Design Formulae - Unprotected Steel Members

PrEN1993-1-2 (2003) and PD7974-3 (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 cross-section, the increase of temperature ΔΘ_{a, t} [K] in an unprotected steel member during a time interval Δt is given by:

(1)

where

ρa	is the unit mass of steel [kg/m3];
Am	is the surface area of the member per unit length [m2];
Am / V	is the section factor for unprotected steel members [m-1];
ca	is the specific heat of steel [J/kgK];
	is the net heat flux per unit area [W/m2];
ksh	is the correction factor for the shadow effect (ksh = 1.0 if the shallow effect is ignored);
Δt	the time interval [seconds];
V	is the volume of hte member per unit length [m3].

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 BS5950-8 (2003) and the “Yellow Book” published by the Association of Specialist Fire Protection (ASFP 2002).