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The surface of a structural member exposed to
a fire is subject to heat transfer by convection and radiation.
Generally, the radiation is more dominant than the convection after
the very early stages of the fire. The thermal actions can be represented
by the net heat flux to the surface of the member.
On the fire exposed surfaces, the net heat flux  [W/m2]
considering heat transfer by convection and radiation can be determined
by:
For non-fire exposed (unexposed) surfaces of members
subjected to partial heating conditions, such as the unexposed
side of walls and slabs, heat will transfer from the member to
the boundary as the member will have a higher temperature. The
heat transfer analysis according to Eq.(1) can be applied, considering
different boundary conditions. The following modifications in the
heat transfer can be considered (Purkiss 1996):
- For a surface exposed to ambient conditions, the gas temperature
is taken to be equal to ambient temperature with both radiation
and convection heat transfer considered.
- Alternatively, for a surface exposed to ambient conditions,
a fixed temperature equal to ambient temperature can be imposed
on the boundary nodes of the surface.
- For a surface with insulation, the boundary can be treated
as a no heat-flow condition.
It is worth noting that the heat transfer to the
boundary has an important effect on the thermal response of the
region within the members close to the unexposed surface. The effect
is smaller in the region close to the fire exposed surface.
Convection
The net heat flux  [W/m2]
due to convection is given by:
 |
(2) |
where
| αc |
is the coefficient of heat transfer by convection as given
in Table 1 [W/m2K]; |
| Θg |
is the gas temperature in the vicinity of the fire exposed
member [°C]; |
| Θm |
is the surface temperature of the member [°C]. |
Table
1 Convection coefficients αc according
to EN1991-1-2 (2002)
|
| Fire model or exposed condition |
αc[W/m2K] |
| Standard fires |
25
|
| External fires |
25
|
| Hydrocarbon fires |
50
|
| Parametric fires |
35
|
| Unexposed side of separating members |
| -withough radiation |
4
|
| -with radiation |
25
|
Radiation
The exact formula for the heat flux due to radiation
is complicated, in which the parameters involved depend on the
type of surface, the type of flame and the temperature. For simplicity,
EN1991-1-2 (2002) provides an approximation of the net heat flux
[W/m2] due to radiation as follows:
 |
(3) |
where
| εf |
is the emissivity of the fire (=1.0); |
| εm |
is the surface emissivity of the member (see Table 2); |
| Φ |
is the configuration factor (≤ 1.0); |
| Θr |
is the effective radiation temperature of the fire environment
[°C]; |
| σ |
is the Stephan Boltzmann constant (=5.67 × 10-8 W/m2K4). |
Table 2 Emissivity
of materials according to Eurocodes
|
| Material |
Emissivity εm |
Reference |
| Carbon steel |
0.7
|
prEN1993-1-2 |
| stainless steel |
0.4
|
prEN1993-1-2 |
| Concrete |
0.7
|
EN1992-1-2 |
| Others |
0.8
|
EN1991-1-2 |
The configuration factor Φ takes into account
of varying radiative heat flux levels on the fire exposed surface
of the members depending on the position and shallow effects. Annex
G (informative) of EN1991-1-2 gives the method for calculating
the value of Φ, which will be discussed in the next section.
Conservatively, Φ can be taken as 1.0.
Configuration Factor
Annex G (informative) of EN1991-1-2 (2002) provides
the simple method for calculating the configuration factor Φ for
the determination of the thermal actions for external members.
The configuration factor Φ measures the fraction
of the total radiative heat leaving a radiating surface that arrives
at a receiving surface, depending on the size of the radiating
surface and the distance and the orientation between the two surfaces
(see
Figure 1).
Basically, the value Φ of for a member surface
exposed to a fire depends on two effects:
- Position effect – the position and the size of the
fire
- Shadow effect – the radiation from other parts of
the member
The radiative heat transfer to a convex member
surface is determined by the position effect, whereas the transfer
to a concave surface is determined by both the position and shadow
effects.
The assumptions made in the calculation of Φ for
an external member include:
- All radiating surfaces are taken as rectangles in shape,
including windows and other openings in fire compartment walls
and the equivalent rectangular surfaces of flames.
- The value of Φ is determined for the mid-point P of
each face of a rectangular envelope drawn around the cross-section
of the member receiving the radiative heat transfer, as shown
in Figure 2. This accounts for the
shadow effect in an approximate way.
The calculation procedure Φ of is explained
in the following steps:
- Choose a point P on the member.
- Locate the point X on the radiating surface by drawing a horizontal
line perpendicular to the receiving surface from P to the plane
containing the radiating surface. The distance s from P to X
is the shortest distance from P to the receiving surface.
- Divide the receiving surface into different zones by drawing
a horizontal and a vertical line through X. Normally, it contains
four zones if the whole radiating surface is visible from P as
shown in Figure
3(a). It will only contain two zones if the radiating surface
is only partially visible as shown in Figure
3(b).
- The Φ of the receiving surface is the sum of the contributions
from each visible zone on the radiating surface.
- If X lies outside the radiating surface, the effective Φ is
determined by adding the contributions of the two extending rectangular
zones from X to the farther side of the radiating surface, then
subtracting the contributions of the two rectangular zones extending
from X to the nearer side of the radiating surface.
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