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1. Department of Civil and Structural Engineering Annex B[informative] THERMAL ACTIONS FOR EXTERNAL MEMBERS Eurocode 1 Actions on structures BS EN 1991 Part 1-2:2002 General actions – Actions on structures exposed to fire

2. Thermal Calculation 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. Thermal Calculation

3. Usage conditions 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 conditions

4. Usage conditions 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 window Av,1 - summation of window area on side 1 W2 - wall width perpendicular to side 1 Usage conditions

5. Wind effect 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. Wind effect 45⁰ 135⁰ wind Flame deflection due to wind - Horizontal cross section

6. No forced draught 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 draught

7. No forced draught 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 draught

8. No forced draught Flame height 2h /3 2h /3 eq eq L L H H No forced draught L L L L w 2h /3 2h /3 t eq L eq L h 1 h 1 eq eq Flame dimensions – No through draught

9. No forced draught Flame width Flame 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 flame If a wall is present above window, then LH = heq/3 if heq1.25wt 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 draught

10. No forced draught Length of flame along axis When LL > 0 Lf = LL + heq/2 if wall exist above window or if heq1.25 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 window Tw = 520/(1-0.4725(Lf wt/Q))+To with Lf wt/Q < 1 Emissivity of flame at window The flame emissivity at window is taken as εf = 1.0 The temperature of flame along the axis Tz = (Tw – To)(1-0.4725(Lx wt/Q))+To with Lx wt/Q < 1 No forced draught

11. No forced draught 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 draught

12. No forced draught Effect of projection above window c e d b c No forced draught b a a a-b-c = Lf a-b-c-d-e = Lf and wa = a b Vertical cross section: Deflection of flame due to balcony

13. No forced draught 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 No forced draught

14. Forced draught 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 = (Afqf,d)/τF = (Afqf,d)/1200 Fire compartment temperature, Tf Tf = 1200((Afqf,d)/ 17.5 – e -0.00228Ω + To Forced draught

15. Forced draught Flame height For general conditions the equation is simplified with u = 6 m/s as, Forced draught

16. Forced draught Flame height - Flame dimensions for through draught or forced draught L H H L L h eq Forced draught w w f h t eq L f

17. Forced draught 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) / heq0.22 Forced draught

18. Forced draught Flame width In 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 by wf = wt + 0.4 LH Flame length along axis The length of flame along axis, Lf, from tip of flame to the window is found using simple Pythagoras formula Lf = (LL2 + LH2)1/2 Temperature of flame at window Tw = 520 / (1- 0.3325 Lf (Av) 1/2 / Q) + To; with LfLf (Av)1/2 / Q < 1 The flame emissivity at the window, εf = 1.0 Forced draught

19. Forced draught 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 coefficient αc=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 Forced draught As per EN1991-1-2, αc= (1/ deq)0.4 ............. But has error in units 9.80

20. Forced draught Effect of projection above window - Deflection of flame due to balcony/awning b Forced draught c awning a a b f f

21. The End