Civil Engineering Reference
In-Depth Information
advanced methods based on computational fl uid dynamics.
The remainder of this section deals with simple post-fl ashover
calculation models for establishing compartment time-
temperature response.
A number of attempts have been made to utilise the simpli-
city of the standard fi re curve and to relate actual fi re severity
to an equivalent period within a standard test. Time equiva-
lence is an extremely useful tool for demonstrating compliance
with regulations in a language clearly understood by building
control authorities. The basic concept considers equivalent
fi re severity in terms of the temperature attained by a struc-
tural element within a fi re compartment and the time taken to
achieve the same temperature in a standard fi re test. The con-
cept is illustrated in
Figure 11.4
. Alternative formulations con-
sider the normalised heat input from a standard furnace. The
vast majority of the research effort into time equivalence has
been initiated by the steel industry and the results are therefore
largely applicable to protected steel specimens. However, if
the data exist, there is no reason why the concept should not be
extended to cover other forms of construction.
The concept of time equivalence relates the severity of a real
compartment fi re in an actual building to an equivalent period
of heating in a standard furnace test. This equivalent period is
then compared with the design value of the standard fi re resist-
ance of the individual structural members, which must satisfy
the following relationship:
widely used is that in the fi re part of Eurocode 1 which is of
the form:
t
e,d
= (
q
f,d
×
w
f
×
k
b
) ×
k
c
(11.3)
where:
q
f,d
is the design fi re load density per unit fl oor area (MJ/m² )
k
b
is the conversion factor for the compartment thermal prop-
erties (min.m²/MJ)
w
f
is the ventilation factor
k
c
is a correction factor dependent on the structural material
Detailed guidance is available on the use of the method (Lennon
et al
., 2006).
The time equivalent method represents a sort of 'halfway
house' between nominal and natural fi re models to describe
severity in a language understood by designers, manufactur-
ers and regulators. A more rational approach is to consider
fi re behaviour purely in relation to the factors that infl uence
fi re growth and development independent of any reference to
standard test procedures. A number of simplifi ed models exist
to calculate the time-temperature response caused by a fi re
within a building compartment. The most commonly used and
widely validated method is the parametric approach set out in
the fi re part of the Eurocode 1 for Actions on Structures. The
temperature-time curves in the heating phase are given by:
t
e,d
<
t
, d
(11.2)
where,
t
e,d
is the design value of time equivalence and
t
, d
is the
design value of the fi re resistance of the member. A number of
methods are available to calculate time equivalence. The most
θ
g
= 1325(1 − 0.324
e
−0.2
t
*
− 0.204
e
−1.7
t
*
− 0.472
e
−19
t
*
)
(11.4)
where:
θ
g
= temperature in the fi re compartment
(ºC)
t *
= t.Γ
(h)
t = time
(h)
Γ = [
O
/
b
]
2
/(0.04/1160)
2
(-)
1200
Atmosphere (fire)
and should lie between 100 and 2200 (J/m² s
½
K)
ρλ
b
ρλ
c
=
Atmosphere
(furnace)
1000
O = opening factor (
A
(m
½
)
AAh
Ah
Ah
/
/
A
)
v
Ah
Ah
v
v
Ah
/
/
/
A
t
A
v
= area of ventilation openings
(m² )
Max. Steel Temp.
800
h = height of ventilation openings
(m)
A
t
= total area of enclosure (including openings) (m² )
600
Steel (fire)
ρ = density of boundary enclosure
(kg/m³ )
c = specifi c heat of boundary enclosure
(J/kgK)
400
λ = thermal conductivity of boundary
(W/mK)
Steel (furnace)
200
The theory assumes that temperature rise is independent of fi re
load. In order to account for the depletion of the fuel or for the
active intervention of the Fire and Rescue Service or suppres-
sion systems, the duration of the fi re must be considered. This
is a complex process and depends on the rate of burning of the
material which itself is dependent on the ventilation and the
physical characteristics and distribution of the fuel.
0
0
te
15
30
45
60
75
90
Time [mins]
Figure 11.4 Graphical representation of the concept of time
equivalence (t
e
)
