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doi: 10.1680/mosd.41448.0169
CONTENTS
11.1 Introduction 169
11.2 Compartment timetemperature response 169
11.3 Heat transfer 174
11.4 Mechanical (structural) response 178
11.5 Conclusion 180
11.6 References 180
ICE Manual of Structural Design: Buildings 2012 Institution of
Civil Engineers www.icemanuals.com 169
ice | manuals
11.1 IntroductionThe traditional means of ensuring compliance
with the require-ments of the Building Regulations for structural
fire safety is to rely on the results from standard fire tests on
individual elements or components. At the simplest level structural
fire engineering is based on simple prescriptive rules and guidance
which ensure sufficient passive fire protection is applied to
structural members or that minimum dimensions are satisfied to
ensure load-bearing capacity and/or the separating function is
maintained for a period corresponding to the recommended fire
resistance requirement from the regulatory guidance.
In this way, structural engineers have been involved in fire
engineering for many years without necessarily being aware of it
and most probably being unaware of the background to the
development of the regulations and the guidance that under-pins
them. For example, a structural engineer responsible for designing
a reinforced concrete framed building will specify the overall
dimensions, size and position of reinforcement dependent on the
ambient temperature design considerations in terms of loading and
environmental conditions. In the vast majority of cases, the
structural fire engineering will simply consist of checking in the
tables produced in BS 8110 Part 2 to ensure that the design meets
the minimum dimensions and minimum depth of cover to the
reinforcement for the specified fire resistance period.
Within this simple process there are a large number of impli-cit
considerations on the likelihood of a fire occurring: the
con-sequences in terms of life safety should a fully developed fire
occur, the thermal exposure within the fire compartment and the
consequent temperature distribution through the structural member.
To a large extent structural fire engineering design simply
consists of making explicit decisions rather than relying on the
implicit assumptions within the prescriptive approach.
The three-stage approach to structural fire engineering design
is illustrated schematically in Figure 11.1.
11.2 Compartment timetemperature responseThe first step in a
structural fire engineering design is to evalu-ate an appropriate
compartment timetemperature response to be used for the subsequent
heat transfer and structural response calculations. This initial
process can itself be further subdivided into two important
preliminary tasks: the choice of appropriate design fire
scenario(s) and the selection based on the design fire scenarios
adopted of an appropriate design fire.
11.2.1 Design fire scenario(s)
The appropriate design fire scenarios should be determined on
the basis of an overall fire risk assessment taking into account
the nature and distribution of fire load within the project and
the
Chapter 11
Structural fire engineering designTom Lennon Principal
Consultant, BRE Global, UK
The purpose of this chapter is to explain the methodology
underpinning the structural fire engineering design process.
Structural fire engineering design consists of three basic
components: choosing an appropriate design fire, using this
information to derive the temperatures of the structural elements
and assessing the structural behaviour with respect to the
temperatures derived. For each element of the structural fire
engineering design process there are a number of options available
to the designer depending on the complexity of the project, the
state of knowledge with regard to the structural material chosen
and the objectives of the fire engineering design strategy.
Detailed information on the design methodology in this area is
available in the Institution of Structural Engineers Guide to the
Advanced Fire Safety Engineering of Structures (2007).
Fire analysis (compartment timetemperature)
Heat Transfer Analysis (determination of material
temperatures)
Structural analysis (determination of mechanical response)
Figure 11.1 Three stages of structural fire engineering
design
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The principal choice facing the designer at this stage of the
process is whether to use a nominal fire curve or a natural fire
model to evaluate the compartment timetemperature response. Nominal
fires are representative fire curves for the purposes of
classification and comparison but bear no relation-ship to the
particular characteristics of the building under con-sideration.
Natural fires are calculation techniques based on a consideration
of the physical parameters specific to a particu-lar building or
fire compartment. Figure 11.3 illustrates the options available to
the designer when choosing to model com-partment time-temperature
behaviour.
11.2.2.1 Nominal fire curves
Nominal or standard fire curves are the simplest and most
com-monly adopted means of representing a fire. They have been
developed to allow classification and assessment of construc-tion
products using commercial furnaces. Although they do not represent
real fire scenarios they have been developed from experience of
real fires. A number of different curves exist. The choice of curve
for a particular situation will depend on the
presence of likely ignition sources and the impact of detection
and suppression systems.
The design fire scenarios selected will identify specific
com-partment geometries with their own associated fire loads and
ven-tilation conditions and should be based on a reasonable worst
case scenario. The choice of design fire scenario will dictate the
choice of the design fire to be used in subsequent analysis.
To take a simple example, an appropriate design fire sce-nario
within a medium rise residential building consisting of a number of
separate dwellings would be a fire within a single dwelling bounded
by fire resisting construction. Given the pres-ence of sufficient
oxygen for combustion, sufficient fire load and an ignition source
a fully developed fire within a single dwelling would be one design
fire scenario to be considered.
11.2.2 Design fire
For each design fire scenario adopted, a design fire will be
cho-sen that represents the likely risk within that area. Normally
the design fire is only applied to one fire compartment at a time,
i.e. in the example above it would not be normal practice to assume
that two dwellings were fully involved in a fire at the same time.
The extent of the fire to be considered will, to a large extent, be
governed by the compartmentation in place within the building.
This stage of the process involves the selection of an
appro-priate model representing the fire within the compartment
under consideration. In many cases, the type of occupancy will play
a major role in defining the type of model to be used. Given a fire
load and an ignition source there are three options in terms of
fire development: either (i) the fire is extinguished due to manual
or automatic suppression or lack of oxygen, (ii) the fire remains
localised due to a lack of oxygen or insufficient fuel load or
(iii) the fire becomes fully developed. For the designer, detection
and the active intervention of third parties (such as the Fire and
Rescue Service) are not taken into account, therefore the chief
consideration is to decide if the fire will remain local-ised or
grow into a fully developed fire. In terms of structural
considerations, the most serious situation is where flashover
occurs within the compartment and all combustible materials become
involved in the process. Such a situation would require the
adoption of a post-flashover fire model.
Combustion behaviour within a fire compartment is a com-plex
process involving a mass balance where the energy released from
combustion of the fire load is utilised in convective heat flow
through openings where hot gases inside the compartment are
replaced by incoming cold air, radiated heat flow through the
openings and heat losses to the compartment boundaries. For
uncontrolled compartment fires this complex process can be
simplified into a three phase behaviour characterised by the
transition point known as flashover. Compartment fire behav-iour is
illustrated schematically in Figure 11.2.
Localised fire models are available in codes and standards but
are not considered further here as, for structural fire
engi-neering it is the post-flashover situation which represents
the most serious threat to structural stability.
Time
FLASHOVER Naturalfire curve
Tem
pera
ture
Ignition - Smouldering Heating Cooling
Standardfire curve
Figure 11.2 Three phase fire behaviour
Available fire models
Nominal (standard) fire curves suitablefor the vast majority of
structures
Equivalent time of fire exposure
Parametric curves
Zone models
CFD analysis
Figure 11.3 Available options for modelling fire behaviour in
order of increasing complexity
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In addition to the problems associated with the relation-ship
between the standard thermal exposure and real fires, a number of
difficulties arise in extrapolating the results from standard tests
to predict structural behaviour under realis-tic conditions. The
geometric limitations of specimen size mean that it is not possible
to simulate complicated three-dimensional structural behaviour. No
allowance can be made during the test for the beneficial or
detrimental effects of restraint to thermal expansion provided by
the surrounding cold structure. The nature of the test means that
only ideal-ised end conditions can be used and only idealised load
levels and distributions are adopted. During a fire some degree of
load shedding will take place from the areas affected by fire to
the unheated parts of the building. In the standard test, no
allowance can be made for alternative load-carrying mecha-nisms or
alternative modes of failure that are a function of the building
rather than the element of structure. In particu-lar, the standard
fire test does not address the important role that connections play
in maintaining overall global structural stability.
A reliance on the results from standard tests and, in
par-ticular, the use of tabulated values for generic products has
retarded our understanding of structural behaviour in fires.
Structural fire engineering attempts to go beyond a blind reli-ance
on prescriptive guidance, to consider the physical char-acteristics
that contribute to fire development and evaluate the material and
mechanical response of the structure to the increase in
temperature.
Although the standard fire curve is the most well known a number
of other nominal curves exist for special circum-stances. These
include the external fire curve where the structural element is
subject to heating from flames emerg-ing from openings. For
situations such as petrochemical plants where the calorific value
of combustibles is signifi-cantly higher than the cellulosic
material assumed for normal building design a number of hydrocarbon
fire curves exist. In recent years a number of high profile tunnel
fires have caused great damage and loss of life. In such
applications an even more severe exposure than the hydrocarbon
curve may be appropriate to simulate the effect of a fire involving
large petrol tankers in a confined space. The most onerous exposure
has been developed in the Netherlands as the RWS curve which
reaches temperatures of 1350C. Other curves include the German RABT
curve which achieves a maxi-mum temperature of 1200C.
11.2.2.2 Natural fire models
All of the nominal fire curves discussed above are
post-flashover models of fire behaviour under various conditions.
They are models loosely based on observed behaviour in real fires
but are not based on any physical parameters. Natural fire models
are based on the physical parameters that influence fire growth and
development and range from simple models for both localised fires
and post-flashover fire behaviour to
end-use. Different curves are used for testing and assessment
depending on whether the structural element or product is to be
used in the construction of a normal building (office, dwelling,
etc.), the petrochemical or offshore industry or for tunnels.
The most well known and widely adopted nominal fire curve is the
so-called standard fire enshrined in National, European and
international standards. The standard fire curve is based on a
cellulosic (i.e. wood/paper/fabric) fire within a compartment and
is described by the following equation:
g = 20 + 345 log10 (8t + 1) (11.1)As with many other nominal
fire curves it is characterised by a steadily increasing
temperature and does not incorporate a descending branch or cooling
phase.
The standard curve has been adopted throughout the world for a
number of reasons: to provide evidence of regulatory compliance; to
assist in product development; and to provide a common basis for
research into the effect of variables other than temperature. As
such it has proved remarkably successful over a long period of
time. It has the advantage of familiar-ity for designers,
regulators and specifiers. The existence of a large body of test
data facilitates the continuing use of the standard curve and
enables tabulated data for generic materi-als to be developed. It
is simple to use and clearly defined and allows for a direct
comparison of the performance of products tested under nominally
identical conditions.
However, the standard fire test suffers from a number of
drawbacks when any attempt is made to extrapolate test results to
performance in real life situations. These drawbacks arise as a
consequence of simplistic assumptions regarding the thermal
exposure and the support and loading conditions of the test
spec-imen. Whilst the standard curve incorporates the transient
nature of fire development there is no direct relationship between
per-formance in a standard test and the duration of a real fire.
This is a source of some confusion as many observers conclude that
60 minutes fire resistance means that the element of structure will
survive for 60 minutes in a real fire. In reality, the element of
construction may perform satisfactorily for a longer or shorter
period depending on the severity and duration of the fire and the
boundary conditions and loading present in the building at the time
of the fire. The temperature within a furnace is relatively uniform
compared to the temperature within a real fire com-partment.
Spatial temperature differences (particularly during the growth
face) may lead to longitudinal and cross-sectional thermal
gradients within structural members that are not present during a
furnace test which in turn could lead to deformations not observed
during a standard test. For certain forms of con-struction, direct
flame impingement during a real fire may have important
implications which cannot be observed in a standard test. As
mentioned above, a real fire consists of three distinct phases. The
relative durations of these three phases may have a significant
impact on the performance of elements of structure. Such behaviour
cannot be addressed by an ever increasing curve where temperature
rises at a decreasing rate with time.
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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/m ) k b is the conversion factor for the compartment thermal
prop-
erties (min.m /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
timetemperature 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:
g = 1325(1 0.324 e 0.2 t * 0.204 e 1.7 t * 0.472 e 19 t * )
(11.4)
where:
g = temperature in the fi re compartment ( C) t* = t. (h) t =
time (h)
= [ O / b ] 2 /(0.04/1160) 2 (-) b cb cb c=b c b c b c and
should lie between 100 and 2200 (J/m s K) O = opening factor ( / )A
hA h( /A h( /( /A h( / Av t( /v t( /( /v t( /( /A h( /v t( /A h( /(
/A h( /v t( /A h( / Av tA (m
)
A v = area of ventilation openings (m ) h = height of
ventilation openings (m)
A t = total area of enclosure (including openings) (m ) =
density of boundary enclosure (kg/m ) c = specifi c heat of
boundary enclosure (J/kgK)
= thermal conductivity of boundary (W/mK)
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.
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:
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
Atmosphere (fire)Atmosphere(furnace)
1200
1000
800
600
400
200
00 15 30 45 60 75 90te
Steel (fire)
Tem
pera
ture
[deg
C]
Steel (furnace)
Max. Steel Temp.
Time [mins]
Figure 11.4 Graphical representation of the concept of time
equivalence (t e )
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limiting values. The temperaturetime curves for the cooling
phase are then given by:
g = max 625(t* t*max) for t*max 0.5(h) (11.6)
g = max 250(3 t*max)(t* t*max) for 0.5 < t*max < 2(h)
(11.7)
g = max 250(t* t*max) for t*max 2(h) (11.8)The relevant input
parameters for the parametric approach are illustrated
schematically in Figure 11.5.
The concept of time equivalence and parametric fire expo-sure is
illustrated by reference to a simple worked example below.
Time Equivalence Design information:Compartment in 4 storey
office buildingFloor area: Af = 6 m 6 m = 36 mDesign fire load
density: = 570 MJ/m (80% fractile value
for offices from PD 6688-1-2: 2007)Compartment construction:
roof formed from hollowcore
concrete slabs, walls and floor lined with plasterboard
The parametric approach is a relatively straightforward
cal-culation ideally suited for modern spreadsheets. It provides a
reasonable estimate of the average timetemperature response for a
wide range of compartments and represents a major advance compared
to a traditional reliance on nominal fires which bear little or no
relationship to a realistic fire scenario. The parametric fire
curves comprise a heating phase repre-sented by an exponential
curve up to a maximum temperature max occurring at a corresponding
time of tmax, followed by a linearly decreasing cooling phase.
The maximum temperature in the heating phase occurs at a time
given by:
tmax = max[(0.2 103 qt,d / Olim); tlim] (11.5)
where:
qt,d = qf,d Af / At
and tlim = 25 min for a slow fire growth rate, 20 min for a
medium fire growth rate and 15 min for a fast fire growth rate.
For most practical combinations of fire load, compartment
geometry and opening factor tmax will be in excess of these
Area of bounding
surfaces At
Area of ventilation Av
Height of ventilation openings h
Opening factor Avh/At = O
Density of compartment boundaries
Specific heat of
compartment boundaries c
Thermal conductivity
of compartment boundaries
Thermal properties b = (c)
Timetemperature response in heating phase
Fire load density qfd
Compartment floor area Af
Fire growth rateslow/medium/fast
qt,d = qf,d . Af/At tlim
tmax = max [(0.2x10-3.qt,d /O) ; tlim
Figure 11.5 Input values for parametric calculation
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The parametric time factor is a function of the opening factor O
and the thermal inertia b
= ( O / b ) 2 /(0.04/1160) 2 = (0.066/945) 2 /(0.04/1160) 2 =
4.1
Fire load
q f,d = 570 MJ/m q t,d = q f,d A f /A t = 570 36/153.6 = 133.6
MJ/m Maximum temperature will be at time
t max = (0.2 10 3 q t,d / O ) = 0.2 10 3 133.6/0.066 = 0.4 hours
(24min)
The heating and cooling phases can then be constructed using the
relevant formulae above to give the compartment time-temperature
response illustrated in Figure 11.6 .
11.3 Heat transfer Heat transfer analysis is undertaken to
determine the tempera-ture rise and distribution of temperature
within the structural members. Thermal models are based on the
acknowledged principles and assumptions of heat transfer. They vary
in complexity ranging from simple tabulated values to com-plex
calculation models based on fi nite difference or com-putational fl
uid dynamics. The heating conditions considered extend to cover
natural fi re scenarios. However, the validity of some of the
simpler methods and most of the tabular data is restricted to a fi
re exposure corresponding to the standard fi re curve.
Whatever model is adopted the analysis needs to consider
transient behaviour which covers:
Heat transfer within the element including conduction for solid
elements but also any radiative or convective components
particu-larly where the construction includes cavities and/or
voids.
Moisture migration.
Chemical reactions and phase changes.
In order to undertake the analysis, knowledge of material
prop-erties at elevated temperature is required specifi cally:
thermal conductivity;
specifi c heat;
density;
emissivity;
initial moisture content;
charring rate if appropriate.
As the guidance in this manual is aimed principally at
practis-ing structural engineers the fundamental theory is not
consid-ered and the focus is on tabulated data and simple
calculation
Ventilation area A v = 3.6 m 2 m = 7.2 m Height of compartment H
(m) = 3.4 m Total area of enclosure A t = (2 6 6) + (4 3.4 6) =
153.6 m Opening factor O = A v h / A t = 7.2 2 / 153.6 = 0.066 m
1 Calculation: Ventilation factor: w f = (6/ H ) 0.3 [0.62 + 90(0.4
v ) 4 ] 0.5 v = A v / A f = 7.2/36 = 0.2 (this is within the limits
in the
Eurocode) giving w f = 1.95 Thermal properties of compartment
linings: The factor k b is
dependent on the thermal inertia of the construction materials
as defi ned by the factordependent on the thermal inertia of the
construction materials
b cb cb c=b c b c b c where: = density (kg/m ) c = specifi c
heat (J/kgK) = thermal conductivity (W/mK) Although no information
on the thermal properties of com-
monly used construction materials is provided in the Eurocode
(or the National Annex and associated NCCI), some guidance is
available in the literature. Table 11.1 sets out the appropriate
values for the current case taken from published data.
The b value to be used for design is a weighted average where b
= b j A j /A j . Here the relevant b value = 945J/m s K . From
Table B.1 of the NCCI this corresponds to a value of k b = 0.07 .
Note: If no detailed information is available on the thermal
properties of the compartment linings or if there are uncertainties
about the fi nal construction or changes may be made over the
course of the buildings design life then the default value of k b =
0.09 should be used.
The equivalent time of fi re exposure is then given by:
t e,d = 570 1.95 0.07 = 78 min (11.9)
The above example of a corner offi ce compartment is used to
illustrate the parametric approach.
Design information:
Floor area A f = 36 m
Design fi re load density = q f,d = 570 MJ/m
Opening factor O = 0.066 m -1
Thermal inertia b = 945 J/m s K
Table 11.1 Thermal properties of compartment linings
Construction Material Thermal inertia (b value J/m s K with b =
c )
Area (m )
Ceiling Concrete 2280 36
Floor Plasterboard 520 36
Walls Plasterboard 520 76.8
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11.3.1 Concrete
For materials with a high thermal conductivity (such as steel)
it is generally possible to ignore thermal gradients within the
member and assume a uniform temperature. However, for concrete
members having a low thermal con-ductivity and including free and
chemically bound mois-ture, the calculation of heat transfer to the
structure can be very complex. A number of different methods may be
used to derive the temperature distribution within the member.
Eurocode 2 includes a number of temperature profiles for slabs,
beams and columns with the temperature profile for slabs also being
applicable to walls subject to heating from one side. The
temperature profiles are presented for specific fire resistance
periods and are therefore applicable only to a heating regime
corresponding to a standard fire exposure. In principal, the
calculation methods for which the temperature profile is input data
could be used to determine performance due to different thermal
exposure but there are no validated test data to support this.
11.3.2 Structural steel
Steel loses both strength and stiffness with increasing
tem-perature. It should be borne in mind that the determination of
strength reduction factors for hot rolled steel is dependent not
only on the material but also on the test method, the heat-ing rate
and the strain limit used to determine steel strength. The
differences between test data are significant. The British
models. The structural Eurocodes provide methods for
deter-mining temperature distributions subject to certain
conditions. The thermal modelling approaches set out in the
Eurocodes are summarised in Table 11.2.
Heat transfer methods for materials that incorporate free
moisture should consider the effect of moisture migration with time
through the member in order to provide an accurate predic-tion of
the temperature of the element with time. This is gener-ally
accomplished through the incorporation of mass transfer in the
model providing additional information on the pressure field due to
steam production which, in certain cases, may influence the
tendency of a material to spalling. For many simple models, the
influence of moisture is either implicitly included (empiri-cal
models and tabulated data) or conservatively ignored.
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
1.20Time (hrs)
Tem
p (C
)
HeatingCooling
Figure 11.6 Parametric curve
Table 11.2 Thermal modelling options in the structural
Eurocodes
Eurocode Material Tabular data
Simple model
Advanced model
EN 1992-1-2 Concrete Yes No Yes
EN 1993-1-2 Steel No Yes Yes
EN 1994-1-2 Composite (steel and concrete)
Yes Yes Yes
EN 1995-1-2 Timber No Yes No
EN 1996-1-2 Masonry Yes Yes Yes
EN 1999-1-2 Aluminium No Yes Yes
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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 a,t for an
unprotected member during a time interval t is given by:
a t a t a t a t sh m
a aa anet dk k
A V A V mA Vm m A V m c
h t h t neh tnet dh tt d, ,, ,a t, ,a t sh, ,sh ne, ,net d, ,t
dc, ,c/A V/A V A V / A V sec= = = sh = sh m = m k = k h t= h t h t
= h t ne h t ne = ne h t ne t d h t t d = t d h t t d fo= fo= r 5r
5tr 5t= r 5= = r 5= t= tr 5t= t (11.10)
where
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
k
A V
A VA V
A V
sh
m bA Vm bA V
mA VmA V
m bA Vm bA V
mA VmA V
=
09[ /A V[ /A Vm b[ /m bA Vm bA V[ /A Vm bA V ]m b]m b/A V/A
V
[ /A V[ /A Vm b[ /m bA Vm bA V[ /A Vm bA V ]m b]m b/A V/A V
(11.11)
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
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
550 C 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).
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ICE Manual of Structural Design: Buildings 2012 Institution of
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periods for different types of masonry. For insulation pur-poses
the calculation of the temperature rise of the unexposed face is
reasonably well understood and the Eurocode includes
temperature-dependent material properties for use in thermal
modelling. However, the issue of free and chemically bound water
needs to be addressed to be able to accurately refl ect the delay
in reaching temperatures signifi cantly above 100 C. Other issues
that need to be considered include the presence of voids in hollow
masonry blocks and ancillary products (such as metal wall ties)
leading to localised areas of high conduction.
11.3.5 Aluminium
Although not readily associated with fi re resistant structural
design, BS EN1999-1-2 provides guidance on the use of simple and
advanced calculation models for aluminium structures subject to fi
re. The code effectively utilises many of the proce-dures set out
in BS EN1993-1-2 in terms of the calculation of heat transfer to
external members (Annex B), and in the verifi -cation methods
related to aluminium temperature development and calculation of the
resistance of cross-sections. The most signifi cant difference
between the two codes is that the thermal and structural material
property data only extend up to 500 C at which point the strength
and stiffness of aluminium is zero. The reduction in strength with
temperature for aluminium depends on the specifi c alloy adopted.
Figure 11.7 illustrates the lower range of values for the 0.2%
proof strength ratios for the alloys covered in the Eurocode.
rise a,t of a protected steel member during a time interval t is
given by:
a ta tp p
p a aag t g t a t a t
g tg t
A Vp pA Vp pd cp ad cp a
t e t e
,a t,a t, ,g t, ,g t a t, ,a t
/ / / g t,g t
/ (A V/ (A V )
( /( / )
( ) ( ) ( ) t e( )t e t e ( ) t e / ( ) /
=
t e t e ( ) ( ) t e ( ) t e t e ( ) t e
1 3( /1 3( /( /1 3( /( /+( /1 3( /+( /
( ) 1 ( ) 10 10 ( ) 10 ( )
(11.12)
With a,t 0 and
=c
cd A V
p pp p
a aa ap pd Ap pd A /
where
p is the thermal conductivity of fi re protection material
[W/mK];
a,t is the steel temperature at time t [ C]; g,t is the ambient
gas temperature at time t [ C]; g,t is the increase of ambient gas
temperature during time
interval t [K];
a is the unit mass of steel [kg/m 3 ];
p is the unit mass of fi re protection material [kg/m 3 ];
A p / V is the section factor for steel members insulated by fi
re protection material [m 1 ];
A p is the appropriate area of fi re protection material per
unit length [m 2 ];
c a is the temperature-dependent specifi c heat of steel
[J/kgK];
c p is the temperature-independent specifi c heat of fi re
pro-tection material [J/kgK];
d p is the thickness of fi re protection material [m];
t is the time interval [seconds];
V is the volume of the member per unit length [m 3 ].
11.3.3 Composite steel and concrete construction
The European fi re design standard for composite construc-tion
provides a conservative estimate of the temperature rise in
composite slabs through tabulated data treating the composite slab
as if it were a solid slab. The temperatures at a distance x from
the underside of the exposed slab are related to specifi c standard
fi re resistance periods in Table 11.3 .
11.3.4 Timber and masonry
In general there is no need to determine the temperature
distri-bution through a timber structural element as capacity is
related to a residual undamaged section below the char layer where
the material is assumed to maintain its ambient temperature
prop-erties in terms of strength and stiffness. The important
aspect in this case is the calculation of the depth of
charring.
The fi re part of Eurocode 6 provides tables of minimum
dimensions to achieve specifi ed periods of fi re resistance; it
also includes time-temperature graphs for various fi re
resistance
Table 11.3 Temperature distribution in a solid normal weight
concrete slab of 100 mm thickness. Data taken from BS EN 1994-1-2.
Permission to reproduce extracts is granted by BSI
Depth x (mm)
Temperature c ( C) for standard fi re resistance ofR30 R60 R90
R120 R180 R240
5 535 705
10 470 642 738
15 415 581 681 754
20 350 525 627 697
25 300 469 571 642 738
30 250 421 519 591 689 740
35 210 374 473 542 635 700
40 180 327 428 493 590 670
45 160 289 387 454 549 645
50 140 250 345 415 508 550
55 125 200 294 369 469 520
60 110 175 271 342 430 495
80 80 140 220 270 330 395
100 60 100 160 210 260 305
(Note: for lightweight concrete the values may be reduced to 90%
of those given) For the temperature of the reinforcement and the
temperature of the steel decking the Eurocode presents a method
based on the use of coeffi cients to determine the temperature for
specifi c periods of fi re resistance.
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178 www.icemanuals.com ICE Manual of Structural Design:
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250 300 350 400 450 500temperature deg C
0.2%
pr
oo
f str
engt
h ra
tio
Figure 11.7 0.2% strength ratios (lower limits) for aluminium
alloys
11.4 Mechanical (structural) responseOnce the thermal analysis
has been carried out to ascertain the compartment atmosphere
temperatures and the heat transfer to the structure has been
completed it is then necessary to assess the effect of the
increased temperatures on the resistance of the structural members.
In reality, steps 2 and 3 of the fire engin-eering design (heat
transfer and structural response) will gen-erally be undertaken in
tandem, with the rules for calculating or looking up member
temperatures within the same standards as the rules for evaluating
member capacities.
The most comprehensive suite of design standards for undertaking
structural fire engineering design are the struc-tural Eurocodes.
The fire codes cover actions on structures exposed to fire as well
as design procedures for concrete, steel, composite steel and
concrete, timber, masonry and alu-minium. All these codes have now
been published by BSI for use in the UK along with a National Annex
setting out Nationally Determined Parameters for those areas where
National choice is allowed. Before looking at the methods for
determining structural response it is necessary to look at the
relationship between design loading at ambient tempera-ture and the
design load case for the ultimate limit state for the accidental
design situation of a fire. This is the subject of the next
section.
11.4.1 Load effects at the fire limit state
Traditional design procedures for steel structures are based on
limiting the temperature rise of the steel section to a set value
generally termed the critical temperature for steel. Similarly
tabulated values in the National code for the fire design of
con-crete structures specify minimum cover distances to ensure that
the temperature of the reinforcement does not exceed a specified
limiting value. Such methods are independent of the load applied
under fire conditions and offer simplified often conservative
solutions to the majority of fire design scenarios.
The development of structural fire engineering has high-lighted
the importance of load in determining the fire resist-ance of
structural elements. A major change in the design methodology for
steel structures in fire came about with the publication in 1990 of
BS 5950 Part 8. Although this code is still based on an evaluation
of the performance of structural steel members in the standard fire
test it allows architects and engineers an alternative approach of
designing for fire resist-ance through calculation procedures. It
recognises that there is no single failure temperature for steel
members and that structural failure is influenced not only by
temperature but also by load level, support conditions and the
presence or other-wise of a thermal gradient through and/or along
the member. The code allows for the consideration of natural fires
but does
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Structural fire engineering design
ICE Manual of Structural Design: Buildings 2012 Institution of
Civil Engineers www.icemanuals.com 179
G permanent action (dead load)
P relevant representative value of a pre-stressing action (where
present)
Ad design value of an accidental action
1 factor for frequent value of a variable action
2 factor for quasi-permanent value of a variable action
Qk characteristic value of a single variable action (Qk,1 is the
characteristic value of the leading variable action often the
imposed load)
In the fire situation, Ad is the effect of the fire itself on
the struc-ture, i.e. the effects of restrained thermal expansion,
thermal gra-dients, etc. However, where the design is based on the
standard fire situation then such indirect actions need not be
considered.
EN 1990 allows the use of either 1 or 2 with the main vari-able
action. EN 1991-1-2 recommends the use of 2. However, the UK
National Annex for use with EN 1991-1-2 specifies 1 to be used in
the UK. The value of the partial factors for specific types of
occupancy and design situations is shown in Table 11.4.
It is important to understand the significance of the reduced
partial factor for imposed loading and the effect that this has on
different structural forms. Effectively a reduction in the imposed
load will increase the fire resistance of the structural member.
Consequently those forms of construction where the imposed load is
a relatively high proportion of the total load (such as steel frame
construction) may be able to reduce the levels of fire protection
required by taking advantage of the spare capacity in the member.
Conversely for those forms of construction (such as reinforced
concrete) where the imposed load is a relatively small proportion
of the total load the poten-tial benefits of a fire engineering
solution taking into account residual capacity are limited. The
relationship between the
not provide any detailed information or guidance. Load fac-tors
and material strength factors specific to the fire limit state are
given. These are partial safety factors which deal with the
uncertainties inherent in probabilistic distributions for loading
and material properties and represent reductions from ambient
temperature design in recognition of the small probability of
excessive loads being present at the same time as a fire occurs. In
2003, BS5950 Part 8 was updated to provide consistent information
with the fire part of Eurocode 3.
The national code for the design of concrete structures, BS 8110
Part 2, did not reflect the important role that load level plays in
determining performance under fire conditions. Load effects are
allowed for in Eurocode 2 for the tabulated data for concrete
structures with dimensions dependent on load level for columns and
load-bearing walls.
An accurate assessment of the performance of a structural member
during a fire requires knowledge of both the reduction in material
properties with increasing temperature and an accu-rate assessment
of the loads acting on the structure at the time of the fire. Load
effects can have a significant impact on the fire resistance of a
structure and this is reflected in the requirement for realistic
load levels to be in place during standard fire tests. As material
properties reduce with increasing temperature the load-bearing
failure criterion is reached when the residual strength of the
element equals the load applied. Load level can also have a
significant impact on other types of construction such as timber or
light steel framing that rely on sacrificial linings for fire
resist-ance. Increased loading leads to increased deflections at
the fire limit state which can cause gaps to open between panels
thereby compromising the assumed level of fire protection.
Loads are factored and a number of load cases considered for the
ambient temperature situation to account for uncertain-ties and the
potential for adverse conditions. Fire in terms of the Eurocode
system is an ultimate limit state accidental action and, as such,
is subject to specific partial factors that reflect the reduced
likelihood of the full ambient temperature design loading being
present at the same time as a fire occurs. In the European system
in order to determine the calculation of the load effects at the
fire limit state the designer must be familiar with the Basis of
Design EN 1990 which provides the required load combinations and
with the fire part of the Eurocode for Actions on Structures EN
1991-1-2 which, in addition to spe-cifying the fire design to be
adopted also specifies the mechan-ical actions for structural
analysis. In particular, EN 1991-1-2 specifies the partial factor
for imposed (assuming leading vari-able action) loading for the
fire limit state. Fire loading is an ultimate limit state
accidental design situation of the form:
Ed = E (Gk,j; P; Ad; (1,1 or 2,1)Qk,i) for j 1; i > 1
(11.13)
where
E the effect of actions (Ed is the design value of the effect of
actions)
Table 11.4 Values of partial factors (fi) to be used for the
accidental fire limit state. Data taken from BS EN 1990. Permission
to reproduce extracts is granted by BSI
Action 1 2
Imposed loads in buildings 0.5 0.3
Category A: domestic, residential 0.5 0.3
Category B: office areas 0.7 0.6
Category C: congregation areas 0.7 0.6
Category D: shopping areas 0.9 0.8
Category E: storage areas 0.7 0.6
Category F: traffic area, 30 kN 0.5 0.3Category G: traffic area,
30160 kN 0 0
Category H: roofs
Snow load: H 1000m a.s.l. 0.2 0Wind loads on buildings 0.2 0
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180 www.icemanuals.com ICE Manual of Structural Design:
Buildings 2012 Institution of Civil Engineers
A knowledge of the reduction in material strength and stiffness
at elevated temperature and familiarity with reduction factors to
be used for given temperatures.
A detailed breakdown of the various calculation methods
avail-able is beyond the scope of this publication.
11.5 Conclusion Many structural engineers will be unfamiliar
with the principles of structural fi re engineering design. In
recent years, a number of specialist consultants have emerged
offering fi re engineering solutions, largely for prestigious
projects where the potential benefi ts of adopting a fi re
engineering design approach out-weigh the additional design cost to
the client. There is a funda-mental lack of understanding of the
principles of structural fi re engineering design. In reality, the
design methodology, as set out in the fi re parts of the structural
Eurocodes, is based on the principles adopted for normal
temperature design. One of the aims of this simplifi ed guidance is
to demystify the subject so that it can be readily understood and
used by structural engi-neers familiar with the underlying
principles and assumptions of design for the ambient temperature
condition.
11.6 References Association for Specialist Fire Protection
(2007). Fire Protection for
Structural Steel in Buildings , 4th edn. Aldershot: ASFP.
Institution of Structural Engineers (2007). Guide to the
Advanced
Fire Safety Engineering of Structures . London: ISE. Lennon , T.
, Moore , D. B. , Wang , Y. C. and Bailey , C. G. (2006).
Designers Guide to EN1991-1-2, EN1992-1-2, EN1993-1-2 and
EN1994-1-2: Handbook for the Fire Design of Steel, Composite and
Concrete Structures to the Eurocodes . London: Thomas Telford.
11.6.1 Standards and statutory instruments BSI (August 1985).
Structural Use of Concrete Part 2: Code of
Practice for Special Circumstances . London: BSI, BS 8110- 2.
BSI (May 1987). Fire Tests on Building Materials and Structures
Part
20: Method for Determination of the Fire Resistance of Elements
of Construction (General Principles) . London: BSI, BS 476- 20.
BSI (November 1999). Fire Resistance Tests Part 1: General
Requirements . London: BSI, BS EN 1363- 1.
BSI (2002). Eurocode Basis of Structural Design . London: BSI,
BS EN 1990 :2002.
BSI (November 2002). Eurocode 1: Actions on Structures Part 12:
General Actions Actions on Structures Exposed to Fire . London:
BSI, BS EN 1991- 1-2.
BSI (March 2003). Application of Fire Safety Engineering
Principles to the Design of Buildings Part 1: Initiation and
Development of Fire within the Enclosure of Origin (Sub-system 1) .
London: BSI, PD 7974- 1:2003.
BSI (2003). Structural Use of Steelwork in Building Part 8: Code
of Practice for Fire Resistant Design . London: BSI, BS 5950-
8:2003.
BSI (December , 2004). Eurocode 5: Design of Timber Structures
Part 12: General Rules Structural Fire Design . London: BSI, BS EN
1995- 1-2:2004.
reduction factor fi and the ratio of the dead and imposed loads
is illustrated in Figure 11.8 where:
fi
fik fk f i kk fi kk f
G k G k Q kG QG Qk fG Qk fk fG Qk f i kG Qi kk fi kk fG Qk fi kk
fG Q G Q G k G Q G k Q kG QQ k Q k G Q Q k
=G Q+G Qk fG Qk f+k fG Qk fG Q+G Q G Q + G Q
,
, ,Q k, ,Q k
1
1 1Q k1 1Q kQ kG QQ k1 1Q kG QQ k, ,1 1, ,Q k, ,Q k1 1Q k, ,Q k
(11.14)
with:
Q k,1 = characteristic value of the leading variable action
(imposed load)
G k = characteristic value of a permanent action (dead load)
G = partial factor for permanent actions (1.35) Q,1 = partial
factor for variable action 1 (1.5) = combination factor (= 0.5 for
residential and offi ce appli-
cations from UK National Annex to EN 1991-1-2)
11.4.2 Calculation methods
A number of calculation methods are available ranging from
simple tabulated data through to advanced numerical methods.
Advanced numerical methods which consider nonlinear behav-iour at
elevated temperature require specifi c areas of expertise and in
general would not be available to practising structural engi-neers.
The fi re parts of the structural Eurocodes include tabulated data
and simplifi ed calculation methods which can be used by engineers
familiar with ambient temperature design procedures. The nature of
the calculation procedures is determined in part by the current
state of knowledge with respect to the behaviour of the specifi c
construction materials at elevated temperature. However, there are
some common principles that apply to all materials. Simple
calculation methods are based on:
A knowledge of the design procedures at ambient temperature.
An understanding of the partial factors for load effects to be
used at the fi re limit state.
3.00.0 0.5 1.0 1.5 2.0 2.50.2
0.3
0.4
0.5
0.6
0.7
0.8
Q k,1/ G k
fi
Figure 11.8 Relationship between reduction factor fi and ratio
of dead and imposed loads for values of the partial factor for the
fi re situation fi
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Structural fire engineering design
ICE Manual of Structural Design: Buildings 2012 Institution of
Civil Engineers www.icemanuals.com 181
11.6.2 Recommended readingBuchanan, A. H. (2002). Structural
Design for Fire Safety. Chichester:
John Wiley.Drysdale, D. (2002). An Introduction to Fire
Dynamics, 2nd edn.
Chichester: John Wiley.Franssen, J. M. and Zaharia, R. (2005).
Design of Steel Structures
Subjected to Fire. University of Liege.Lennon, T. (2011).
Structural Fire Engineering Design. London:
Thomas Telford/IHS BRE Press.Purkiss, J. A. (2007). Fire Safety
Engineering Design of Structures,
2nd edn. Oxford: Butterworth Heinemann.
11.6.3 Useful
websiteswww.access-steel.com/www.concretecentre.com/technical_information/performance_and_
benefits/fire_resistance/concrete_fire_forum.aspx
www.eurocodes.co.ukwww.istructe.org/Pages/default.aspxwww.mace.manchester.ac.uk/project/research/structures/strucfire/www.steelinfire.org.uk/
BSI (February, 2005). Eurocode 2: Design of Concrete Structures
Part 12: General Rules Structural Fire Design. London: BSI, BS
EN1992-1-2:2004.
BSI (April, 2005). Eurocode 3: Design of Steel Structures Part
12: General Rules Structural Fire Design. London: BSI, BS
EN1993-1-2:2005.
BSI (June 2005). Eurocode 6: Design of Masonry Structures Part
12: General Rules Structural Fire Design. London: BSI, BS
EN1996-1-2:2005.
BSI (December 2005). Eurocode 4: Design of Composite Steel and
Concrete Structures Part 12: General Rules Structural Fire Design.
London: BSI, BS EN1994-1-2:2005.
BSI (April 2007). Eurocode 9: Design of Aluminium Structures
Part 12: Structural Fire Design. London: BSI, BS
EN1999-1-2:2007.
BSI (June, 2007). Background Paper to the UK National Annex to
BS EN1991-1-2. London: BSI, Published Document PD
6688-1-2:2007.
International Organization for Standardization (1975). Fire
Resistance Test Elements of Building Construction. Geneva: ISO, ISO
834.