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

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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

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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

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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

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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

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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

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dra

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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

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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

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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

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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

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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

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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