Civil Engineering Reference
In-Depth Information
Steel data used in the National and European codes show that
for a temperature of 550°C structural steel will retain 60% of
its room temperature strength while the corresponding fi gure
obtained from the ECCS relationship for the same temperature
is closer to 40%. The use of the British Steel data is justifi ed
by their improved correlation with large-scale beam and col-
umn tests, both in terms of the heating rates and the strains
developed at the defl ection limits imposed by the standard fi re
resistance tests. This simplifi ed presentation does not itself
take into consideration the fact that values above unity exist
within the lower range of temperatures. The fi ne detail in the
temperature-dependent material properties is principally of
interest to those involved in the numerical modelling of mate-
rial and structural behaviour. What is abundantly clear is that
both strength and stiffness decrease with increasing tempera-
ture and that this reduction is particularly signifi cant between
400 and 700°C.
Because of the perceived poor performance of steel ele-
ments in fi re discussed above, the most common method of
'designing' for fi re is to design the steel structure for the ambi-
ent temperature loading condition and then to protect the steel
members with proprietary fi re protection materials to ensure
that a specifi c temperature is not exceeded or, in the light of the
discussion above, that a specifi ed percentage of the ambient
temperature loading capacity is retained.
Traditional fi re design methods for structural steel are based
on the concept of a single 'critical' temperature. Due to the
relationship between steel strength and temperature the fi g-
ure of 550ºC is generally adopted as the critical temperature
for steel. In reality there is no single critical temperature as
the capacity of the structure is a function of the load applied
at the fi re limit state. This is discussed further in the section
dealing with the calculation of the mechanical response of
structural elements.
The rate of increase in temperature of a steel cross-section
is determined by the ratio of the heated surface area (A) to the
volume (V). The ratio A/V is known as the section factor and
is analogous to the earlier concept whereby the rate of tem-
perature rise was related to the ratio of the heated perimeter
(H
p
) to the area of the section (A). A steel section with a large
surface area will be subject to a greater heat fl ux than one with
a smaller surface area. The greater the volume of the section
the greater will be the heat sink effect. Therefore, a small thick
section (such as a UC section) will heat up to a given tempera-
ture more slowly than a long thin section. In terms of applying
passive fi re protection the greater the section factor the greater
the thickness of protection required to limit the temperature of
the steel to a given temperature.
The most common method used in the UK to relate pro-
tection thickness to section factor for a given fi re resistance
period and a specifi ed critical temperature is the 'Yellow
Book' published by the Association for Specialist Fire
Protection (2007).
The European fi re design standard for steel structures
includes methods for calculating the temperature rise in both
unprotected and protected steel assuming a uniform tempera-
ture distribution through the cross-section. The increase of
temperature Δθ
a,t
for an unprotected member during a time
interval Δt is given by:
AV
AV
∆
m
AV
m
(11.10)
=
k
k
AV
m
m
m
AV
m
/
AV
AV
h
h
h
h
∆
∆
∆
∆
∆
∆
∆ fo
t
t
t
t
t
fo
r
r
∆
∆
∆
t
∆
t
≤
≤
5
t
sec
sh
td
at
at
ne
θ
at
at
k
sh
ne
netd
netd
td
t
at
,
at
,
sh
ne
,
netd
td
,
ρ
c
c
ρ
a
a
ρ
where
ρ
a
is the unit mass of steel [kg/m
3
] ;
A
m
is the surface area of the member per unit length [m
2
] ;
A
m
/
V
is the section factor for unprotected steel members [m
−1
] ;
c
a
is the specifi c heat of steel [J/kgK];
h
.
net,d
is the net heat fl ux per unit area [W/m
2
] ;
k
sh
is correction factor for the shadow effect (
k
sh
= 1.0 if the
shallow effect is ignored);
∆
t
is the time interval [seconds];
V
is the volume of the member per unit length [m
3
].
For circular or rectangular cross-sections fully engulfed by fi re
the shadow effect is not relevant and
k
sh
= 1.0 otherwise: for I
sections under normal fi le actions for the other cases
09[
AV
A
mb
AV
/
mb
A
mb
AV
A
mb
AV
m
mb
mb
A
mb
AV
AV
AV
AV
k
(11.11)
m
AV
m
AV
=
sh
[
AV
A
mb
AV
m
mb
A
mb
/
mb
A
mb
AV
mb
A
mb
AV
AV
AV
AV
m
AV
m
AV
In the above equation the value of
A
m
/ V
should not be used
if it less than 10 m
−1
. [
A
m
/ V
]
b
is the box value of the section
factor.
The
k
sh
correction for the 'shadow effect' accounts for the
fact that members with geometry similar to I and H sections
are shielded from the direct impact of the fi re in some parts of
the surface.
The above method requires integration with respect to time
with the calculated temperature rise substituted back into the
equation for each time step. This can be realised using a simple
spreadsheet based method. For greater accuracy temperature-
dependent values for specifi c heat and thermal conductivity
could be used (where known).
For protected members a similar procedure is adopted tak-
ing into account the relevant material properties of the pro-
tection material. The method is applicable to non-reactive fi re
protection systems such as board or spray protection but is not
appropriate for reactive materials such as intumescent coatings.
Assuming a uniform temperature distribution the temperature
