PrEN199312 (2003) and PD79743 (2003) provide
a similar approach for calculating the thermal response of unprotected
steel members. This approach can be extended to other metals including
wrought iron, cast iron, aluminium alloys and stainless steels.
The temperature rise in a metal member subjected
to a fire is largely dependent on its section factor (A_{m }/
V). The larger the section factor, the more rapidly a member
increases in temperature. Members with a small section factor have
a slow rate of temperature rise, and in some cases they have sufficiently
large thermal capacity that they do not require any additional
fire protection.
Assuming an equivalent uniform temperature distribution
in a crosssection, the increase of temperature ΔΘ_{a,
t} [K] in an unprotected steel member during a time interval Δt
is given by:

(1) 
where
ρ_{a} 
is the unit mass of steel [kg/m^{3}]; 
A_{m} 
is the surface area of the member per unit length [m^{2}]; 
A_{m} / V 
is the section factor for unprotected steel members [m^{1}]; 
c_{a} 
is the specific heat of steel [J/kgK]; 

is the net heat flux per unit area [W/m^{2}]; 
k_{sh} 
is the correction factor for the shadow effect (k_{sh} =
1.0 if the shallow effect is ignored); 
Δt 
the time interval [seconds]; 
V 
is the volume of hte member per unit length [m^{3}]. 
For cross sections with a convex shape, such as
rectangular or circular hollow sections, fully embedded in fire,
the shadow effect does not play role and it can be taken as k_{sh} =
1.0. Otherwise, the correction factor for the shadow effect k_{sh} is
given by:

(2) 
where A_{m} / V ≥ 10m^{1};
and [A_{m} / V]_{b} is box value of the
section factor.
The section factor A_{m }/ V is
defined by both the geometry and configuration of members exposed
to fire. Figure
1 illustrates the section factors of some typical unprotected
steel members. The section factors associated with many common
steel members can be found in BS59508 (2003) and the “Yellow
Book” published by the Association of Specialist Fire Protection
(ASFP 2002).
