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

∆T
s
ki
=
dics
p
s
H
p
A
where φ is as defined above, and
step.
( T − T )
f s
∆t
− e
1+
φ
3
φ
10
−1∆T
f
2.8
∆ T
f
is the change in fire temperature over the time
The time step limit in seconds for this case can be defined as follows:
c
∆ =
s s
A
t
ρ 1 φ + < 60 2.9
k
i
3 H
p
A time shift is often used to account for the delay time provided by the presence of the
insulation which would allow for the heat capacity of the insulation, as in the time that
it takes the insulation to heat up. This time shift can be described by either of the
methods shown below:
or
φ
A
cs
ρ
sdi
φ
t =
1
+
from Wickstrom 2.10a
8 H
p
ki
3
φ
A
cs
ρ
sdi
φ
t =
1
+
from Melinek and Thomas 2.10b
6 + 2φ
H
p
ki
3
The differences between these two equations can be seen in Figure 2.3 below:
1000
800
600
400
Spreadsheet
200
ENV 1993-1-2
0
0 20 40 60 80 100 120 140
-200
Time (min)
ENV 1993-1-2 spreadsheet
Figure 2.3: Comparison between the EC3 formula, equation 2.8, and the spreadsheet method
This method give results that are very close to those found from the spreadsheet
method. The ENV formula gives a slight dip at the start of the test similar to the curve
from the ECCS equation, but of much smaller magnitude. The curve then follows the
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