FIRE DESIGN OF STEEL MEMBERS - Civil and Natural Resources ...

insulation has on the rise of the steel temperature. By assuming that the exterior
surface of the insulation is the same temperature as the surroundings, ie. the same
temperature as the fire, a heat transfer coefficient is not required. This method also
assumes that the steel is at the same temperature as the internal surface of the
insulation.
The change in temperature of protected steel over a time period is given by:
H
A
( k d ρ c )
p
∆ Ts
= i i s s
2.3
ρ
sc
s
ρ c
( T − T ) ∆t
f
s
s
1 H
2
d
A
ρic
p
s
+
i i
where d i is the thickness of the insulation (m)
ρ i is the density of the insulation
c i is the specific heat of the insulation
To perform the spreadsheet analysis, a table is set up similar to Figure 2.1, without
requiring the column for the heat transfer coefficient, and replacing equation 2.1 with
equation 2.3.
EC3 (1995), recommends a slightly different formula for equation 2.3, where a 3 is
used instead of the 2 in the brackets {}, and also includes an extra term to account for
the increase in fire temperature over the time step ∆t, (Buchanan, 1999). See Section
5.7 for more detail on alternative methods of estimating the temperatures of protected
steel by a time step method.
The middle term in brackets, {}, accounts for the heat or energy absorbed by the
insulation and is valid more for ‘heavy insulation’. To determine whether the
protection will absorb much heat as to significantly affect the temperature of the steel,
ECCS, (1985), suggests calculating whether the heat capacity of the insulation is more
than half the heat capacity of the steel, using the following formula:
ρ c A > 2ρ
c A
2.4
s
s
s
i
i
i
22