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

ρ s is the density of steel (kg/m 3 )
c s is the specific heat of steel (J/kg K)
∆t is the time step (min)
Using an initial time step of 1 minute gives a temperature of the steel of 20°C for 2
minutes before the curve starts to rise, which makes comparisons at the start of the test
difficult. The time steps can be made smaller to allow slightly greater accuracy and a
quicker reaction to the rise in atmospheric temperatures. In this report the time step is
reduced to 0.2 minutes, (12 secs) for the first 2 minutes, then increased to 0.5 minutes,
(30 seconds) for a further 4 minutes, and then increased to a final time step of 1
minute. This makes a significant difference to the temperature rise at the start of the
ISO 834 fire curve as the fire increases in temperature dramatically during the early
stages of the fire. Changing the time step in the early stages of the fire does not affect
the fire or steel beam temperatures during the latter stages of the fire.
The total heat transfer coefficient, h t , is the sum of the radiative and convective heat
transfer coefficients, h r and h c . The value of the convective heat transfer coefficient,
h c , used in this report is 25 W/m 2 K as recommended by the Eurocode for standard
fires, (Buchanan 1999). Since the radiative heat transfer depends on the temperatures
of the steel element and its surroundings, this component of the total heat transfer
coefficient must be calculated at each time step, using the following formula:
h
t
4 4
( T − T )
f
( T − T )
f
s
= 25 + σε 2.2
s
where σ is the Stefan-Boltzman constant (5.67 x 10 -8 kW/m 2 K 4 )
ε is the emissivity for the fire
The Eurocode recommends using a value of 0.56 for the emissivity, but for this project
a value of 0.5 has been used as this is the default setting in the SAFIR programme, and
is recommended by other authors (Martin and Purkiss, 1992)
2.1.3 Protected steel:
The method for determining the temperatures of the steel in beams that have fire
protection applied to them is very similar to that outlined in Section 2.1.2 for
unprotected beams, but with different formulas to account for the effect that the
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