ISO/TR 12471:2004

TECHNICAL ISO/TR
REPORT 12471
First edition
2004-11-15
Computational structural fire design —
Review of calculation models, fire tests
for determining input material data and
needs for further development
Conception de calcul des feux de structures — État des travaux des
modèles de calcul et d'essais au feu pour la détermination des données
de base requises et des besoins du développement ultérieur

Reference number
©
ISO 2004
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ii © ISO 2004 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Internationally applied methods for structural fire engineering design . 1
2.1 Models for thermal exposure. 2
2.2 Models for structural behaviour . 6
[56]
3 Characteristics of a reliability-based structural fire engineering design . 7
3.1 Structural fire engineering design based on FORM approximation. 7
3.2 Structural fire engineering design based on practical design format. 10
[56]
4 Predictive model capabilities: uncertainties of design components . 13
5 Main components of structural fire engineering design. 17
5.1 Design fire exposure. 17
5.2 Thermal material properties and transient temperature state. 25
5.3 Mechanical material properties and structural behaviour. 29
6 Need for further development of calculation models and related computer programs
for structural fire design: Examples . 40
6.1 Complete process of structural fire design . 40
6.2 Main components of structural fire design . 41
6.2.1 Fire exposure. 41
6.2.2 Thermal and mechanical behaviour. 41
7 Need for fire tests to determine input material data for structural fire design. 42
7.1 Properties related to fire load density and fire exposure . 42
7.2 Thermal material properties. 43
7.3 Mechanical material properties . 44
Bibliography . 46

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 12471 was prepared by Technical Committee ISO/TC 92, Fire safety, Subcommittee SC 2, Fire
containment.
iv © ISO 2004 – All rights reserved

Introduction
Considerable advances have been made in recent years in understanding the behaviour of fires in their
development and impact upon buildings. Coupled with developments in computational techniques, it is now
possible to predict how structures will behave at the fire limit state (i.e. under fire conditions).
As a result of the high level of international fire research in recent decades, more and more components and
systems are becoming amenable to analytical and computer modelling. Considerable progress has been
made concerning such phenomena and procedures as:
 reaction of materials to fire;
 fire growth in a compartment;
 fully developed compartment fire;
 fire spread between buildings;
 fire behaviour of load-bearing and separating building structures;
 smoke filling in enclosures and smoke movement in escape routes and multi-storey buildings;
 interaction of sprinklers and fire, including sprinkler and fire venting interaction;
 process of escape; and
 systems approach to the overall fire safety of a building, in its most general form comprising fire
development models interacting with human response models.
This progress in fire research has led to consequent changes in the field of codes, specifications, and
recommendations for fire engineering. Some characteristic trends in these changes are:
a) improved connection to real fire scenarios;
b) increase in extent of design, based on functional requirements and performance criteria;
c) development of new test methods, that are, as far as possible, material-independent and related to well-
defined phenomena and properties;
d) increase in application of reliability-based analytical design;
e) extended use of integrated assessments; and
f) introduction of goal-oriented systems of analysis of total, active and passive fire protection for a building.
The most manifest verification of these developing trends probably relates to the fire engineering design of
load-bearing and separating structures. An analytical determination of the fire resistance of structural
elements is being approved by authorities in more and more countries as an alternative to the internationally
predominant design that is based on the results of the standard fire resistance test and connected
classification. The further step to permit a general practical application of an analytical design, based on a
natural compartment fire concept, was taken by Swedish authorities as early as 1967. Since then, a few other
countries have been officially open to the possibility of structural fire design.
A significant contribution was made by the Fire Commission of the Conseil International du Bâtiment, CIB
W14, in the form of a state-of-the-art report, in 1983. The report presented a conceptual approach towards a
[1]
probability-based design guide on structural fire safety , supplemented in 1986 by a model code/design
[2]
guide . These design guides are important aids in drafting corresponding national regulations and
recommendations. For European countries, the Eurocodes (see references [3] to [10] in the Bibliography)
issued as European Prestandards and supplemented with national application documents, certainly will
contribute to increased practical use of analytical structural fire design methods.
A problem arises between material-related codes and the general code. The material-related codes focus very
strongly on the fire design, based on thermal exposure according to the standard fire resistance test.
However, the general code, specifying the basis of design and mechanical and thermal actions on
fire-exposed structures, also gives some guidance, in the form of informative annexes, regarding the
alternate structural fire design, based on a parametric fire exposure determined by fire models or specified
temperature-time curves.
An analytical fire engineering design can now be performed in most cases for steel structures. Validated
material models for the mechanical behaviour of concrete under transient high-temperature
[11] to [13] [14] to [16]
conditions and thermal models for a calculation of the charring rate in wood exposed to fire ,
developed in recent decades, have significantly enlarged the area of practical application of an analytical
structural fire design. To support this application, design diagrams and tables have been computed and
published, giving directly, on the one hand, the temperature state of the fire-exposed structure, and on the
other, a further transfer to the corresponding load-bearing capacity of the structure, for instance see
references [17] to [47] in the Bibliography.
The following clauses begin with a summary of internationally applied methods for a structural fire engineering
design. With this survey as general background, the characteristics of a reliability-based approach are
described. In order to review the need for further development of calculation models and for fire tests to get
the input data required for the design, the design alternative, based on a simulated fire exposure, has been
chosen for presentation. For other design alternatives, applied in practice, the need for calculation models and
related input data is less comprehensive than for the more general approach being dealt with. The
presentation is followed by a discussion about uncertainty in the design process.
Following this background presentation of the reliability-based design process and its inherent uncertainties,
the remaining document is devoted to related deterministic models, comprising the fire exposure and the
thermal and mechanical behaviour of the structure. These models are supplemented with a survey of the
material input data required for the structural fire engineering design. Finally, conclusions are drawn regarding
the need for further development of calculation models and tests to determine the input material data required
for the structural fire design.

vi © ISO 2004 – All rights reserved

TECHNICAL REPORT ISO/TR 12471:2004(E)

Computational structural fire design — Review of calculation
models, fire tests for determining input material data and needs
for further development
1 Scope
This Technical Report gives a review of the advances that have been made in measuring and understanding
how structural materials respond to fire in terms of changes in their elevated temperature, and physical and
mechanical characteristics, and to identify areas where further work is necessary to generate the data
required. Analytical methods for heat transfer are combined with mechanical models to calculate structural
behaviour from single elements up to complete frames under real fire and ISO Standard furnace heating
conditions. This Technical Report reviews advances in computational analysis and indicates how these can be
used with probabilistic analysis to provide a risk-based approach to structural fire engineering design.
2 Internationally applied methods for structural fire engineering design
The methods available at present for a structural fire engineering design can systematically be characterized
[1] [2] [37]
with reference to the matrix according to Table 1 .
The matrix is based on two types of models for the thermal exposure of the structure (H1 and H2) and three
types of models for the mechanical behaviour of the structure (S1, S2 and S3).
Table 1 — Matrix of thermal exposure and structural behaviour models, characterizing available
methods for structural fire engineering design
Model for structure
S1 S2 S3
Element Substructure Complete structure
Model for thermal exposure
Nominal temperature-time curves
Calculation
Test or calculation
H1 exceptionally testing
(deterministic)
(deterministic)
Real fire
Calculation
Calculation Calculation (probabilistic) in
H2
(probabilistic) (probalistic) special cases and for
research
2.1 Models for thermal exposure
Model H1 describes the thermal exposure according to the standard fire resistance test of structural elements
[48]
as specified in the ISO 834 and in corresponding national standards, or according to some other nominal
[3]
temperature-time curve . A fire design, based on this thermal exposure, represents the internationally
prevalent situation for load-bearing and separating structural elements.
In the standard fire resistance test, the specimen is exposed in a furnace to a temperature rise that is
controlled so as to vary with time within specified limits according to the standard temperature-time curve
TT−= 345 log 8t+1 (1)
( )
to10
where
t is the time, in minutes;
T is the furnace temperature at time t, in °C;
t
T is the furnace temperature at time t = 0, in °C.
o
For calculations, it is normally more favourable to use the following expression for the standard temperature-
time curve
−−−0,2tt1,7 19t
TT−= 1025 1− 0,324e − 0,204e − 0,472e (2)
()
t o
that describes Equation (1) to a fairly high degree of accuracy, as shown in reference [49] in the Bibliography.
In Equation (2), then t is time, in hours.
Other nominal temperature-time curves are the hydrocarbon curve
−−0,167tt2,5
TT−= 1080 1− 0,325e − 0,675e (3)
t o()
representing thermal exposure on structural members due to hydrocarbon type fires, and the external fire
curve
−−0,32tt3,8
TT−= 660 1− 0,687e − 0,313e (4)
t o()
representing thermal exposure on the outside of external walls and on other external members as beams and
[3]
columns . See Figure 1.
In the test, the time to reach the decisive limit state with respect to the load-bearing and/or separating function
of the structural element defines its fire resistance, normally expressed in minutes. As an alternative, the fire
resistance can be determined by calculation.
Internationally, the standard fire resistance test is considered to be one of the fire test methods most
thoroughly dealt with. In spite of this, the test can be criticized. In its present form, the test procedure is
insufficiently specified in several respects, such as the heating and restraint characteristics, the environment
of the furnace, and the thermocouples for measuring and regulating the furnace temperature. The
specification of the test load is practically related to national building codes and regulations, which can vary
considerably with respect to the load level required from country to country. Current activities within CEN and
ISO are aimed at improving the test specifications.

2 © ISO 2004 – All rights reserved

Key
t time, min
T temperature, °C
t
1 hydrocarbon
2 standard (ISO)
3 external
T = 20 °C
o
Figure 1 — Temperature T as function of time t according to Equations (1) to (4)
t
Irrespective of the fire resistance being determined by testing or by calculation, it is important to consider that
the standard fire resistance test does not represent the real fire exposure in a building, nor does it measure
the behaviour of the structural element as a part of an assembly in the building. It is further essential to have
in mind that the standard fire duration, applied in a test, does not represent the real fire duration. What the test
or the corresponding calculations do is to grade structural elements. The building codes and regulations then
require different grading levels of elements depending on the circumstances.
Model H2 describes a thermal exposure, based on a simulated real fire and either computed by solving the
energy and mass balance equations of the compartment fire or determined from some systematized design
[3]
basis, for instance, the parametric fire as specified in Eurocode 1 , or the set of gas temperature-time curves,
illustrated and explained later in connection with Figure 13.
The two examples of design bases for the fully developed compartment fire exposure are both derived under
the assumptions that
 combustion of the fire load takes place entirely within the fire compartment,
 the fire process is ventilation-controlled, and
 gas temperature is uniform within the fire compartment at any time,
giving a conservative solution. The specified fire exposure considers the influence of the opening factor of the
compartment Ah A and the thermal properties of the surrounding structures of the compartment,
t
expressed by the thermal inertia λρc . A is the total area of the window and door openings, in m ; h is the
mean value of the heights of the openings, weighted with respect to each individual opening area, in m; A is
t
the total area of the surfaces bounding the compartment, opening areas included, in m ; λ is the thermal
−1 −1 −3 −1 -1
conductivity, in W⋅m ⋅°C ; ρ is the density, in kg⋅m ; and c is the specific heat, in J⋅kg ⋅°C , of the
compartment boundaries.
The parametric fire specifies the temperature-time curves of the heating phase of the compartment fire as the
standard gas temperature-time curve according to Equation (2) with the real time t replaced by a modified time
*
tt= Γ (5)
where

Ah A 1160

t
−2 −1/2 −1
Γ=× [J⋅m ⋅s ⋅°C] (6)

0,04
λρc


The duration of the heating phase is given by the modified duration time
qΓ
*4−
t
t=×1,3 10 [h] (7)
d
A hA
t
where q is the design value of the fire load density per unit area of the total surfaces, bounding the fire
t
−2
compartment, in MJ⋅m .
For the decay period, the parametric fire exposure is specified by the following formulae:
** *
T = T −−625 (t t ) for t hu 0,5
tt,max d d
** * *
T=T −−250 (3 t ) (t−t ) for 0,5 < t < 2 h
tt,max d d d
** *
T = T −− 250 (t t ) for t hW 2 (8)
tt,max d d
**
where T is the maximum temperature in the heating phase, i.e. for t = t , in °C.
t,max d
When applying a Model H2 description of the thermal exposure, the design normally consists of an analytical
or numerical procedure. Exceptionally, the design can refer to a full-scale test.
As a means to connect the thermal exposure according to the standard temperature-time curve, Equation (1)
or (2), and the thermal exposure, based on a simulated real fire (Model H2), the concept of the equivalent
time of fire exposure has been introduced. In practice, the concept can be used, for instance, for giving an
improved classification for fire ranking or grading of structural elements.
In principle, the equivalent time of fire exposure is defined as that length of the heating period of the standard
fire resistance test that gives the same decisive effect on a structural element with respect to a limit state as
the complete process of a simulated real fire exposure. The concept is further explained by Figure 2, in which
the full-line curves show the time variation of the gas temperature T and the load-bearing capacity R(t) of a
t
structural element for a simulated real compartment fire exposure and the dash-line curves the standard
temperature-time curve according to ISO 834 T and the corresponding time curve of the load-bearing
t,ISO
capacity R(t),ISO. The minimum load-bearing capacity of the structural element during the simulated real fire
exposure, transferred to the same value of the load-bearing capacity at the standard thermal exposure,
determines the equivalent time of fire exposure t .
e
For steel structures, the minimum load-bearing capacity during a simulated real fire exposure normally
corresponds to the maximum steel temperature T , provided that the temperature can be dealt with as
s,max
uniformly distributed over the cross-section of the structure. This simplifies the definition of the equivalent time
of fire exposure as shown in Figure 3.
4 © ISO 2004 – All rights reserved

Key
t time
T temperature
R load-bearing capacity
simulated real compartment fire exposure.
thermal exposure according to the standard fire resistance test, ISO 834.
Figure 2 — Definition of equivalent time of fire exposure t
e
Key
t time
T gas temperature at time t
t
T steel temperature
s
Figure 3 — Equivalent time of fire exposure t as defined by the maximum steel temperature T
e s,max
during a simulated real compartment fire exposure, exemplified for a protected structural steel
element
When determined according to Figures 2 and 3, the equivalent time of fire exposure depends on parameters
influencing the simulated real fire exposure as well as on structural parameters (for protected steel structures:
the thermal material properties and the geometry of the protection and the steel profile). For fire-exposed steel
structures, references [18], [23], [50] and [51] include a design basis for a direct practical determination of this
differentiated form of the equivalent time of fire exposure.
For more rough estimations of the equivalent time of fire exposure t , the following formula has been derived,
e
[50], [52], [53]
taking into account only the factors affecting the simulated real fire exposure :
q
tf
= 0,067  [min] (9)
t
e
0,5
(/Ah )
A
t
f
where
−2
q is the fire load density per unit area of the total surfaces, bounding the fire compartment; in MJ⋅m ;
tf
A is the total area of window and door openings; in m ;
h is the mean value of the heights of the openings, weighted with respect to each individual opening
area, in m;
A is the total interior area of the surfaces, bounding the compartment, opening areas included, in m .
t
By using fictitious values of the fire load density q and the opening factor (/Ah ) , the influence of varying
A
t
tf f
[18]
thermal properties of the surrounding structures of the fire compartment can be considered .
Summing up, the formula given by Equation (9) connects in a simplified way the thermal exposure according
to the standard fire resistance test, ISO 834, and the thermal exposure of simulated, fully developed
compartment fires. The formula has been verified for application mainly to steel structures and those
reinforced concrete structures, where the critical concern is yielding of the reinforcement under bending
conditions. At very low opening factors, the formula may give a considerable overestimation of the fire
severity. There is also a limitation of the validity of the formula to compartments of moderate size, i.e.
compartments with a size representative of dwellings, ordinary offices, schools, hospitals, hotels, and libraries.
The technical basis for the formula is for small compartments. A study of the applicability of available
relationships for the equivalent time of fire exposure to buildings with large compartments is reported in
reference [54]. In reference [55], formulae for the equivalent time of fire exposure, from Ingberg to Eurocode 1,
are systematically reviewed and compared with experimental data for compartment fires.
2.2 Models for structural behaviour
Model S1 comprises single structural elements, e.g. beams, columns, walls, floors, and roofs. The model may
simulate either a structural element or a single element isolated from the complete structure and described by
simplified end conditions in the fire analysis.
Model S2 means a substructure, which approximately describes the mechanical behaviour of a part of the
complete load-bearing system of the building. Compared to the real structure, a substructure is analysed with
simplified boundary conditions at its outer ends or edges.
Model S3 describes the mechanical behaviour of the complete load-bearing structure of the building, acting
as, for instance, a two- or three-dimensional frame, a beam-slab system or a column-beam-slab system.
In the matrix given in Figure 1, the thermal exposure models and the structural models are combined in the
sequence of improved idealization. In principle, each element in the matrix then represents a particular design
procedure. The matrix therefore can be considered as a type of classification system for methods of structural
fire engineering design. It is, however, evident that not all models can be used in all combinations and the aim
should be to provide a sensible pairing at each level of advancement. In the matrix, reference is made to
these aspects. In principle, a structural fire engineering design offers a problem-oriented choice for the
combination of the thermal exposure model and the structural behaviour model. The final choice may also
depend on national preferences, the complexity of application, and the particular design situation.
6 © ISO 2004 – All rights reserved

[56]
3 Characteristics of a reliability-based structural fire engineering design
[57], [58]
Essential components of a rational design methodology include, in the ideal case :
 analytical modelling of relevant processes; verification of validation and accuracy; determination of critical
design parameters;
 formulation of functional requirements, independent of choice of design process and expressed either in
deterministic or probabilistic terms;
 determination of design parameter values; and
 verification by reliability analysis that the choice of safety factors leads to safety levels that are consistent
with the expressed functional requirements.
For the probabilistic model to be integrated with the analytical model(s) of the relevant processes, the
following levels can be distinguished:
 an exact evaluation of the failure probability, using multi-dimensional integration or Monte Carlo
simulation;
 an approximate evaluation of the failure probability, based on first order reliability methods (FORM); and
 a practical design format calculation, based on partial safety factors and taking into account characteristic
values for action effects and response capacities.
For practical purposes, an exact evaluation of the failure probability is not feasible. Also, the FORM
approximations are too cumbersome for everyday design, but may be applied in special cases. For normal
design, the practical design formats have to be used.
The procedure for a reliability-based structural fire engineering design, related to a FORM approximation and
a practical design format calculation, is illustrated by flow diagrams in Figures 4 and 6, respectively. For
generality, the procedure is demonstrated for a load-bearing structure of charring material, for instance,
[39], [59]
a timber structure .
3.1 Structural fire engineering design based on FORM approximation
Following the flow diagram in Figure 4 for a structural fire engineering design, based on a FORM
approximation, the characteristics of the fire load and fire compartment constitute the basis for determining the
fire exposure, expressed by the gas temperature or the heat flow to the structure as a function of time and
either computed by solving the energy and mass balance equations of the compartment fire or chosen from
some systematized design basis.
Together with construction data of the structure and information on the thermal, moisture mechanics and
combustion properties of the structural material at elevated temperatures, the fire exposure gives the reduced
cross-section of the structure and the associated transient temperature and moisture conditions. With the
mechanical properties of the structural material as further input data, the transient temperature and moisture
states for the uncharred part of the cross-section then has to be transferred to the time variation of the load-
bearing capacity of the structure during the fire exposure, expressed, for instance, as the bending moment
M (t) in a decisive section. The load, statistically representative for the fire situation, gives a maximum load
R
effect with a bending moment M (t) in the section for the load-bearing capacity M (t).
S R
Figure 4 — Structural fire engineering design, based on first order reliability method (FORM)
8 © ISO 2004 – All rights reserved

The quantities M (t) and M (t) define the safety margin Z(t), as
R S
Z()t = ()t − ()t (10)
MM
RS
The related failure probability P(t) and the safety index β (t), defined as the quotient between the average
f
safety margin and the standard deviation, can then be calculated by the formulae:
Pt() = f [Z(t)]dZ (11)
∫
−∞ Z
−1
β ()t = φ [1− Pt()] (12)
f
where
f [Z(t)] is the probability density function of the safety margin Z(t);
Z
−1
ϕ is the inverse of the standardized normal distribution.
The design criterion implies that the minimum value of the safety index for the structure during the relevant fire
exposure β = [β (t)] shall meet the required value of the safety index β , i.e.
fm f min r
ββ 0− W (13)
fm r
At the determination of the safety margin Z(t), the failure probability P(t), and the safety index β (t), the
f
following uncertainties have to be taken into account:
 the uncertainty in specifying the loading and of the model for calculating the load effect on the structure;
 the uncertainty in specifying the fire load and the characteristics of the fire compartment;
 the uncertainty in specifying the design data of the structure and the thermal, moisture mechanics,
combustion, and mechanical properties of the structural material; and
 the uncertainty of the analytical models for calculating the compartment fire and the related heat transfer
to the structure, the size of reduced cross-section and the associated temperature and moisture states,
and the load-bearing capacity of the structure.
The required value of the safety index β depends on the probability of occurrence of a fully developed
r
compartment fire p ; the reduction of this probability due to fire-fighting by the fire brigade p and to the effect
1 2
of an installed fire extinguishment system p , if any; and the consequences of a structural failure. For the
detailed technique of deriving required values of the safety index β , see for instance references [1], [2] and
r
[60] to [62]. Example values of p , p and p are given in references [1], [2] and [63].
1 2 3
In Figure 5, example values of β are for industrial buildings and a safety class, representative of the main
r
load-bearing structure and separating structures bounding the fire compartment. The β values are given as a
r
function of the floor area of the fire compartment A and the probability of occurrence of a fully developed
f
compartment fire per year and unit area p = p p p .
1 2 3
Key
3 2
A compartment floor area, 10 m
f
β required value of the safety index
r
Figure 5 — Example values of β as function of fire compartment floor area A and probability p of
r f
occurrence of a fully developed compartment fire
3.2 Structural fire engineering design based on practical design format
As mentioned, for normal applications of a reliability-based structural fire engineering design, the practical
design format has to be used and the flow diagram in Figure 6 illustrates the procedure for such a design.
For a load-bearing structure, the design format condition implies that the design minimum value of the
load-bearing capacity R (t) during the fire exposure shall meet the design load effect on the structure S , i.e.
d d
= [(t)] W (14)
RR S
dd min d
The condition must be fulfilled for all relevant types of failure. For a separating structure, the design format
condition comprises requirements with respect to insulation and integrity. The insulation condition then implies
that the design maximum value of the temperature on the unexposed side of the structure T (t) during the fire
sd
exposure shall meet the temperature T , acceptable with respect to the requirement to prevent a fire spread
cr
from the fire compartment to an adjacent compartment, i.e.
= [(t)] u (15)
TT T
sd sd max cr
For the integrity requirement, there is no analytically expressed design format condition available.
Consequently, this condition has to be proved experimentally, when decisive.
In the practical design format, the probabilistic influences are considered by specifying characteristic values,
expressed as a specified fractile, and related partial safety factors for the fire load, such structural design data
as imperfections, the thermal material properties, the mechanical material properties and the loading. In
deriving the partial safety factors, all uncertainties listed above in connection with the presentation of the
design based on FORM approximations have to be included.
The functional requirements specified for the design should be differentiated with respect to type of
occupancy, type and size of building, number of floors, size and location of fire compartment, and the
importance of the structure or structural element to the overall stability of the building. This may be considered
by a system of safety classes associated with different failure probabilities, the probability of the occurrence of
a fully developed compartment fire included. In design verification, this safety differentiation is accounted for
by applying different partial safety factors for different safety classes or by applying corresponding safety
differentiation factors γ .
n1
10 © ISO 2004 – All rights reserved

Figure 6 — Structural fire engineering design, based on partial safety factors (practical design format)
For a certain occupancy, provisions employed for reducing the frequency of a fully developed fire for a
particular project, i.e.
 available force of fire brigades, and
 approved alarm and sprinkler systems
should be considered. In design verification, this frequency differentiation is accounted for by applying
different partial safety factors, depending on employed provisions and fire compartment size, or by applying
corresponding frequency differentiation factors γ .
n2
Summing up, the design format condition to be verified for a load-bearing structure reads:
= ( , , .)W ( , ,Q .)
RRRR SG
ddn d1d2 dd
d1
γ
n
or
( γγ, , .)W ( ,ψ , QQ, ) (16)
RR R SG
dk1 k2 d k
r1 r2 iik, k, ind
γ
n
where
R is the design value of the ultimate load-bearing capacity, determined by its lowest value during
d
the relevant fire exposure;
R , R , γ are design values, characteristic values and partial safety factors, respectively, related to the
di ki ri
ultimate load-bearing capacity and accounting for the uncertainties in heat exposure and
thermal and mechanical response, see Figure 6;
S is the design load effect subject to fire, determined by considering an accidental load
d
combination of the form
+ ψ QQ + (17)
G
k
∑iik, k, ind
i
where all actions, permanent loads (actions) G , variable loads (actions) Q and indirect
k k, i
actions due to fire exposure Q , are given by their characteristic values; ψ are combination
k, ind i
coefficients, generally different for i = 1 and i > 1, and all other load factors are set to
[2], [3]
unity ;
γ (= γ γ ) is a safety and frequency differentiation factor, accounting for different safety
n n1 n2
classes (γ ) and active fire protection measures (γ ).
n1 n2
In Equation (16), the safety and frequency differentiation factor γ has been allocated to the design
n
load-bearing capacity R . Alternatively, γ may be applied to affect the design fire load, thus modifying the
d n
design fire exposure, as shown in Figure 6.
Methods for the determination of values of the partial safety factors γ and the safety and frequency
ri
differentiation factor γ are presented in references [1], [2] and [62], in which example values of the factors are
n
[3] to [9]
also given. Factor values for practical design are also specified in the Eurocodes , and in reference [44].
12 © ISO 2004 – All rights reserved

[56]
4 Predictive model capabilities: uncertainties of design components
The rapid progress in analytical and computer modelling of phenomena and processes of importance for a fire
engineering design underscores the need for internationally standardized procedures for evaluating the
predictive capabilities of the models and for documenting the computer software. Two ASTM Standard
[64], [65]
Guides contribute to this task.
An evaluation of the model capabilities is critical in establishing both the applicability and limitations of the
[64]
models for a specific use. The process recommended in the Standard Guide :
 includes a brief description of the model and the scenario for which evaluation is sought;
 presents methodologies for conducting an analysis to quantify the sensitivity of model predictions to
various uncertainty factors;
 provides several alternatives for evaluating the accuracy of the predictions of the model; and
 gives guidance on the relevant documentation required to summarize the evaluation process.
A documentation of the computer software is necessary to ensure that users can judge the adequacy of the
scientific and technical basis for the models, select the appropriate computer operating environment, and use
the software effectively within the specified limitations. Adequate documentation also will help to prevent
unintentional misuse of the computer software. The guidelines in reference [65] are presented in terms of
three types of documentation:
a) technical document,
b) user's manual, and
c) installation, maintenance, and programming manual.
Systematic studies of the predictive capabilities of models and related computer software, used for describing
the simulated fire exposure and the thermal and mechanical behaviour of fire-exposed structures, are still rare
in the literature. A few such studies, carried out and reported during the last few years, however, seem to
indicate that the situation is now going to improve. Compartment fire modelling is dealt with in references
[66] to [68] and modelling of the thermal and mechanical behaviour of structures subject to fire in references
[69] and [70]. In references [66] and [68], general categories are identified regarding possible sources of error
in using a computer model to predict the value of a state-variable such as temperature or heat flux. The
categories specified are
 unreality of the theoretical and numerical assumptions in the model,
 errors in the numerical solution techniques,
 software errors,
 hardware faults, and
 application errors.
[67]
The report specifies for ten zone models and three field models for the compartment fire degree of
validation, limitations, restrictions on compartment size, number of vents and number of fuels that can be
accommodated, and number of organizations using the model. Useful conclusions are drawn with respect to
input/output data, experience of using the models, model validation, and potential limitations. The survey,
presented in reference [69], discusses the theoretical background of seven thermal and 14 structural
behaviour, fire-dedicated, computer programs, together with their strengths and weaknesses. The differences
between the programs were found to lie mainly in the material models adopted, the material data input, the
user-friendliness and documentation of the software. The majority of available fire-dedicated structural
programs still require significant development, and as most of them are not user-friendly or properly
documented, using them effectively and universally would be very difficult.
Applied to fire-exposed steel columns, reference [70] reports comparative calculations of the structural
behaviour by five computer programs. In terms of the ultimate resistance of the columns, the calculated
results are very similar, with a maximum difference between two programs of 6 %. Greater differences are
observed for the displacements of the columns, probably due to different ways of considering the residual
stresses at increasing temperature in the programs. When evaluating the results, it is important to note that
the same mechanical behaviour model for steel at transient elevated temperatures, the model described in
reference [5], was used in all computer programs.
Very few sensitivity and uncertainty studies relevant to structural fire desig
...