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.

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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.