The section factor Am/V
The section factor is the ratio between the surface exposed to fire Am and the volume V of the member, per unit length, in m−1. A slender section, with a large surface relative to its mass, heats up quickly; a massive one, slowly.
| Section | Am/V |
|---|---|
| I/H section exposed on all sides | perimeter / area |
| I/H section exposed on 3 sides (under a slab) | (perimeter − top flange width) / area |
| Hollow section exposed around its full perimeter | outer perimeter / area ≈ 1 / t |
EN 1993-1-2 (cl. 4.2.5, Table 4.2) gives the expressions for each case. The value should not be taken less than 10 m−1.
Shadow factor ksh
For I/H sections, the zones between the flanges receive less radiation. This is accounted for by the shadow factor (cl. 4.2.5.1):
For hollow sections exposed around the full perimeter, ksh = 1. Taking ksh = 1 is always conservative.
Heating of unprotected steel
The temperature increase of the steel over a time interval Δt (cl. 4.2.5.1):
- ḣnet is the net heat flux, by convection and radiation, from EN 1991-1-2 (cl. 3.1), with steel emissivity εm = 0.7.
- ca is the specific heat of steel, temperature-dependent, with a sharp peak around 735 °C (the phase change of steel).
- ρa is the density of steel, 7850 kg/m³.
Heating of protected steel
For a member with fire protection (cl. 4.2.5.2):
- Ap/V is the section factor of the protected member: contour (paint, sprayed coating applied to the section) or box (boards).
- λp, cp and ρp are the thermal conductivity, specific heat and density of the protection material.
- dp is the protection thickness, in metres.
How the protection thickness is determined
- Calculate the critical temperature θa,cr of the member.
- Take the required duration from the fire resistance class (for example 90 min for R 90).
- The required thickness is the smallest thickness dp for which the steel temperature at the end of the required duration stays below θa,cr.
The thermal properties of protection products come from their tests (the EN 13381 series), declared by the manufacturer. For intumescent paints, manufacturers usually provide thickness tables directly, by section factor and critical temperature.
Informative material summarising the provisions of EN 1993-1-2 and EN 1991-1-2. It does not replace the text of the standards, the protection manufacturer's documentation or verification by a qualified engineer.