Design Formulae - Protected Steel Members

PrEN1993-1-2 (2003) and PD7974-3 (2003) provide a similar approach for insulated steel members with non-reactive fire protection materials. The insulating materials can be in the form of profiled or boxed systems, but do not include intumescent coatings. Assuming uniform temperature distribution, the temperature increase Δθ_{a, t} of an insulated steel member during a time interval Δt (= 30 sec) is given by:

but Δθa, t ≥ 0 if Δθg, t > 0

(1)

with

where

λp	is the thermal conductivity of fire protection material [W/mK];
Θa,t	is the steel temperature at time t [°C];
Θg,t	is the ambient gas temperature at time t [°C];
ΔΘg,t	is the increase of ambient gas temperature during time interval Δt [K];
ρa	is the unit mass of steel [kg/m3];
ρp	is the unit mass of fire protection material [kg/m3];
Ap/V	is the section factor for steel members insulated by fire protection material [m-1];
Ap	is the appropriate area of fire protection material per unit length [m2];
ca	is the temperature dependent specific heat of steel [J/kgK];
cp	is the temperature independent specific heat of fire protection material [J/kgK];
dp	is the thickness of fire protection material [m];
Δt	is the time interval [seconds];
V	is the volume of the member per unit length [m3].

Figure 1 illustrates some design values of the section factors A_p/V for insulated steel members. It is worth noting that the area Ap of the fire protection material is generally taken as the area of its inner surface. For hollow encasement with a clearance around the steel members, the value of A_p is taken as that for hollow encasement without a clearance.

Sketch	Description	Section factor Ap/V
	Contour encasement of uniform thickness
	Contour encasement of uniform thickness, exposed to fire on 3 sides
	Hollow encasement of uniform thickness (The clearance c1 and c2 < h/4)
	Hollow encasement of uniform thickness, exposed to fire on 3 sides (The clearance c1 and c2 < h/4)
Figure 1 Section factor for insulated steel members (EN1993-1-2: 2003)

For moist fire protection materials, the steel temperature increase ΔΘ_a may be modified to allow for a time delay td in the rise of the steel temperature when it reaches 100°C, due to the latent heat of vaporization of the moisture, as shown in Figure 2.

Figure 2 Evaluation of moisture plateau for protection materials (DDENV13381-4: 2002)

The calculation method for t_d is given in DDENV13381-4 (2002).

In PD7974-3, the time delay t_d is defined as the dwell time which can be approximated by:

(2)