Presentation for Tutorial Website - Brief Information on Eurocode 3 - Fire

1. Department of Civil and Structural Engineering HEAT TRANSFER TO EXTERNAL STEELWORK Eurocode 3 Design of Steel Structures BS EN 1993 Part 1-2:2005 General rules – Structural fire design

2. Content of BS EN 1993-1-2 CONTENT

3. Heat transfer to structural elements Column not engulfed in flame Column engulfed in flame HEAT TRANSFER Beam not engulfed in flame Beam fully or partially engulfed in flame

5. All openings in the fire compartment are assumed to be rectangular.

6. Determination of parameters such as compartment fire temperature, size and temperature of flames projecting out of the window, convection and radiation characteristics as per Annex B in EN 1991-1-2.

7. Elements distinguished as member engulfed or not engulfed in flame depending on the relative position with respect to the openings

8. Radiative heat transfer for an element which is not engulfed with flame projecting out from the windows.

9. Convective heat transfer when element is engulfed with flame and also heat transfer by radiation of flame engulfing it and also from compartment opening. ASSUMPTIONS

10. Heat Balance Member not engulfed in flame Average steel temperature Tm [K] is found by iterative solution of the σ Tm4 + α Tm = Iz + If + 293α Where, σ Stefan Boltzmann constant taken as 56.7x10-12 kW/m2K4 α Coefficient for heat transfer by convection [kW/m2K] IzHeat flux by radiation from the flames [kW/m2] If Heat flux by radiation from the opening [kW/m2] HEAT BALANCE

11. Heat Balance Member engulfed in flame Average steel temperature Tm [K] is found by iterative solution of σ Tm4 + α Tm = Iz + If + α Tz Where, Tz Temperature of flame [K] IzHeat flux by radiation from the flames [kW/m2] If Heat flux by radiation from the opening [kW/m2] HEAT BALANCE

13. Beam not engulfed in flame

14. Column engulfed in flame

15. Beam fully or partially engulfed in flameHEAT BALANCE

16. Heat transfer If = ϕfεf (1-az) σ Tf4 Where, Φf Overall configuration factor for heat transfer by radiation from the opening for that member εf Opening emissivity az Flame absorptivity Tf Fire temperature [K] Opening Emissivity εfmust be taken as 1. Flame absorptivity azis calculated depending on the type of the member and the situation. Radiative heat flux If HEAT TRANSFER

17. Configuration factors To find temperatures of external members, all radiating surfaces are assumed to be rectangular in shape. A rectangular envelope is drawn outer to the member cross-section receiving the heat transferred by radiation The ϕ value must be determined at the midpoint P at each and every face. CONFIGURATION FACTORS Envelope P P P P P P P

18. Configuration factors 1. Receiving surface in a plane parallel to the radiating surface CONFIGURATION FACTORS a = h/s; b = w/s s distance between P and X h Radiating surface zone height w zone width

19. Configuration factors 2. Receiving surface in a plane perpendicular to radiating surface CONFIGURATION FACTORS

20. Configuration factors 3. Receiving surface in a plane at an angle θ to the radiating surface CONFIGURATION FACTORS

21. Overall configuration factors Overall configuration factor for an opening OVERALL CONFIGURATION FACTORS dicross section dimension of member face i Ci Coefficient for protection for member with face i Ci = 0 for a protected face Ci = 1 for an unprotected face Configuration factor ϕf,i for a member with face i must be taken zero when the opening is not visible.

22. Overall configuration factors Overall configuration factor for flame OVERALL CONFIGURATION FACTORS Configuration factor becomes zero when the flame is not visible to the memberface taken into consideration. Heat screen can be used to protect the member face. When a member face isimmediately near to wall of the compartment, then it is considered as protected when there is no gap in that part of wall. Rest of the member faces are considered to be unprotected.

23. Member face numbering Beam Column Beam 2 Column 3 4 Member face numbering 1 1 3 4 Envelope 2 Envelope 1 and 2 are perpendicular to radiator 3 and 4 are parallel to radiator 4 out of sight to radiator Column face numbering - Plan Beam face numbering - Section

24. Member dimensions - Column Column Column d 1 d (3) Member dimensions - Column 1 (3) d d 2 (4) (2) 2 s s Column opposite opening Column between opening

25. Member dimensions - Beam Beam Beam (2) d d 1 1 (4) (4) d d (3) (3) 2 2 Member dimensions - Beam s Beam parallel to wall Beam perpendicular to wall

26. Column not engulfed in flame Column not engulfed in flame Column not engulfed in flame

27. Column not engulfed in flame Radiative heat transfer - Column opposite opening Openings Flames No forced Draught: Column placed opposite an opening Column not engulfed in flame Openings Flames Forced Draught: Column placed opposite an opening

28. Column not engulfed in flame Radiative heat transfer - Column opposite opening Heat flux due to radiation when the column is placed opposite to a window opening Iz = ϕzεz σ Tz4 Where, ϕzOverall configuration factor for flame heat of column εzFlame emissivity Tz Temperature of flame [K] Column not engulfed in flame

29. Column not engulfed in flame Radiative heat transfer - Column opposite opening 2h/3 Equivalent front rectangle z 2h/3 Column Column not engulfed in flame Column Section Plan No forced draught: Wall above and h < 1.25w

30. Column not engulfed in flame Radiative heat transfer - Column opposite opening x 2h/3 Equivalent front rectangle z 2h/3 Column not engulfed in flame Column x Column Section Plan No forced draught: Wall above and h > 1.25w or no wall above

31. Column not engulfed in flame Radiative heat transfer - Column opposite opening x Equivalent front rectangle x h z Column not engulfed in flame w + 0.4x Column Column Forced draught

32. Column not engulfed in flame Radiative heat transfer - Column between opening n openings m openings Flame side m Flame side n No forced Draught: Column placed opposite an opening Column not engulfed in flame n openings m openings Flame side m Flame side n Forced Draught: Column placed opposite an opening

33. Column not engulfed in flame Radiative heat transfer - Column between opening Heat flux due to radiation when the column is placed between window openings Iz = (ϕz,mεz,m + ϕz,nεz,n) σ Tz4 Where, ϕz,mOverall configuration factor for flame heat of column on side m ϕz,nOverall configuration factor for flame heat of column on side n εz,mTotal flame emissivity on side m εz,mTotal flame emissivity on side n Column not engulfed in flame

34. Column not engulfed in flame Radiative heat transfer - Column between opening 2h/3 Equivalent side rectangle z 2h/3 Column not engulfed in flame Column Column Section Plan No forced draught: Wall above and h < 1.25w

35. Column not engulfed in flame Radiative heat transfer - Column between opening x 2h/3 z 2h/3 Equivalent side rectangle Column not engulfed in flame Column Column Section Plan No forced draught: Wall above and h > 1.25w or no wall above

36. Column not engulfed in flame Radiative heat transfer - Column between opening x x s s h w + 0.4s Column not engulfed in flame Column Equivalent side rectangle Column Section Plan Forced draught

37. Column not engulfed in flame Flame Emissivity - Column opposite an opening Emissivity of flame εz when a column is placed opposite an opening is given by using the flame thickness λ at the top of opening. In case when there is no balcony or awning, flame thickness is given as ‘No forced draught’ λ = 2h/3 ‘forced draught’ λ = xbut λ hx/z h, x and z are taken as per Annex B of EN 1991-1-2 Column not engulfed in flame

38. Column not engulfed in flame Flame Emissivity - Column between two openings Total emissivities εz,m and εz,n when a column is placed between two openings is given by using the flame thickness λ as follows For side m: For side n: Where, m number of openings on side m n number of openings on side n λi flame thickness for opening i, which is taken as equal to the width of the opening or window, wi in ‘no forced draught’ condition. Column not engulfed in flame

39. Column not engulfed in flame Flame thickness ‘No forced draught’ λ = wi ‘forced draught’ λ = wi + 0.4s Where, wi Opening width s horizontal distance taken perpendicular from wall of the compartment to the centreline of the column Column not engulfed in flame

40. Column not engulfed in flame Temperature of flame,Tz ‘No forced draught’ l = h/2 ‘Forced draught’ l = 0 column opposite an opening l = sX/xcolumn between openings, where l is distance on the flame axis to distance s measured from the wall of compartment. Column not engulfed in flame Flame absorptivity, az ‘No forced draught’ - taken as zero. ‘Forced draught’ - equal to the emissivity of flame εz.

41. Beam not engulfed in flame Beam not engulfed in flame Beam not engulfed in flame

42. Beam not engulfed in flame Heat transfer by radiation Bottom of beam does not go below the top level of the opening The two ways of beam orientation with respect to the external - Beam parallel to compartment wall - Beam perpendicular to compartment wall Beam not engulfed in flame

43. Beam not engulfed in flame Average steel temperature, Tm – Beam parallel to wall Is calculated at a point on the beam directly above the centre of the opening. Iz = ϕzεz σ Tz4 Where, ϕz Overall configuration factor of flame opposite to the beam εz Emissivity of flame Tz Temperature of flame Beam not engulfed in flame

44. Beam not engulfed in flame Average steel temperature, Tm – Beam perpendicular to wall Is calculated at every 100mm distance along the length of the beam. Iz = (ϕz,mεz,m + ϕz,nεz,n ) σ Tz4 Where, ϕz,m Overall configuration factor of beam heated by flames on side m ϕz,n Overall configuration factor of beam heated by flames on side n εz,m Emissivity of flames on side m εz,n Emissivity of flames on side n Tz Temperature of flame Beam not engulfed in flame

45. Beam not engulfed in flame Emissivity of flame, εz- Beam parallel to wall In case when there is no balcony or awning, flame thickness is given as ‘No forced draught’ λ = 2h/3 ‘Forced draught’ λ = xbut λ hx/z h, x and z are taken as per Annex B of EN1991-1-2 Beam not engulfed in flame

46. Beam not engulfed in flame Emissivity of flame, εz,m and εz,n- Beam perpendicular to wall For side m: For side n: Where, m number of openings on side m n number of openings on side n λi opening width Beam not engulfed in flame

47. Beam not engulfed in flame Flame thickness - λi ‘No forced draught’ λi = wi ‘Forced draught’ λi = wi + 0.4s Where, wi Opening width s horizontal distance taken to the point on beam from wall of the compartment Beam not engulfed in flame

48. Beam not engulfed in flame Beam not engulfed in flame Equivalent side rectangle 2h/3 Beam z 2h/3 Equivalent front rectangle Beam not engulfed in flame Beam Equivalent front rectangle Section Plan No forced draught: Wall above and h<1.25w

49. Beam not engulfed in flame Beam not engulfed in flame x Equivalent side rectangle 2h/3 Beam z 2h/3 Beam not engulfed in flame Equivalent front rectangle Beam Equivalent front rectangle Section Plan No forced draught: Wall above and h>1.25w or no wall above

50. Beam not engulfed in flame Beam not engulfed in flame Equivalent side rectangle x x Beam z h s w + 0.4s Equivalent front rectangle Beam not engulfed in flame Beam Equivalent front rectangle Section Plan Forced draught

51. Beam not engulfed in flame Flame temperature, Tz ‘No forced draught’ l = h/2 ‘Forced draught’ l = 0 beam parallel to external wall on top of opening l = sX/xbeam perpendicular to external wall with no awning on top of opening, where l is distance along the flame axis to distance s measured from the wall of compartment. Beam not engulfed in flame Flame absorptivity, az ‘No forced draught’ - is taken as zero. ‘Forced draught’ - equal to the emissivity of flame εz.

52. Column engulfed in flame Column engulfed in flame Column engulfed in flame

53. Column engulfed in flame Radiative heat flux Iz with, Iz,1 = C1 εz,1 σ Tz4 Iz,2 = C2 εz,2 σ Tz4 Iz,3 = C3εz,3 σ To4 Iz,4 = C4 εz,4 σ Tz4 where, Iz,i Heat flux due to radiation on column due to flame εz,1 Flame emissivity with respect to face i of the column i indicator for column face Ci Coefficient of protection for face i Tz Temperature of flame To Temperature of flame at opening Column engulfed in flame

54. Column engulfed in flame Column engulfed in flame d λ λ 1 3 4 λ d λ 3 1 4 λ 1 d 2 Column Column engulfed in flame Flame λ 2 Column Flame Section Plan Forced draught

55. Column engulfed in flame Column engulfed in flame d λ 3 1 λ d λ 3 1 4 λ 1 d Flame Axis 2 Column Flame Column engulfed in flame λ λ 2 4 Column Flame Section Plan No forced draught condition

56. Column engulfed in flame Column engulfed in flame d λ 1 3 λ d λ 3 1 4 λ 1 d Flame Axis 2 Flame Column λ Column engulfed in flame λ 2 4 Column Flame Section Plan Forced draught: Flame axis intersects column axis above top of opening

57. Column engulfed in flame Column engulfed in flame d λ 1 3 λ d λ 3 1 4 λ 1 d Flame Axis 2 Flame Column λ Column engulfed in flame λ 2 4 Column Flame Section Plan Forced draught: Flame axis intersects column axis above top of opening

58. Column engulfed in flame Emissivity of flames εz,ifor each face of column is found from ε stated in Annex B, EN 1991-1-2, replacing flame thickness λ with dimension λi Temperature of flame Tz No forced draught’ l = h/2 Forced draught’ l = (λ3 + 0.5 d1) X/x but l 0.5hX/z, where l is distance along the flame axis to the level where λ1 is measured with condition that there is no balcony or awning above the opening. Flame absorptivity az Where εz,1 ,εz,2 andεz,3 are the emissivities of flame for column faces 1, 2 and 3. Column engulfed in flame

59. Beam fully or partially engulfed in flame Beam fully or partially engulfed in flame Beam fully or partially engulfed in flame

60. Beam fully or partially engulfed in flame Radiative Heat Transfer Assumptions Beams bottom not going below the top level of the adjoining opening There are two separate cases, - Beam parallel to the fire compartment wall - Beam perpendicular to the fire compartment wall Beam fully or partially engulfed in flame

61. Beam fully or partially engulfed in flame Beam engulfed in flame – No forced draught d λ λ 1 λ λ 4 3 d 4 3 1 λ 2 d 2 Beam fully or partially engulfed in flame λ 1 Opening Flame Compartment wall Section Elevation Beam perpendicular to wall Beam parallel to wall

62. Beam fully or partially engulfed in flame Beam engulfed in flame – No forced draught d d λ λ λ 1 1 4 3 3 λ 2 d h d 2 z 2 Beam fully or partially engulfed in flame λ λ 1 1 Flame Flame Section Section Top of flame below top of beam Beam immediately adjacent to wall

63. Beam fully or partially engulfed in flame Beam engulfed in flame – Forced draught d λ Upper surface of flame 1 3 λ 4 λ 2 d d 2 Beam fully or partially engulfed in flame 2 λ 1 λ 1 λ d 3 1 Flame Flame Section Section Beam not adjacent to wall Beam immediately adjacent to wall

64. Beam fully or partially engulfed in flame The average temperature Tm Found at a point along the length of beam just above the midpoint of opening when the beam is parallel to the external wall. In the case of beam perpendicular to the external wall is found by taking maximum of calculated values at every 100mm along the length of beam. Heat flux due to radiation Iz due to flame is found by with, Iz,i heat flux due to radiation Iz from flame to beam face i i Indicator for face of beam Beam fully or partially engulfed in flame

65. Beam fully or partially engulfed in flame The average temperature Tm Found at a point along the length of beam just above the midpoint of opening when the beam is parallel to the external wall. In the case of beam perpendicular to the external wall is found by taking maximum of calculated values at every 100mm along the length of beam. Heat flux due to radiation Iz due to flame is found by with, Iz,i heat flux due to radiation Iz from flame to beam face i i Indicator for face of beam Beam fully or partially engulfed in flame

66. Beam fully or partially engulfed in flame No forced draught - Flame above the top of the beam and when the flame is below the top of beam. Following equations are used when top of flame is over the upper part of beam Iz,1 = C1 εz,1 σ To4 Iz,2 = C2 εz,2 σ Tz,24 Iz,3 = C3 εz,3 σ (Tz,14 + Tz,24)/2 Iz,4 = C4 εz,4 σ (Tz,14 + Tz,24)/2 where, εz,i emissivity of flame for face i of the beam To Temperature at opening Tz,1 Temperature of flame at bottom level of beam Tz,2 Temperature of flame at top level of beam Beam fully or partially engulfed in flame

67. Beam fully or partially engulfed in flame No forced draught In case the beam is parallel and directly adjoining the compartment wall, C4 is taken equal to zero. In case top of flame reaches only below the beam top, Iz,1 = C1 εz,1 σ To4 Iz,2 = 0 Iz,3 = (hz/d2) C3 εz,3 σ (Tz,14 + Tx4)/2 Iz,4 = (hz/d2) C4 εz,4 σ (Tz,14 + Tx4)/2 where, Tx Temperature of flame at tip [813 K]. hzHeight of the flame top measure from beam bottom. Beam fully or partially engulfed in flame

68. Beam fully or partially engulfed in flame Forced draught In the case of forced draught condition - Beams placed directly adjoining to the external wall, or - Beam placed not directly adjoining to the external wall When the beam is placed parallel to the wall and away from the wall or even when the beam is perpendicular to the wall following equations are used Iz,1 = C1 εz,1 σ To4 Iz,2 = C2 εz,2 σ Tz,24 Iz,3 = C3 εz,3 σ (Tz,14 + Tz,24)/2 Iz,4 = C4 εz,4 σ (Tz,14 + Tz,24)/2 Beam fully or partially engulfed in flame

69. Beam fully or partially engulfed in flame Forced draught If a beam is positioned parallel and directly adjoining to the compartment wall, the bottom face is considered engulfed in flame, while on one side and top of beam is only exposed to radiative heat transfer from the upper portion of the frame. Iz,1 = C1 εz,1 σ To4 Iz,2 = ϕz,2 C2 εz,2 σ Tz,24 Iz,3 = ϕz,3 C3 εz,3 σ (Tz,14 + Tz,24)/2 Iz,4 = 0 Where ϕz,i configuration factor relative to the upper portion of the flame, for face i of the beam, from Annex G in EN 1991-1-2. Beam fully or partially engulfed in flame

70. Beam fully or partially engulfed in flame Emissivity of flame εz,i Flame emissivity εz,i for each face of beam if found using the formula stated in Annex B of 1991-1-2, using flame thickness λi corresponding to each face of the beam. Flame Absorptivity Absorptivity of flame az is found by using the expression az = 1 – e-0.3h Beam fully or partially engulfed in flame

71. The End