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1/3/2008 1
Fire Safety of Wood Floor Assembly:
Model and Full-Scale Test
Hisa TakedaFire Research Canada (LGS)
Sub-floor
Joist
Ceiling
F I R E
Model employs two dimensional heat conduction equation to calculate the flow of heat through the ceiling, wood joist and sub-floor.
Cpρ(∂T/∂t) = ∂/∂x(k∂T/∂x)+∂/∂y(k∂T/∂y)
Sub-floor
Joist
Ceiling
Boundary condition at the surface of the ceiling which is exposed to fire can be described by this equation,
-ks(∂T/∂x) = hf(Tf - Tsf) + εffσ(Tf4 - Tsf
4)
εff is the effective emissivity calculated from the
furnace gas emissivity εf and surface emissivity
of the ceiling(gypsum board) εs.
εff = 1 / ( 1 / εf + 1 / εs - 1 )
Sub-floor
Joist
Ceiling
Boundary condition at the sub-floor surface facing
the inside the room
k(∂ T/ ∂ x) = ha(Ta - Tga) + εffσ(Ta4 - Tsa
4)
Sub-floor
Joist
Ceiling
The boundary condition at the surface of the ceiling board facing cavity-k(∂T/∂x) = h(Tcf - Tc) + F12σ (Tcf
4 - Tcs4) + F13σ
(Tcf4 - Tcw
4)
View factors F12 and F13 for radiation heat exchange in the ceiling cavity
YL
F12
Joist
F13 F13
Sub-floor
Ceiling
0
10
20
30
40
50
60
70
80
0 50 100 150 200
Distance YL (mm)
%F1313
F12F12
F
Sub-floor
Joist
Ceiling
The boundary condition at the joist surface -k(∂T/∂y) = h(Tcf - Tcw) + F31σ (Tcf
4 - Tcw4) +
F32σ (Tcs4 - Tcw
4)
View factors F21 and F31 for radiation heat exchange in the ceiling cavity
Sub-floor
XL F31
JoistF32
Ceiling
0
10
20
30
40
50
60
0 50 100 150 200 250
Distance XL (mm)
%F32F32
F31F31
Boundary condition at the interface between
ceiling and wood joist, wood joist and sub-floor
can be described using continuity equation,
k(∂ T/ ∂ x) o = k(∂ T/ ∂ x) w
Initial condition can be described by using initial
temperature in the assembly,
T = Ta at any x and y
TF = Ta
0
0.1
0.2
0.3
0.4
0.5
0 200 400 600 800 1000
Temperature (C)
Ther
mal
con
duct
ivity
(W/m
C)
Gypsum boardGypsum board
WoodWood
0
5
10
15
20
25
30
0 200 400 600 800 1000Temperature (C)
Spec
ific
heat
(J/g
C) Gypsum boardGypsum board
WoodWood
Gypsum boardGypsum board
WoodWood
0
20
40
60
80
100
0 200 400 600 800 1000
Temperature (°C)
Mas
s(%
)
Gypsum boardGypsum board
WoodWood
Full-Scale Test
Test floor was 4.8m long and 3.9m wide.
The ceiling was exposed to heat in a propane
fired horizontal furnace, in accordance with
CAN/ULC-S191-M89(ASTM E119) standard.
Test specimen:
2 x 10 wood joist
½ inch type X gypsum board as a ceiling
5/8 inch plywood as a sub-floor.
Wood joist 235 x 38
3874
11 joists @ 406 O.C.
[ FROM FULL-SCALE TEST]
Visual observations demonstrate that gypsum
filler-compound used to cover fasteners and
joints, loosens and begins to fall from the ceiling,
5 minutes after exposure to the fire, and after 15
minutes almost all filler compound fell from the
ceiling.
CeilingFiller
Joist
Joist
Joint
Joist
Ceiling tends to separate
Once the joints open, the gypsum ceiling board
was seriously heated by convection and radiation.
Therefore the temperature of the board rapidly
increases and the ceiling tends to separate from
the assemblies.
AA
BB CC
DD
A
B C
D
TEMP (C)
A
FIREJoint No Joint
B
CD
A
1000
0500 TIME (min)
0
200
400
600
800
1000
0 10 20 30 40 50
TIME (min)
TEM
PER
ATU
RE
(C)
B
ASTM E119ASTM E119Furnace
ACBB
AA
CC
DDD
FIREJoint No Joint
B
CD
AE
CA
B
E
Char formation in joists
25 26 27 28 29 min
Char formation in joists
30 31 32 33 34 min
Yield Stress of Wood
0
20
40
60
80
100
0 100 200 300 400
TEMPERATURE (C)
% Compressive stress by BenichouTensile stress by Benichou
Kacikova
Modulus of Elasticity of Wood
0
20
40
60
80
100
0 100 200 300 400
Konig
Glos
Kacikova
Benichou
%
TEMPERATURE (C)
Resistive moment
Applied load
Deflection (model)
Deflection (test)
The results show that the model prediction for the joist deflection agrees well with the test results.
The model predicted the mechanical failure occurred at 28min 49sec. Actual test was terminated at 30min, because the flame penetrated through the sub-floor
Mechanical failure
0
20
40
60
80
100
120
0 10 20 30 40
Thickness of ceiling (mm)
Tim
e (m
in)
0
20
40
60
80
100
0 2000 4000 6000 8000
Load (N/m2)
Tim
e of
mec
hani
cal f
ailu
re (m
in)
1/3/2008 35
Concluding Remarks
1. A computer model to predict the fire resistance of load bearing wood-framed floor / ceiling assemblies has been developed.
1/3/2008 36
2. The model includes the heat transfer model to calculate the flow of heat in the floor / ceiling assemblies and the mechanical model to calculate the strength of the assemblies.
1/3/2008 37
3. The results from the heat transfer model had a good agreement with the results from the full-scale tests.
Char formation in wood joists predicted by the model were favourably consistent with the pictures of the actual char formation in wood obtained from the full-scale tests.
1/3/2008 38
4. Structural model predicted the deflection and strength (resistive moment) of wood joists. The results were compared to the results from the full-scale tests and a good agreement was observed.
1/3/2008 39
5. Calculated results show that the thickness of ceiling would be rather important for fire resistance of floor / ceiling assemblies.