3.7 Design Fires
3.7.3 Eurocode Parametric Fires
The Eurocode 1 Part 1.2 (CEN, 2002b) gives an equation for ‘parametric’ fires, allowing a more realistic time–temperature relationship to be produced for any combination of fuel load, ventilation openings and wall lining materials. The Eurocode parametric fire curves have been derived to give a good approximation to the burning period of the Swedish curves shown in
1200
1000
800
600
400
200
00 30 60 90 120 150 180
Time (min)
Temperature (°C)
ISO 834 ASTM E119 External fire Hydrocarbon fire
Figure 3.19 Nominal time–temperature curves for post‐flashover fires
t* t (3.26) where t is the time (in hours), and
F F b b
v ref
ref
/ /
2
2
b is thermal inertia k cp (Ws0.5/m2K) and Fv is the ventilation factor (m0.5) given by:
Fv A H Av v/ t
Equation 3.25 is a good approximation to the ISO 834 standard fire curve for temperatures up to about 1300 °C. Hence the Eurocode parametric fire curve is close to the ISO 834 curve for the special case where Fv Fref and b bref. Larger ventilation openings or more highly insulated compartments will result in higher room temperatures. Smaller openings and poorly insulated compartments will result in lower temperatures. In the Eurocode, the value of Fref is 0.04 and the value of bref is 1160 such that
F b
v/ /
0 04 1160
2 2
. (3.27)
The above formulation of the parametric fire curve assumes that the walls and ceiling of the fire compartment are made from one layer of material, with thermal inertia k ρ cp. If there are two or more layers of different materials, the Eurocode gives a formula for calculating an effective value of the b term.
For a wall with material 1 on the fire side and material 2 protected by material 1, and thick- nesses s1 and s2 of the two layers, the thermal properties b k cp are called b1 and b2, respectively. If a heavy material is insulated by a lighter material such that b1 < b2 the value of the lighter material in layer 1 should be used in the calculations, so that b = b1. If a light material is covered by a heavier material (as in sandwich panel construction) such that b1 > b2
then the b value depends on the thickness of the heavier material and the time of the heating period of the fire. The limiting thickness slim,1 of the fire‐exposed material is calculated from:
s t k
lim cmax
p ,1
3600 (3.28)
where tmax is the time of the heating period of the fire (in hours) and the thermal properties are for material 1.
If s1 slim,1 then b b1, and if s1 slim,1 then b (s s1/ lim,1)b1 (1 s s1/ lim,1)b2.
3.7.3.2 Duration of Burning Period
For ventilation controlled fires, the duration of the burning period td (in hours) in the Eurocode simplifies to:
t e F E
d t v A H
v v
0 0002 0 0002
. .
/ (3.29)
where et is the fuel load (MJ/m2 total surface area) and E is the total energy content of the fuel (MJ).
For fuel controlled fire scenarios, the Eurocode sets the duration of burning tlim as 25, 20 or 15 min, depending on a slow, medium or fast fire growth rate, respectively. The typical fire growth rate in various occupancies (hence the duration of burning tlim) is given in Annex E of Eurocode 1 (CEN, 2002b), as shown in Table 3.5.
3.7.3.3 Decay Period
The Eurocode time–temperature relationship in the cooling phase of the parametric fire is given by:
T Tmax 625 t* tmax* x fortmax* 0 5. (3.30a) Table 3.5 Fire growth rate for different occupancies
Occupancy Fire growth rate Duration of burning (min)
Dwelling Medium 20
Hospital (room) Medium 20
Hotel (room) Medium 20
Library Fast 15
Office Medium 20
Classroom of a school Medium 20
Shopping centre Fast 15
Theatre (cinema) Fast 15
Transport (public space) Slow 25
Source: Adapted from Eurocode 1 Part 1.2 (CEN, 2002b).
T Tmax 250 3 tmax* t* tmax* x for0 5. tmax* 2 0. (3.30b) T Tmax 250 t* tmax* x fortmax* 2 0. (3.30c) where tmax* ( .0 0002 /e Ft v)
and x t t
t t t t
max lim
lim max max lim
1 0.
*
if / if with lim Fv lim
b
, / .
/ 0 04 1160
2
2 and Fv lim, 0 0001. e tt/lim tlim 25min,20min,15min 3.7.3.4 Time–temperature Curves
Figure 3.20 shows the Eurocode time–temperature equation plotted for a range of ventilation factors, fuel loads and materials. The temperatures in the burning period have been calculated from the equations described above, from Eurocode 1 Part 1.2 (CEN, 2002b). In each part of Figure 3.20, curves have been drawn for three fire loads and for two types of construction materials, showing the significant dependence of fire temperatures on the thermal properties of the bounding materials. The fire loads are 400, 800 and 1200 MJ/m2 floor area, for a room 5 × 5 m in plan and 3 m high. The materials are normal weight concrete (b = 1900 Ws0.5/m2 K) and gypsum plaster board (b = 522 Ws0.5/m2 K). A typical commercial office building with a
Temperature (°C)
Temperature (°C)
1400 1400
1200 1200
1000 1000
800 800
600 600
400 400
200 200
0 0
Time (min)
0 30 60 90 120 150 180 Time (min)
0 30 60 90 120 150 180
Concrete Concrete
Gypsum Gypsum Fv= 0.08
ISO 834 ISO 834
Fv= 0.12
Figure 3.20 Parametric time–temperature curves. Fuel load is 400, 800 and 1200 MJ/m2 floor area
mixture of these materials on the walls and ceiling would give curves between these two, similar to a building made from lightweight concrete.
It is observed that, with the exception of the fire in the room lined with gypsum and a 400 MJ/m2 fuel load, the fires with opening factors 0.02 and 0.04 have the same general shape for concrete or gypsum. The different descending branch is due to t*max for the 400 MJ/m2 case lying between 0.5 h and 2 h while the rest have t*max values greater than 2 h. For Fv = 0.08 and 0.12 there are instances with curves of different shapes. This is because the relative amounts of ventilation are higher so that the fire becomes fuel controlled and therefore burns more rapidly. The temperatures are therefore dictated by the rapid fire growth rates (from Table 3.5);
their maximum temperatures are recorded at the time tlim.