown in Figure 3. Elements 1 to 10 are assigned inside the material specimen and elements 11 to 18 are the convective elements exposed to fire and free air. The finite element package used was LIBRA” and it was executed on an IBM-PC 486. The geometrical data of the sample and the physical properties of the materials were keyed in. The initial temperature and the time step were selected. The heat transfer coefficient is an important factor. For this geometry with the free convection flow at the surface of a horizontal plate with length L and temper-
W. K. Chow and Y. Y. Chan
Density P 0%
m-7
2740 720 1860 7830
Thermal conductivity k (W m-’ OC-‘)
Specific heat c(J kg-’ “C-‘)
221 0.16 0.72 45.3
896 1255 780 5000
ature difference ST with the ambient air, the convective heat transfer coefficient h, (Wm-* ‘C-‘) is given by”: h, =
1.32
In this study, values of convective heat transfer coefficient h, at the free boundary were taken to be from 7.5 Wm-* ‘C-’ to 9.5 Wm-* oC -’ for the hot surface, and 4.5 Wm-’ “C-’ for the cold surface. At the side exposed to the fire, the heat transfer is not only due to convection of hot gas but also thermal radiation. A total heat transfer coefficient htot including convection and radiation was used instead of the convective heat transfer coefficient h,. Values of the h,,, are related to the gas temperature and the properties of the material surface. The radiant heat transfer factor RHTF is an important parameter for modelling in radiation boundary elements. This is defined through the Stephan-Boltzman constant u and the grey body shape factor v (for simplicity of selecting materials) by: RHTF = (~1,
(5)
Values of RHTF for the hot side of the materials were taken to be 6.1 X 10m9at the hot surface and 1.7 X 1O-9 at the cold side. A piece of aluminium of length 19 mm, width 255 mm and height 60 mm as in Figure I was used with five thermocouples placed along the length of the material. The distance between each .node was about 4.75 cm. Results for the temperature predicted by the finite
T Height/mm i
Element l-10 : Test Specimen Element 11,12,15,16 : Convective Elements Element 13,14,17,18 : Radiative Elements Figure 3
Elements used in the materials
133
134
Computer
of fire resistance: W. K. Chow and Y. Y. Chan
simulation
500
7 ,u 400 \ b 8
O0 0
/ 0
300
0
-Predicted : Node 1 x Measured: Node 1 -Predicted : Node 3 +Measured:Ncde3 -Predicted : Node 5 o Measured: Node 5 -Predicted : Node 9 A Measured: Node 9
A
& El 2 200 3 5 2
0
100
0
4
Timet/min Predicted and measured temperature
in aluminium
element package and those measured experimentally are shown in Figure 4. Very good agreement is found between the two, but the predicted and measured temperature gradients between the nodes are very small. A cement mortar block of length 50 mm, width 255 mm and height 65 mm with a mixing ratio of cement to sand to water of 1:3:0.5 was made with six thermocouples placed inside during the mixing process. The distance between each node was about 10 mm. The temperatures predicted by the finite element package are shown together with the experimental results in Figure 5. This time, the two sets of curves do not agree well with each other and the predicted results do not match too well with the experimental results. For example, the measured temperature remained constant for some time because water inside the cement mortar was being evaporated. This was not predicted by the finite element analysis package as phase transition phenomena are not included in the model. A piece of hardwood of length 45 mm, width 250 mm and height 94 mm was used for the third set of measurements. Ten thermocouples each separated by 5 mm were placed along the length of the materials. The
6
8
10
12
Timet/min Figure 6
Figure 4
2
-Pre&ted : Node 1 .Munued:Nodel
Predicted and measured temperature in wood
experimental and numerical results for the materials’ temperature are shown in Figure 6. Again, the predicted results did not match well with the experimental results. The predicted temperature gradients were always higher than the measured values. This is because combustion occurred when the temperature of the wood heated up to 200°C. A charred layer was formed at 280°C and a flame was found at the surface when the temperature rose above 400°C. Different element sizes were used to check for the results predicted by the computer program. Aluminium, hardwood and cement mortar as described in Tuble 1 were selected for the study. The samples were divided into four, eight and 16 elements along the length for aluminium and five, 10 and 20 elements for hardwood and cement mortar along the length as described in Figure 7. The predicted temperatures along the direction of heat flow at 30 min are compared and shown in Figures &I, b and c. The deviation of the predicted temperatures at the same position in each case was found between the cases with the smallest and largest number of elements but the maximum value was smaller than 3°C. The percentage derviation PD, of the temperature T,, predicted at the nodes for the case with the largest
-Length/mm
____(
(a) 5 Elements 12
13
14
15
Along Length 16
17
18
19
20
21
22
HEAT
Height 1
--
2
12345678901
3
4
5
6
7
-Length/mm
8
9
10
1
(mm)
-
(b) 10 Element Along Length -Predicted : Node 1 xMcasurcd:Nodel -Predicted : Node 3 + Measurcd:Nude3 --predicted : Node 5 oMcasured:Node5
HEAT
11
24
l6
a#
1
3
5
7
30 9
I
(c)
Timet/min
Predicted and measured temperature
in cement
mortar
I
34
36
38
s
7
15
17
3
40
41
tbl Y
1
2468024680 3
5
Figure 7
Height (mm)
7
,
-Length/mm
Figure 5
32
20 Element
Different element sizes
II
l3
19
-
Along Length
21
Computer
simulation
of fire resistance: W. K. Chow and Y, Y. Chan
135
number of elements with respect to the case with the smallest number of elements TSE for each sample was calculated by:
@4 Elements ~8 Elements o 16 Elements
PD
=
TLE - TsE x TSE
100%
(6)
Values of PD at 30 min after starting the furnace were from 0% to 0.02% for aluminium, 0% to 6.92% for hardwood and 0.16% to 1.44% for cement mortar. This indicates that the results did not depend on the element size.
Two-dimensional heat transfer model 5 00
15
10
20
Extension of the finite element package to study the thermal fire resistance of materials in a two-dimensional image was investigated. The samples used were also aluminium, hardwood and cement mortar with three sides of the sample exposed to fire. A sample of aluminium of size 19 mm by 60 mm was divided into 4 X 3 and 18 X 3 elements; a sample of hardwood of size 45 mm by 94 mm was divided into 5 X 3 and 10 X 3 elements; and cement mortar of size 50 mm by 65 mm was divided into 5 X 3 and 10 X 3 elements as shown in Figures 9 to II. The temperatures at each node point inside the material were predicted by the finite element package LIBRA”. The predicted temperatures at 30 min are also shown in the figures. The difference in the predicted temperatures for the two cases was less than 5°C.
Node number
800
600
400
200
Thermal fire resistance of structural elements
0”““““““““““’ 0
5
10
15
20
Node number
0)
600 1
I @5 Elements
* 10 Elements 020 Elements
loo”““““““““““’ 5 0 (cl
10
15
20
Node number
Figure 8 Predicted (a) aluminium, (b) hardwood, and (c) cement mortar temperatures for different numbers of elements
The computer program was applied to study the thermal fire resistance of three types of structural elements: a sheet of steel, a wooden door and a concrete beam. A steel enclosure is usually required to have a fire resistance period of 2 h. The thermal fire resistance of a sheet of steel of length 1 m, height 2 m and thickness 0.03 m is studied. The physical properties of steel are shown in Table 2. In the fire test, one side of the steel sheet was subjected to the BS476 standard fire curve while the other side was exposed to the atmosphere. A one-dimensional simulation was performed with the elements shown in Figure 12(a). The predicted temperatures at different nodes are almost the same. The results at node 1 are shown in Figure 12(b). The critical temperature for steel is 55O”C, at which the yield strength would change from 450 MPa to 40 MPa. It is found from Figure 12(b) that the maximum temperature of the steel was about 382°C within 2 h. This is less than the critical temperature of 550°C and so the steel would have a fire resistance period longer than 2 hours. Wooden doors are another building element which are required to have a fire resistance period longer than half an hour. The thermal fire resistance of a wooden door of length 0.84 m, height 2 m and thickness 0.05 m was studied with the physical properties the same as the
Computer
136
simulation
of fire resistance: W. K. Chow and Y. Y. Chan
(I) 4x3 Elements
767.4
Httt
767.3
5 7683
767.3
6 1 768.4
’’
1 769
767.3
7 1
767.4
8 1
16f .3
2 768.9
Htrt
” 768.5
3 768.9
768.9
169
19mm
1
I
Heat
(b) 8x3 Elements 767.4
167.3
761.3
161.3
167.4
Heat Htrt
767.4
768.9
768.9 768.9
768.9
768.9
768.9 768.9
767.4
1 Httt
Figure 9
Predicted
aluminium
temperature
at 30 min
hardwood shown in Tuble I. In the simulation, one side of the door was exposed to the BS476 standard fire curve. The door was divided into 10 elements along its width. The simulation results within 2 h for nodes 1, 3, 5, 8 and 11 are shown in Figure 13. The maximum
temperature at the hot side of the door rose to about 1000°C and the temperature on the cold side was about 60°C. In fact, when the door reached a temperature of about 5OO”C, the major components would ignite and burn. Cracks would form on the hot surface
Computer simulation of fire resistance: W. K. Chow and Y. Y. Chan (8)Sx3
Elements
734.9
T
439.7
314.1
314.1
439.7
734.9
l
7
T’ 11 313mm A!-()
Hest
137
12
808.4
5665
6
94mm
13 428.4
7
1
900.2
A 461.7
a62.8
808.4
10
Hest
A 4617
844.1)
ib
566.S
9
A 581.9
15
428.4
8
A 807.5
14
1144.8
5819
807.5
1
862.8
900.2
I
Heat
(b) 10x3 Elements 738.2
T 313mm
445.8
320.0
320.0
26
21
_k r
94mm
14
15
16
9004
L
17
6 8
r
863.2
1
Heat
463.6
463.6
1
27 431.4
431.4
808.4
Heat
738.2
445.8
808.1
7 8
t 845.1
863.2
900.4
&ha
k----d r
Figure 10
45mm 1
Predicted hardwood temperature at 30 min
and the door could no longer be stable. From the curve, the fire resistance period of the wooden door is found to be at least 30 min and at this time, the temperature on the other side is very low. The thermal fire resistance of a lightweight concrete beam of length 0.3 m and width 0.4 m with no reinforcement was studied. Three sides of the beam were exposed to the BS standard fire. The predicted results after 2 h of fire exposure are shown in Figure 24. The
temperatures at the two bottom corners were about 1047°C and the temperatures at 6 cm depth were about 150°C. The compressive strength of structural concrete would be reduced by 40% when the temperature is higher than 500°C. At temperatures above 6OO”C, aggregates would begin to spa11 but this would occur only in the outer layer of 3 to 5 cm. Therefore, the concrete beam has a fire resistance period of 2 hours and within this period, no serious damage would be found.
Computer
138
simulation
of fire resistance:
W. K. Chow and Y. Y. Chan
(I) 5x3 Eltmcnts
414.4
5953
417.2
417.2
474.4
595.3
Heat Heat
770.1
819.4 k
1Omm
744.9
>i
I
I
50mm
k
4
I
Heat
(b) 10x3 Elements
Heat Heat
819.9
792.4
770.8
755.2
745.8
742.6
745.8
770.8
819.9
50mm
Figure 11
Predicted
cement
mortar
temperature
at 30 min
Conclusion In this paper, the finite element package LIBRA” was further applied for studying the thermal fire resistance of building materials. Results were verified by experimental studies. Both one- and two-dimensional heat transfer simulation were studied. It was found that the
package can be used to study the thermal fire resistance of materials where there is no phase transition upon heating. However, this is not so good for the materials such as concrete or wood where phase transition or combustion of materials occurred. This can be improved by including phase transitioni3,‘4 phenomena in the model.
Computer
simulation
of fire resistance:
139
W. K. Chow and Y. Y. Chan
lm >I 10l
1
5
8 0
3
7 9 0 6
1 1 1
t
l-Dimensional
heat flow
t (4
Fire -Measured -BS 476
1200
,u \ 1000 b
: Node 1
1
800
g
5
0
0
30
Heat
of the durasteel
120
90
Timet/min
(b) Figure 12 (4 Geometry
60
sheet; (b) predicted
temperature
of the durasteel
sheet
l_
m
*Node 1 o.Node 3 &Node 5 ONode 8 *Node 11 ” 0
20
Figure 13
(a) Geometry
of the wooden
door; (b) predicted
temperature
in the wooden
40
60 Timet/min
(b)
door
80
100
120
Computer
140
I-
300mm
simulation
of fire resistance: W. K. Chow and Y. Y. Chan
References
-4
1
675.3
2 3 -
HEAT
4
5 6 450mm 7
Y 8 9 10 II
1047
1047 c
t
HEAT
12 13
14
Figure 14
Temperature
contour
predicted
on concrete
column
Fire tests on building materials and structures. BS476 Parts 20 to 22, British Standards Institution, UK, 1987 Malhotra, H. L., Design of Fire-Resisting Structures, Surrey University Press, London 1982 Wade, L. V. and Krokosky, E. M., Finite element prediction of fire proofing effectiveness. J. Mater. 1982, 4 (4), pp. 496-500 Haksever, A. A practical method for the calculation of the nonsteady temperature fields in solid bodies. Fire Mater. 1985, 9 (3) pp. 150-154 Calhoun, P. R. A computer model to simulate fire testing of noncombustible materials. J. Fire Sci. May/Jun 1983, 1, pp. 221-229 Sterner, E. and Wickstrom, U. TASEF - Temperature analysis of structures exposed to fire - User’s manual. SP Report 1990: 05 Fire Technology, Statens Provningsanstah, Sweden, 1990 Fields, B. A. and Fields, R. J. The prediction of elevated temperature deformation of structural steel under anisothermal conditions. NISTIR Report 4497, Centre for Fire Research, NIST, USA 1991 Carslaw, H. S. and Jaeger, J. C. Conduction of’ Heat in Solids Oxford University Press, Oxford 1959 Reddy, J. N. An Introduction to the Finite Element Method McGraw-Hill, New York, 1984 LIBRA Heat Conduction Analysis User> Manual, Intercept Software, Campbell, USA 1988 Chow, W. K. and Lee, P. S. W. Use of the microcomputer based finite element package LIBRA for studying the thermal fire resistance of structural materials. Labor. Microcomput. 1993, 12 (3), pp. 87-92 Ozisik, M. N. Busic Heat Transjkr, McGraw-Hill, New York, 1977 Harmathy, T. Z. Moisture and heat transport with particular reference to concrete. Research Paper 494, Natural Research Council of Canada, Canada 1971 Huang, C. L. D. and Ahmed, G. N. Computational solution for heat and mass transfer in concrete slab under fire. In Numerical Methods in Thermal Problems. eds R. W. Levis and K. Morgan, 1989
Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 095&0618/96 $15.00+0.00 ELSEVIER
Computer simulation of the thermal fire resistance of building materials and structural elements W. K. Chow and Y. Y. Chan Department Hong Kong
of Building Services Engineering,
Received 3 September
The Hong Kong Polytechnic
University,
1994; revised 26 May 1995; accepted 2 June 1995
Prediction of the thermal fire resistance of building materials using a microcomputer based finite element analysis program is further reported in this paper. The thermal behaviour of three samples of commonly used materials including aluminium, hardwood and cement mortar were studied with one side exposed to an electric furnace. A small electric furnace was built with the transient variation of the furnace air temperature following the standard fire curve of British Standard BS476. Thermocouples were put inside the materials for monitoring the increase in temperature. Computer simulations with the finite element package was performed to study the temperature change inside the materials when they were exposed to fire. Results were compared with the experimental measurement on the transient temperature. Sensitivity analysis on the effect of element size was performed to check the results. Good agreement was found in the case of aluminium, but not so good in the cases of the other two building materials where other changes occurred at the same time - moisture evaporation from the cement mortar, and burning of the material of hardwood. Lastly, demonstrations in using the technique to study the thermal fire resistance of steel sheet, wooden doors and concrete beams were reported. Keywords:
fire; resistance; computer
simulations
for testing doors is being planned. Therefore, computer simulation is proposed for assessing the fire resistance of structures and new building products. Analysis of fire resistance for the non-combustible materials can be described as a thermal conduction problem. Usually, numerical methods are employed to predict the thermal fire resistance for those materials3-7. Once the failure criteria like the critical temperature for steel are specified, the model can be applied to predict the thermal fire resistance. In this paper, the use of finite element methods to study the thermal fire resistance of materials is reported. Results are verified by carrying out tests using a small electric furnace which gave exactly the BS476 standard fire curve’. Three samples of aluminium, hardwood and cement mortar were studied. Effects of the element size on the predicted temperature were investigated. Lastly, the method was used to study the thermal resistance of structural elements including steel sheet, wooden doors and concrete beams.
The term ‘fire resistance’ is associated’s2 with the ability of a building element to perform its usual function when exposed to fire. Fire resistance periods are specified for different building elements to denote how long they can stand without loss in function as loadbearing or prevention of fire spreading. Therefore, studying the thermal fire resistance of building structures and elements is essential, and standard tests such as the BS476 part 20’ are needed for evaluating the fire resistance of structures and building components. Either an oil furnace or a gas fuel furnace is used to heat up the structure for testing its stability, integrity and insulation. Stability is the ability for the element to carry the load without collapsing. Integrity is the ability to prevent the formation of cracks or perforations so that smoke and flame cannot spread from one side to the other side of the element. Insulation is the ability to prevent the passage of heat through the element. It is true that the test is deficient in a number of respects. However, the test is required for many applications including doors, beams, columns etc. and those products must be assessed according to this test. Carrying out such a test is very expensive and time-consuming. There is no laboratory in Hong Kong equipped with such a furnace for testing the fire resistance, although construction of a furnace
The physical problem In determining the fire resistance of a building element, one side of the element is exposed to a fire furnace with a standard temperature time curve. Studying the ther-
131
Computer
132
simulation
of fire resistance: W. K. Chow and Y. Y. Chan 6.7cm
ma1 fire resistance of in the material itself is a thermal conduction* problem and so the following equation can be used for describing the temperature T of the material at time t after starting the fire if there is no combustion or phase transition such as evaporation: aT
__=(r
ar
8T + 8T + d2T h2 dy2 az’ 1
(1) Height
w 1.
h (Ta- To>
,
7
In the above equation, X, y and z are the spatial coordinates inside the material, a is the thermal diffusivity of the material expressed in terms of its density p, specific heat capacity c and thermal conductivity k as klpc. The following boundary condition can be used at the surfaces exposed to fire and the other sides: q =
_,’ _
27cm
(2)
where h is the heat transfer coefficient, T, is the surrounding medium temperature and To is the surface temperature of the material. Finite element methodsY can be used to solve Equations (1) and (2). The material isdivided into a set of elements with certain geometric shapes at some nodal points. At each node, a heat balance equation is set up by equating the rate of heat input to the heat stored in the element and the amount of heat transferred to the adjacent elements. Many computer packages for studying the thermal problem by finite element method are available in the market and some of them can be executed on an IBM-286 or above personal computer. There are also three-dimensional versions for these heat transfer models. The finite element heat transfer program, LIBRA” is one of the many personal computer based packages for solving heat transfer problems available in the literature. This had been applied to study the thermal fire resistance of building materials” with verification reports on the thermal behaviour on metal using a smaller furnace. It is used in this paper as the simulation tool. Experiments on thermal fire resistance An electric furnace made of brick was built to verify the predicted results. Cement mortar was used for joining the bricks. The furnace was of length 46 cm, width 46 cm and height 27 cm with an opening of length 25.8 cm and width 6.7 cm at the top as shown in Figure 1. Fireclay brick was used because it has a lower value of thermal conductivity and so only a small amount of heat would be lost to the surroundings. Also the small furnace can be moved easily because of its light weight. An electric furnace was used because it is cleaner, safer and easier to control its temperature compared with a gas furnace. Heating coils of 3 kW were mounted at the bottom of the furnace. Type J and K thermocouples were adhered to the fire and free surfaces of the materials. The furnace temperatures was controlled by varying the input voltage of a transformer to the heating coils.
Figure 1
Furnace
This was calibrated by measuring the transient temperature in the furnace. The input voltage was changed to give a standard temperature/time curve similar to that described in BS476: Part 20’: T = 345 log (8t + 1) + 20
(3)
A comparison between the above temperature/time curve and the measured furnace air temperature is shown in Figure 2. Very good agreement is found. Three materials, aluminium, hardwood and cement mortar, were selected for studying their thermal fire resistance. A summary of their physical properties and dimensions is listed in Tuble I. In the fire tests, one side of the specimen was exposed to fire while the other side was exposed to the atmos-
loo0 1 ,u -. cl” z $
x El Y .!: a
800
600
400
s
2
c4
x Furnace -BBS 476
200
20
10
30
Timet/min Figure 2 Comparison standard fire curve
of
furnace
air
temperature
with
BS476
Computer
simulation
Table 1
Physical properties for materials in the fire test
Material
Physical dimensions length (mm) x width (mm) x height (mm)
Aluminium Hardwood Cement mortar Steel
60 94 70 30
x x x x
255 250 255 2000
x x x x
of fire resistance:
19 45 50 1000
phere. Type K thermocouples were used to measure the furnace air temperature and the temperatures at different positions of the specimens for comparing with the numerical results. Small holes of 1 mm in diameter were drilled along the width of the aluminium and hardwood specimens to accommodate the thermocouples. For the cement mortar, the thermocouples were inserted while mixing the raw materials. The temperature readings were recorded at time intervals of 30 s by a personal computer through the data acquisition unit. To minimize heat loss, the sidewalls of the specimens were covered by fireclay bricks.
Computer simulations One-dimensional simulations were performed first with one side of the materials exposed to fire and the other to ambient. Each sample of the material was subdivided into 18 elements running for the full width of the specimen with four nodal points, giving a total number of 18 nodal points as shown in Figure 3. Elements 1 to 10 are assigned inside the material specimen and elements 11 to 18 are the convective elements exposed to fire and free air. The finite element package used was LIBRA” and it was executed on an IBM-PC 486. The geometrical data of the sample and the physical properties of the materials were keyed in. The initial temperature and the time step were selected. The heat transfer coefficient is an important factor. For this geometry with the free convection flow at the surface of a horizontal plate with length L and temper-
W. K. Chow and Y. Y. Chan
Density P 0%
m-7
2740 720 1860 7830
Thermal conductivity k (W m-’ OC-‘)
Specific heat c(J kg-’ “C-‘)
221 0.16 0.72 45.3
896 1255 780 5000
ature difference ST with the ambient air, the convective heat transfer coefficient h, (Wm-* ‘C-‘) is given by”: h, =
1.32
In this study, values of convective heat transfer coefficient h, at the free boundary were taken to be from 7.5 Wm-* ‘C-’ to 9.5 Wm-* oC -’ for the hot surface, and 4.5 Wm-’ “C-’ for the cold surface. At the side exposed to the fire, the heat transfer is not only due to convection of hot gas but also thermal radiation. A total heat transfer coefficient htot including convection and radiation was used instead of the convective heat transfer coefficient h,. Values of the h,,, are related to the gas temperature and the properties of the material surface. The radiant heat transfer factor RHTF is an important parameter for modelling in radiation boundary elements. This is defined through the Stephan-Boltzman constant u and the grey body shape factor v (for simplicity of selecting materials) by: RHTF = (~1,
(5)
Values of RHTF for the hot side of the materials were taken to be 6.1 X 10m9at the hot surface and 1.7 X 1O-9 at the cold side. A piece of aluminium of length 19 mm, width 255 mm and height 60 mm as in Figure I was used with five thermocouples placed along the length of the material. The distance between each .node was about 4.75 cm. Results for the temperature predicted by the finite
T Height/mm i
Element l-10 : Test Specimen Element 11,12,15,16 : Convective Elements Element 13,14,17,18 : Radiative Elements Figure 3
Elements used in the materials
133
134
Computer
of fire resistance: W. K. Chow and Y. Y. Chan
simulation
500
7 ,u 400 \ b 8
O0 0
/ 0
300
0
-Predicted : Node 1 x Measured: Node 1 -Predicted : Node 3 +Measured:Ncde3 -Predicted : Node 5 o Measured: Node 5 -Predicted : Node 9 A Measured: Node 9
A
& El 2 200 3 5 2
0
100
0
4
Timet/min Predicted and measured temperature
in aluminium
element package and those measured experimentally are shown in Figure 4. Very good agreement is found between the two, but the predicted and measured temperature gradients between the nodes are very small. A cement mortar block of length 50 mm, width 255 mm and height 65 mm with a mixing ratio of cement to sand to water of 1:3:0.5 was made with six thermocouples placed inside during the mixing process. The distance between each node was about 10 mm. The temperatures predicted by the finite element package are shown together with the experimental results in Figure 5. This time, the two sets of curves do not agree well with each other and the predicted results do not match too well with the experimental results. For example, the measured temperature remained constant for some time because water inside the cement mortar was being evaporated. This was not predicted by the finite element analysis package as phase transition phenomena are not included in the model. A piece of hardwood of length 45 mm, width 250 mm and height 94 mm was used for the third set of measurements. Ten thermocouples each separated by 5 mm were placed along the length of the materials. The
6
8
10
12
Timet/min Figure 6
Figure 4
2
-Pre&ted : Node 1 .Munued:Nodel
Predicted and measured temperature in wood
experimental and numerical results for the materials’ temperature are shown in Figure 6. Again, the predicted results did not match well with the experimental results. The predicted temperature gradients were always higher than the measured values. This is because combustion occurred when the temperature of the wood heated up to 200°C. A charred layer was formed at 280°C and a flame was found at the surface when the temperature rose above 400°C. Different element sizes were used to check for the results predicted by the computer program. Aluminium, hardwood and cement mortar as described in Tuble 1 were selected for the study. The samples were divided into four, eight and 16 elements along the length for aluminium and five, 10 and 20 elements for hardwood and cement mortar along the length as described in Figure 7. The predicted temperatures along the direction of heat flow at 30 min are compared and shown in Figures &I, b and c. The deviation of the predicted temperatures at the same position in each case was found between the cases with the smallest and largest number of elements but the maximum value was smaller than 3°C. The percentage derviation PD, of the temperature T,, predicted at the nodes for the case with the largest
-Length/mm
____(
(a) 5 Elements 12
13
14
15
Along Length 16
17
18
19
20
21
22
HEAT
Height 1
--
2
12345678901
3
4
5
6
7
-Length/mm
8
9
10
1
(mm)
-
(b) 10 Element Along Length -Predicted : Node 1 xMcasurcd:Nodel -Predicted : Node 3 + Measurcd:Nude3 --predicted : Node 5 oMcasured:Node5
HEAT
11
24
l6
a#
1
3
5
7
30 9
I
(c)
Timet/min
Predicted and measured temperature
in cement
mortar
I
34
36
38
s
7
15
17
3
40
41
tbl Y
1
2468024680 3
5
Figure 7
Height (mm)
7
,
-Length/mm
Figure 5
32
20 Element
Different element sizes
II
l3
19
-
Along Length
21
Computer
simulation
of fire resistance: W. K. Chow and Y, Y. Chan
135
number of elements with respect to the case with the smallest number of elements TSE for each sample was calculated by:
@4 Elements ~8 Elements o 16 Elements
PD
=
TLE - TsE x TSE
100%
(6)
Values of PD at 30 min after starting the furnace were from 0% to 0.02% for aluminium, 0% to 6.92% for hardwood and 0.16% to 1.44% for cement mortar. This indicates that the results did not depend on the element size.
Two-dimensional heat transfer model 5 00
15
10
20
Extension of the finite element package to study the thermal fire resistance of materials in a two-dimensional image was investigated. The samples used were also aluminium, hardwood and cement mortar with three sides of the sample exposed to fire. A sample of aluminium of size 19 mm by 60 mm was divided into 4 X 3 and 18 X 3 elements; a sample of hardwood of size 45 mm by 94 mm was divided into 5 X 3 and 10 X 3 elements; and cement mortar of size 50 mm by 65 mm was divided into 5 X 3 and 10 X 3 elements as shown in Figures 9 to II. The temperatures at each node point inside the material were predicted by the finite element package LIBRA”. The predicted temperatures at 30 min are also shown in the figures. The difference in the predicted temperatures for the two cases was less than 5°C.
Node number
800
600
400
200
Thermal fire resistance of structural elements
0”““““““““““’ 0
5
10
15
20
Node number
0)
600 1
I @5 Elements
* 10 Elements 020 Elements
loo”““““““““““’ 5 0 (cl
10
15
20
Node number
Figure 8 Predicted (a) aluminium, (b) hardwood, and (c) cement mortar temperatures for different numbers of elements
The computer program was applied to study the thermal fire resistance of three types of structural elements: a sheet of steel, a wooden door and a concrete beam. A steel enclosure is usually required to have a fire resistance period of 2 h. The thermal fire resistance of a sheet of steel of length 1 m, height 2 m and thickness 0.03 m is studied. The physical properties of steel are shown in Table 2. In the fire test, one side of the steel sheet was subjected to the BS476 standard fire curve while the other side was exposed to the atmosphere. A one-dimensional simulation was performed with the elements shown in Figure 12(a). The predicted temperatures at different nodes are almost the same. The results at node 1 are shown in Figure 12(b). The critical temperature for steel is 55O”C, at which the yield strength would change from 450 MPa to 40 MPa. It is found from Figure 12(b) that the maximum temperature of the steel was about 382°C within 2 h. This is less than the critical temperature of 550°C and so the steel would have a fire resistance period longer than 2 hours. Wooden doors are another building element which are required to have a fire resistance period longer than half an hour. The thermal fire resistance of a wooden door of length 0.84 m, height 2 m and thickness 0.05 m was studied with the physical properties the same as the
Computer
136
simulation
of fire resistance: W. K. Chow and Y. Y. Chan
(I) 4x3 Elements
767.4
Httt
767.3
5 7683
767.3
6 1 768.4
’’
1 769
767.3
7 1
767.4
8 1
16f .3
2 768.9
Htrt
” 768.5
3 768.9
768.9
169
19mm
1
I
Heat
(b) 8x3 Elements 767.4
167.3
761.3
161.3
167.4
Heat Htrt
767.4
768.9
768.9 768.9
768.9
768.9
768.9 768.9
767.4
1 Httt
Figure 9
Predicted
aluminium
temperature
at 30 min
hardwood shown in Tuble I. In the simulation, one side of the door was exposed to the BS476 standard fire curve. The door was divided into 10 elements along its width. The simulation results within 2 h for nodes 1, 3, 5, 8 and 11 are shown in Figure 13. The maximum
temperature at the hot side of the door rose to about 1000°C and the temperature on the cold side was about 60°C. In fact, when the door reached a temperature of about 5OO”C, the major components would ignite and burn. Cracks would form on the hot surface
Computer simulation of fire resistance: W. K. Chow and Y. Y. Chan (8)Sx3
Elements
734.9
T
439.7
314.1
314.1
439.7
734.9
l
7
T’ 11 313mm A!-()
Hest
137
12
808.4
5665
6
94mm
13 428.4
7
1
900.2
A 461.7
a62.8
808.4
10
Hest
A 4617
844.1)
ib
566.S
9
A 581.9
15
428.4
8
A 807.5
14
1144.8
5819
807.5
1
862.8
900.2
I
Heat
(b) 10x3 Elements 738.2
T 313mm
445.8
320.0
320.0
26
21
_k r
94mm
14
15
16
9004
L
17
6 8
r
863.2
1
Heat
463.6
463.6
1
27 431.4
431.4
808.4
Heat
738.2
445.8
808.1
7 8
t 845.1
863.2
900.4
&ha
k----d r
Figure 10
45mm 1
Predicted hardwood temperature at 30 min
and the door could no longer be stable. From the curve, the fire resistance period of the wooden door is found to be at least 30 min and at this time, the temperature on the other side is very low. The thermal fire resistance of a lightweight concrete beam of length 0.3 m and width 0.4 m with no reinforcement was studied. Three sides of the beam were exposed to the BS standard fire. The predicted results after 2 h of fire exposure are shown in Figure 24. The
temperatures at the two bottom corners were about 1047°C and the temperatures at 6 cm depth were about 150°C. The compressive strength of structural concrete would be reduced by 40% when the temperature is higher than 500°C. At temperatures above 6OO”C, aggregates would begin to spa11 but this would occur only in the outer layer of 3 to 5 cm. Therefore, the concrete beam has a fire resistance period of 2 hours and within this period, no serious damage would be found.
Computer
138
simulation
of fire resistance:
W. K. Chow and Y. Y. Chan
(I) 5x3 Eltmcnts
414.4
5953
417.2
417.2
474.4
595.3
Heat Heat
770.1
819.4 k
1Omm
744.9
>i
I
I
50mm
k
4
I
Heat
(b) 10x3 Elements
Heat Heat
819.9
792.4
770.8
755.2
745.8
742.6
745.8
770.8
819.9
50mm
Figure 11
Predicted
cement
mortar
temperature
at 30 min
Conclusion In this paper, the finite element package LIBRA” was further applied for studying the thermal fire resistance of building materials. Results were verified by experimental studies. Both one- and two-dimensional heat transfer simulation were studied. It was found that the
package can be used to study the thermal fire resistance of materials where there is no phase transition upon heating. However, this is not so good for the materials such as concrete or wood where phase transition or combustion of materials occurred. This can be improved by including phase transitioni3,‘4 phenomena in the model.
Computer
simulation
of fire resistance:
139
W. K. Chow and Y. Y. Chan
lm >I 10l
1
5
8 0
3
7 9 0 6
1 1 1
t
l-Dimensional
heat flow
t (4
Fire -Measured -BS 476
1200
,u \ 1000 b
: Node 1
1
800
g
5
0
0
30
Heat
of the durasteel
120
90
Timet/min
(b) Figure 12 (4 Geometry
60
sheet; (b) predicted
temperature
of the durasteel
sheet
l_
m
*Node 1 o.Node 3 &Node 5 ONode 8 *Node 11 ” 0
20
Figure 13
(a) Geometry
of the wooden
door; (b) predicted
temperature
in the wooden
40
60 Timet/min
(b)
door
80
100
120
Computer
140
I-
300mm
simulation
of fire resistance: W. K. Chow and Y. Y. Chan
References
-4
1
675.3
2 3 -
HEAT
4
5 6 450mm 7
Y 8 9 10 II
1047
1047 c
t
HEAT
12 13
14
Figure 14
Temperature
contour
predicted
on concrete
column
Fire tests on building materials and structures. BS476 Parts 20 to 22, British Standards Institution, UK, 1987 Malhotra, H. L., Design of Fire-Resisting Structures, Surrey University Press, London 1982 Wade, L. V. and Krokosky, E. M., Finite element prediction of fire proofing effectiveness. J. Mater. 1982, 4 (4), pp. 496-500 Haksever, A. A practical method for the calculation of the nonsteady temperature fields in solid bodies. Fire Mater. 1985, 9 (3) pp. 150-154 Calhoun, P. R. A computer model to simulate fire testing of noncombustible materials. J. Fire Sci. May/Jun 1983, 1, pp. 221-229 Sterner, E. and Wickstrom, U. TASEF - Temperature analysis of structures exposed to fire - User’s manual. SP Report 1990: 05 Fire Technology, Statens Provningsanstah, Sweden, 1990 Fields, B. A. and Fields, R. J. The prediction of elevated temperature deformation of structural steel under anisothermal conditions. NISTIR Report 4497, Centre for Fire Research, NIST, USA 1991 Carslaw, H. S. and Jaeger, J. C. Conduction of’ Heat in Solids Oxford University Press, Oxford 1959 Reddy, J. N. An Introduction to the Finite Element Method McGraw-Hill, New York, 1984 LIBRA Heat Conduction Analysis User> Manual, Intercept Software, Campbell, USA 1988 Chow, W. K. and Lee, P. S. W. Use of the microcomputer based finite element package LIBRA for studying the thermal fire resistance of structural materials. Labor. Microcomput. 1993, 12 (3), pp. 87-92 Ozisik, M. N. Busic Heat Transjkr, McGraw-Hill, New York, 1977 Harmathy, T. Z. Moisture and heat transport with particular reference to concrete. Research Paper 494, Natural Research Council of Canada, Canada 1971 Huang, C. L. D. and Ahmed, G. N. Computational solution for heat and mass transfer in concrete slab under fire. In Numerical Methods in Thermal Problems. eds R. W. Levis and K. Morgan, 1989