Department ofCivil and Structural Engineering
Annex B[informative]
THERMAL ACTIONS FOR EXTERNAL MEMBERS
Eurocode 1BS EN 1991 Part 1-2:2002 General actions – Actions on structures exposed to fire
Actions on structures
Thermal Calculation Th
erm
al C
alcu
latio
n Thermal action for external members - Simplified calculation method
The method is used to determine the maximum compartment fire temperature.
It gives the temperature and size of flame emanating from the openings.
For various parameters, the method considers steady–state condition.
This method is adopted for fire loads greater than 200 MJ/m2.
Usage conditionsU
sage
con
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ns
Usage conditions
If there are more number of windows in a fire compartment, the weighted average height of openings heq, summation of width of windows (wt = ∑wi) and vertical openings total area Av are used.
The compartment dimensions limited to 70m, width to 18m and 5m height.
All along the thickness and width of flame the flame temperature remains uniform.
Usage conditionsU
sage
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Usage conditions
If windows are present only on one side of wall 1, then the D/W ratio
D/W = W2/wt
If more number of windows are present on more than one wall of the fire compartment, then D/W ratio is given as
D/W = (W2 Av,1) / (W1 Av)
Where,W1 - wall width on side 1, generally side containing greatest area of
windowAv,1 - summation of window area on side 1W2 - wall width perpendicular to side 1
Wind effectW
ind
effec
t
Mode of Ventilation
If there are windows present on either side or when the fire is fed with additional external supply of air, then the ‘forced draught’ method is used for calculations. Else, no forced draught conditions are used.
Deflection of flame by wind
Flames coming out of fire compartment are assumed to be in a direction perpendicular to the facade; At an angle 45⁰, due to deflection by wind effects.
135⁰wind45⁰
Flame deflection due to wind - Horizontal cross section
No forced draughtN
o fo
rced
dra
ught
Burning Rate
For most types of furniture found in buildings, τF is about 1200sec so that for a free burning fire of furniture, the rate of burning is
[MW]
Vertical opening area of walls, Av
Height of window, heq
Total enclosure area (ceiling, floor, walls along with windows), At
Ratio of compartment depth to width, D/W
No forced draughtN
o fo
rced
dra
ught
Fire compartment temperature
Tf = 6000(1 – e - 0.1/o) o1/2 (1- e -0.00286 Ω) + To
Flame height
This equation may be simplified by taking ρg = 0.45 kg/m3 and g = 9.81 m/s2 as,
No forced draughtN
o fo
rced
dra
ught
Flame height
wt
L1heq
LL
2h /3eq
LH
2h /3eq L1heq
LL
2h /3eq
LH
eq2h /3
Flame dimensions – No through draught
No forced draughtN
o fo
rced
dra
ught
Flame widthFlame width is taken as window width, wi
Flame depth Taken as 2/3rd of the window height, i.e. 2/3 heq
Horizontal projection of flameIf a wall is present above window, thenLH = heq/3 if heq 1.25wt
LH = 0.3 heq (heq / wt) 0.54 if heq>1.25wt and distance to any other window > 4wt
LH = 0.454 heq (heq / 2wt) 0.54 in other cases
In case of a wall not existing above the window, LH = 0.6 heq (LL / heq) 1/3
No forced draughtN
o fo
rced
dra
ught
Length of flame along axis
When LL > 0Lf = LL + heq/2 if wall exist above window or if
heq 1.25 wt
Lf = (LL2 + (LH - heq/3)2)1/2+heq/2 if wall exist above window or if
heq> 1.25 wt
When LL = 0, then Lf = 0
Flame temperature at windowTw = 520/(1-0.4725(Lf wt/Q))+To with Lf wt/Q < 1
Emissivity of flame at windowThe flame emissivity at window is taken as εf = 1.0
The temperature of flame along the axisTz = (Tw – To)(1-0.4725(Lx wt/Q))+To with Lx wt/Q < 1
No forced draughtN
o fo
rced
dra
ught
The emissivity of flames
εf = 1 – e-0.3 df
Convective heat transfer coefficient
αc = 0.00467 (1/ deq)0.4 (Q/Av)0.6
Effect of projection above window
The flame height LL decreased by Wa(1+√2)
The horizontal projection of the flame LH increased by Wa
As per EN1991-1-2,
αc = (1/ deq)0.4 (Q/Av)0.6
But has error in units
4.67
No forced draughtN
o fo
rced
dra
ught
Effect of projection above window
a
b
c
abc
d
e
a-b-c = Lf a-b-c-d-e = Lf and wa = a b
Vertical cross section: Deflection of flame due to balcony
No forced draughtN
o fo
rced
dra
ught
If the wall does not exist on top of the window or heq>1.25wt
- The flame height LL reduced by Wa
- The projection of flame in horizontal direction LH with the above LL is increased by Wa
Forced draughtFo
rced
dra
ught
Forced Draught
Burning Rate
With ample ventilation known as the free burning condition τF is determined by the burning characteristics of fire load, generally taken as 1200 sec.
The rate of burning is given by
Q = (Af qf,d)/τF = (Af qf,d)/1200
Fire compartment temperature, Tf
Tf = 1200((Af qf,d)/ 17.5 – e -0.00228Ω + To
Forced draughtFo
rced
dra
ught
Flame height
For general conditions the equation is simplified with u = 6 m/s as,
Forced draughtFo
rced
dra
ught
Flame height - Flame dimensions for through draught or forced draught
wt
wf
HL
h eq
heq
H
LL
Lf
Forced draughtFo
rced
dra
ught
Horizontal projection of flame
Comparing the previous equation, as the speed of wind increases, the horizontal projection increases as the height of flame decreases. It is independent of presence of wall above or not.
LH = 0.605 (u2/heq) 0.22 (LL + heq)
For simplified calculations, using u = 6 m/s,LH = 1.33 (LL + heq) / heq
0.22
Forced draughtFo
rced
dra
ught
Flame widthIn forced draught, the flames tend to widen outwards with hot gases away from the opening as shown in the figure above. The width of flame is given bywf = wt + 0.4 LH
Flame length along axisThe length of flame along axis, Lf, from tip of flame to the window is found using simple Pythagoras formulaLf = (LL
2 + LH2)1/2
Temperature of flame at windowTw = 520 / (1- 0.3325 Lf (Av) 1/2 / Q) + To; with Lf Lf (Av)1/2 / Q < 1 The flame emissivity at the window, εf = 1.0
Forced draughtFo
rced
dra
ught
The temperature of flame along axis
Lx is the length of axis at any point of calculation to the window.
Flame emissivity εf = 1 – e
Convective heat transfer coefficientαc =0.0098 (1/ deq)0.4 (Q/(17.5Av) + u/1.6)0.6
The simplified form of the above formula after the inclusion of wind speed, u = 6 m/s,αc = 0.0098 (1/ deq)0.4 (Q/(17.5Av) + 3.75)0.6
As per EN1991-1-2,
αc = (1/ deq)0.4 .............
But has error in units
9.80
Forced draughtFo
rced
dra
ught
Effect of projection above window - Deflection of flame due to balcony/awning
a
b
a
c
b
awning
a-b = L a-b-c = Lf f
The End