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7/30/2019 PERFORMANCE BASED DESIGN FOR FIRE SAFETY
1/23Advances in Structural Engineering Vol. 7 No. 4 2004 311
1. PERFORMANCE BASED DESIGNFOR FIRE SAFETYA rational approach to fire safety assessment is to relate
functional requirements, such as prevention of spreading
heat and smoke, safe evacuation and rescue etc., to fire
resistance considering both local and global stability of
structures. In a performance-based design, the designer
needs to first understand the level of performance is
expected, then to design to these levels and finally to
predict the performance that will be achieved to ensure
the reliability and robustness of the design.
At the beginning of the performance-based analysis
and design, the designer and the stakeholders should
both agree on the project scope, intent and building use.
The designer will then define and prioritize the fire safety
plans and performance criteria and define the fire safety
goals and objectives pertaining to the design intent. The
next step to follow is to determine the implementation of
the selected solutions into the project scope and execution.
The final stage is to establish the necessary verification
and quality assurance to ensure compliance with the
agreed solutions.
In general, a process for performance-based design
would involve the following steps:
1. identify goals and defining stakeholder and design
objectives
2. identify the possible fire scenarios which could
occur during the service life of the structure,
Performance Based Fire Safety Design of
Structures A Multi-dimensional Integration
J. Y. Richard Liew*
Department of Civil Engineering, National University of Singapore, Blk E1A, #05-13, 1 Engineering Drive 2, Singapore 117576
(Received 16 July 2003; Received revised form: 17 November 2003; Accepted: 18 November 2003)
Abstract: Design codes for fire safety in buildings can be either a prescriptive type or
performance-based type. It is now widely recognized that performance-based codes
provide greater advantages over the prescriptive codes in that it allows designers to use
the fire engineering methods to assess the fire safety of the structure. However, as the
assessment of the whole structure performance is not easy, most codes currently used
are still prescriptive codes or a combination of prescriptive codes and performance-
based codes. The key feature for implementing the performance-based fire design
codes is the assessment of the fire resistance of the structure. This paper provides an
overall view on performance-based code and the approaches for designing steel structure
in fire considering a multi-dimensional integration of fire engineering simulation,
emergency evacuation and structural resistance. Various fire models and heat transfer
analysis methods are reviewed and discussed. The basis to modelling of large deflection
and plasticity using appropriate stress-strain relationship at elevated temperature is
explained. Finally, structural response calculations from simplified hand calculation
method to advanced numerical procedures are presented. Future trends for research are
identified.
Key words: fire safety, emergency evacuation, explosion, fire modelling, fire protection, performance-based design, tall buildings,
plastic hinge analysis.
*Corresponding author. Email address: [email protected]; Fax: +65-6779-1635; Tel: +65-6874-2154.
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Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
312 Advances in Structural Engineering Vol. 7 No. 4 2004
3. evaluate the likelihood and consequences of such
scenarios,
4. establish appropriate performance criteria by
ensuring effective evacuation, escape and rescue
and to prevent injury arising from such events,
5. predict the performance of the system based on
available engineering data, and6. ensure robustness of the designs, reliability and
durability of the protection systems, etc.
Although the governing criteria for impairment of
the main safety functions are often non-structural (for
example exposure to heat, temperature, toxic gases etc.),
it is, however, a functional requirement that the structure
would remain stable to allow adequate time for safe
evacuation and rescue. Therefore a quantitative
assessment on fire resistance of a structure is necessary
and this opens up the opportunity in using advanced
simulation tools and computational methods developed
as reported in the recent fire workshops (Liew 2002;Moss 2002).
2. EMERGENCY EVACUATIONThe objective of providing emergency evacuation is to
allow occupants to travel safely to a place of safety in
the event of fire. In general, the procedure involved in
estimating evacuation time is given below:
1. define the space domain to be analyzed
2. estimate the response time of occupants
3. calculate the travel time to a specific location
4. determine whether this location is safe5. if the specific location is safe, record the total
required safe escape time and make sure that it
does not exceed the available safe escape time,
which is determined by untenability condition.
If the specific escape route is not safe, select
another one and repeat Step 3.
A range of possible emergency scenarios may occur in
high-rise and complex buildings for which it is necessary
to develop a range of strategies for managing accidental
fires. The following points are considered when planning
for an evacuation strategy for such systems:
Risk perception in high rise/complex buildings
Types of fire scenarios that may occur and may
need different evacuation strategies
Fire scenarios that will affect building protection
strategies and the emergency plans proposed
Limitations of each emergency plans
Integration of fire service into the emergency
plan
Types of information to be provided to the
occupants
Emergency evacuation training and fire
protection maintenance plan
A major limitation on prediction of incident outcomes
for performance-based design and hazard assessment
is the lack of quantitative data on pre-movement time
and evacuation time, and occupant behaviours for
different fire scenarios and occupancies. There is a need
to study human behaviour during evacuation from a
range of occupancies. Advanced computer software isavailable to predict the evacuation time considering the
effects of exposure to fire effluence on occupant
evacuation behaviour. However, improvements are
still needed to include the effects of different warning
systems, information provided to occupants, occupant
characteristics, pre-training, building complexity and
level of fire safety management on pre-movement and
evacuation time. The September 11 incident had shown
that fire service intervention occurred while there were
many occupants still in the buildings, many were in the
process of evacuating while other remained in refuge
were trapped by fire. In order to achieve effective designfor buildings in emergency situations, it is essential to
consider occupants characteristics, their abilities to
evacuate and the effects of exposure to fire effluence on
occupant evacuation behaviour.
3. FIRE MODELLINGFire modelling is a mathematical simulation of the fire
conditions in a compartment and is capable of giving
information based on the parameters which have been
designed. The fire development in a room normally
involves three phases: pre-flashover, post-flashover andfire decay. In the pre-flashover phase, fuels begin to burn
and the gas temperature varies from one point to another
in the compartment. In the post-flashover phase, the
fire develops fully, and the gas temperature increases
rapidly to a peak value and becomes practically uniform
throughout the compartment. The fire has the most
influence on structural design because of high temperature
and radiant heat fluxes produced in this phase. In the fire
decay phase, the available fuel begins to decrease and
the gas temperature falls. There is considerable benefit
when the effects of natural fires in buildings, where the
amounts of the combustible contents are small and the
buildings are of large volume, is considered than using
the standard ISO fire.
For many years, fire engineering research has shown
that overall structure performs better than isolated
members in a fire situation. Numerous studies have been
carried out to determine the temperature reached in real
(natural) fires, to quantify the factors that govern fire
severity and to investigate the parameters that cause
structures to fail in fire. The studies show that the severity
of natural fires in building compartments is governed by
the amount of combustible material (the fire load), the
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J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 313
area of the doors and windows (the ventilation), and the
thermal characteristics of the wall, floor and ceiling
materials. In addition, fire-fighting measures are also
important for the determination of fire exposure.
The following subsections discuss the various models
available for modelling fire of different complexity and
severity.
3.1. Design Fire ModelsDesign fires are derived empirically and may yield
reasonable and consistent predictions provided that the
fire conditions are similar to those in the underlying
assumptions. Standard fire curves such as ISO-834 do
not represent the real fire in a compartment and serve
only as criteria to evaluate the fire resistance capacity of
single structural members. Simplified code prescribed
method often assumes that the fire has a constant
temperature throughout the burning period.
Eurocode 1: Part 1-2 (2001) recommends equationsfor parametric fires, allowing a temperature-time curve
to be produced for any combination of fuel load, opening
factor, height of opening and thermal characteristic of
the boundary materials.
The temperature T (C) and time relation during theheating phase is given as (Eurocode 1: Part 1-2, 2001):
(1)
where t* is the fictitious time given by
t* = t. (2)
t is the time (hr) and
(3)
where b is the square root of thermal inertial of the
boundary material of the compartment and O is the
opening factor (m1/2) given by
(4)
Av is the total area of vertical openings on all walls;
heq is the weighted average of window heights on all
walls andAt is the total area of enclosure (walls, ceiling
and floor, including openings). In case of= 1, Eqn 1approximates the ISO834 standard temperature-time
curve.
Depending on whether the fire is fuel controlled or
ventilation controlled, the duration of the heating phase
tmax (hr) is given as:
(5)
qt,d is the design value of the fire load per total surface area
At of the enclosure. The recommended fire growth rate is
taken as tlim = 25 minutes, 20 minutes and 15 minutes for
slow, medium and fast growth rate, respectively.
The introduction of tlim is to avoid unrealistic short
fire duration when the ratio between the fire load and the
opening factor decreases. Any object or fire load needsa certain amount of time to burn, even if there is
unlimited presence of air (Franssen 1997).
The temperature-time curve during the cooling phase
is given by:
T = Tmax 625(t* t*max.x) for t*max 0.5
T = Tmax 250(3 t*max)(t* t*max.x)for 0.5 < t*max < 2
T = Tmax 250(t* t*max.x) for t*max 2 (6)
in which
t* = t.
t*max = (0.2 103 qt,d/O).
x = 1.0 if tmax > tlim
x = tlim./ t*max if tmax = tlim
Figure 1 shows the parametric fire curves plotted for a
range of opening factors (OF), fuel loads and materials
according to the Eurocode 1: Part 1-2 (2001). Fire curvesare produced for three fire loads, four opening factors
and two types of construction, showing the significant
dependence of fire temperature on the bounding materials.
The fire loads are 400, 800 and 1200 MJ per floor area,
for a room 5 5 m in plan and 3 m high. Feasey &Buchanan (2002) pointed out that the Eurocode equation
gives extremely fast decay rates for large openings in
well insulated compartments (e.g., OF = 0.12 in Figure 1)
and extremely slow decay rates for small openings in
poorly insulated compartments. They proposed some
modifications to the Eurocode formula to give a better
estimation of the temperature-time curve in the fire
decay phase.
3.2. Zone ModelsZone models represent more of the phenomenological
behaviour of fire. They solve the conservation equations
for distinct and relatively large regions. In each zone,
the heat balance equations are solved to generate gas
temperatures. There are several options for calculating
the heat release rate, based on ventilation control, fuel
control or the porosity of wood crib fuels. Other computer
models including ZONE, CSTBZ1, CFAST, BANZFIRE,t = Maximum 0.2 q O, tmax t,d lim[ ]
103
O = A h Av eq t
=( )
( )
O b/
. /
2
20 04 1160
T
e e et t t
=
+ ( ) 20
1325 1 0 324 0 204 0 4720 2 1 7 19
. . .. * . * *
7/30/2019 PERFORMANCE BASED DESIGN FOR FIRE SAFETY
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are summarised in SFPE (2002). Schleich (1996)
developed a realistic fire evolution model, which not
only takes into account the physical factors, but also the
influence of active protection measures in the structure.
The multi-zone fire model (Liew et al. 2002) places
heating boxes one outside another and assumes uniform
heating in each box, as shown in Figure 2. The smallest
box nearest to the heat source has the highest
temperature. The boxes further from the heat source have
lower temperature, and the farthest box has the lowest
temperature. The structural elements enclosed within
each heating box are subjected to a uniform heating
rate, which can be either constant or vary as a function
of time. The temperature-time relationship in each box
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
314 Advances in Structural Engineering Vol. 7 No. 4 2004
1400
1200
1000
800
600
400
200
00 50 100 150 200
Time (min)
T
emperature(C)
250 300 350
ISO 834
Concrete
GypsumOF = 0.02
400
1400
1200
1000
800
600
400
200
00 50 100 150 200
Time (min)
T
emperature(C)
250 300 350
ISO 834
Concrete
Gypsum OF = 0.04
400
1400
1200
1000
800
600
400
200
00 20 40 60
Time (min)
Temperature(C)
80 100
ISO 834
Concrete
GypsumOF = 0.08
120
1400
1200
1000
800
600
400
200
00 20 40 60
Time (min)
Temperature(C)
80 100
ISO 834
Concrete
GypsumOF = 0.12
120
Figure 1. Parametric temperature-time curves (fuel load = 400, 800, 1200 MJ/m2 floor area)
Figure 2. Multi-zone fire model
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may be obtained by calibration with fire tests or from
numerical simulation based on the theory of thermal
energy balance. The air temperature at each time step
can be prescribed.
The multi-zone fire model (Liew et al. 2002)
provides a means to calibrate actual fires. The heat
intensity and the flame size of the actual fires dependon many factors such as fire load, ventilation, active fire
control devices, and so on. If there is such a part in a
structure that is heated significantly more or less than
others, the multi-zone model could be a more suitable
fire model to simulate an open fire. The multi-zone fire
model can be used to simulate uniform heating. In this
case, only one-box is prescribed and all structural
members within this box will be heated simultaneously
under the same fire load.
3.3. Radiation Model
Radiation model may be used to simulate fire as aradiating source with the heat flux intensity defined by
its distance from the source, as shown in Figure 3. The
heat rays are emitted in all directions. The heat intensity
may be constant or vary as a function of time. The heat
flux intensity, q, received by the individual elements is
calculated as (SINTEF 1995):
(7)
where
Ei = total energy emitted from the sourceri = distance between the heat source and the midpoint
of ith element
i = angle between the ray and the element surface
normal (see Figure 3).
The air temperature can be computed by adopting the
Stefan-Boltzman formula once the heat flux intensity is
known (Yao et al. 1995):
(8)
where
= the emissivity coefficient;
qi = the heat flux intensity calculated from Eqn 7;= the Stefan-Boltzman constant of 5.67 108 W/m2K4;TK= the temperature on the spherical surface with a unit
of Kelvin (K).
The radiation model is a convenient way to propose a
simple relationship between the air temperature and its
distance from the fire source. For large and complex
structures, the radiation model is preferred as it is
relatively simpler to use for simulating an open fire.
On the other hand, the multi-zone fire model requires a
descritization of space into finite boxes. Each heating
box needs to be prescribed with an appropriate time-
temperature relationship.
3.4. Computational Fluid Dynamic (CFD)ApproachThe CFD model can be used to represent various types
of walls of different materials and the exact location
and dimensions of openings. The fire compartment to
be modelled by CFD is divided into a number of small
volumes. The fluid dynamics equations are written in
each of these small volumes, and each volume is linked
to the adjacent volumes. The heat transient problems are
expressed in differential equations, and time integrationhas to be performed by solving a large number of
equations in the time domain. The main drawback of
CFD model is that a significant number of parameters
have to be given and many of them are variable with
very little, if any, link to any physical phenomenon. It
requires an experienced user before the any meaningful
Tq
ki=
1 4
qE
r2i
i
i=4
cos
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 315
I = intensity cos()
y
x
z
radius
(x, y, z)
Intensity
Figure 3. Radiation model to simulate open fires
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result can be obtained. Practising engineers often find
difficulties in understanding the hypothesis underlying
the CFD models and they have to be careful in interpreting
the results.
A large amount of results can be produced by CFD
computation. For instance, it provides the temperature
components of the velocity, the pressure, the oxygen
concentration, etc, in every volume at every time step. A
graphical representation of the results is mandatory, see
Figure 4. To some extend, the amount of results can
even create a difficulty if the interest is for the behaviourof structure. An interface is often needed to be created
between the CFD model and the structural model, because
thermal environment in the compartment calculated by
the CFD model would influence the structural element.
The main advantage of CFD models is to model
compartments with complex geometry because only the
flexibility given by the fine discretisation of the space
inherent to CFD models allows a correct representation
of this complexity. Notwithstanding the costs and
problems associated to these models, they are favoured
by researchers who use them as the design tools for fire
analysis. Their application domain is for complex
projects which are very often combined the geometrical
complexity and the financial resources which make the
CFD model an attractive choice.
4. HEAT TRANSFER ANALYSISThe process of heat transfer between a fire and a
structure can be described by the balance between the
net incident thermal radiation and convective heat flux
and the rate of heat conducted in the material. The rate
of heating of any structural member is dependent at any
time on the temperatures of both the fire atmosphere and
the member. Calculation of member temperature requires
solution in time domain via a fairly complex differential
equation. There are two kinds of heat transfer methods
used in fire engineering design: analytical method and
finite element method.
4.1. Analytical MethodDifferent standards or specifications give simplified way
to calculate the net heat flux and temperature development
in the steel member. The heat flux due to convection is
proportional to the temperature gradient between theambient gas temperature and temperature of the steel
member. The heat flux due to radiation is proportional to
the temperature gradient of the forth order of the ambient
gas temperature and the steel temperature. ECCS (1993)
uses a single expression to represent the total heat flux as
(9)
where
As = surface area of the member per unit length exposed
to heating
f= fire temperature at time t
s = temperature of the steel member
h = coefficient of total heat transfer
Based on this heat flow law, the temperature
development in unprotected steel member can be
calculated. Eurocode 3: Part 1-2 (2001) provides a rational
means to estimate steel temperature development by
considering the section factor and configuration factor
for internal steelwork and external steelwork. The
temperature increments in the structural members are
calculated over small time steps. This method is
particularly suitable for calculation using simple
spreadsheet programming.
( )Q h As f s=
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
316 Advances in Structural Engineering Vol. 7 No. 4 2004
8.00
Plot 3dSpeedm/s
7.20
6.40
5.60
4.80
4.00
3.20
2.40
1.60
0.80
0.00
Figure 4. Example of smoke velocity in a fire compartment from CFD model
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For internal steelwork, the increase of temperature
(s) in an unprotected steel section during in a timeinterval tmay be calculated as (Eurocode 3: Part 1-2
2001):
(10)
in which
correction factor for the shadow effect of
flanges, defined as a ratio of the box value of the section
factor to the section factor
specific heat of steel [J/kgK]
density of steel [kg/m3]
section factor for unprotected steel members
Heat transfer coefficient per unit area per degree
Kelvin
t= The time interval [seconds]On the fire exposed surface the heat transfer
coefficient may be determined by considering heat
transfer by radiation and convection as
(11)
where the radiative term may be expressed as:
(12)
where
Stefan-Boltzmann constant of
resultant emissivity using f = 1.0 and
m = 0.7, where f and m are the emissivity of the fire
and the surface of the member,
f and s = Fire and steel temperature, respectively, in
Celsius.
The convective heat transfer coefficient is hnet,c =
25 W/m2K for standard fire, 35 W/m2K for natural fire
and 50 W/m2K for hydrocarbon fire.
The section factor uses the fire exposed
perimeter in calculating an appropriate value of . The
section factors for selected examples are shown in
Figure 5.
For protected steel members under fire, the protection
material of low thermal conductivity reduces the rate of
heat transfer from the fire to the steel section. The
increase in steel temperature in a time increment
due to the heat transfer from the fire through the fireprotection to the steel section may be calculated as:
(13)
in which the relative heat storage in the protection
material is given as
(14)
andsection factor for protected steel member,
where is the inner perimeter of the protection material.
specific heats of steel and protection material
thickness of fire protection material
temperatures of steel and fire at time t
increase of fire temperature during the time step tthermal conductivity of the fire protection material
densities of steel and fire protection material
The temperature development in protected steel
members can be evaluated based on the thermal
properties of the insulation materials.
4.2. Finite Element MethodFinite element method may be used to estimate the
thermal effects on the structural elements by subdividing
the structural element into a number of quadrilateral
heat transfer elements. Heat conduction, heat convection
and exchanges of radiation are calculated on the basis of
the heat transfer element. One simplified approach is to
store the temperature history in each structural member
and then calculate the equivalent nodal expansion based
on the incremental temperature change. Consistent nodal
forces are produced on an elastic element at elevated
s p, =kp =f = s f, =tp =c , cs p =
Ap
A /Vp =
=c
ct
A
V
p p
s s
p
p
/
sp f s
p p s s
f
A V )
t k )ct e=
+
/ (
( / ( )( )
/
1 31
10
ts
Am
A Vm/
r f m= =5 67 10
8. =
hnet r r f s
f s
, ( ) ( )
= + +[ ]
+ +[ ]
273 273
546
2 2
h h hnet net c net r = +, ,
hnet
hnet =A Vm/ =s =cs =
kshadow =
s shadow
m
s s net f s
kA V
ch t= ( )
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 317
B
tD
Am/V = 2(2B+Dt)/A
A = area of the steel section
D
B
Am/V = (3B+2D2t)/A Am/V = 2(B+D)/A
Figure 5. Values of parameter for use in the calculation of Section factor A m/V
7/30/2019 PERFORMANCE BASED DESIGN FOR FIRE SAFETY
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temperatures due to the axial expansion and temperature
gradient increment over the cross-section. These forces
can be used in the structural analysis to determine the
responses of the structure in fire (Ma and Liew 2004).
Although the techniques for solution of the heat
transfer problem are relatively well established, several
complicating factors exist. For examples, physicalproperties such as thermal conductivity, specific heat,
emissivity/absorbtivity and heat transfer coefficients
vary with temperature. Surfaces may also be exposed
to re-radiation from other surfaces. The fraction of
the emitted radiation received is governed by the
configuration factor, which may be tedious to calculate,
especially if shadowing of other members are present.
Numerical method is often used to improve the accuracy
of the heat transfer analysis.
5. MATERIAL BEHAVIOUR AT
ELEVATED TEMPERATUREExperimental evidence shows that the stiffness and
strength of steel deteriorate at elevated temperatures.
Typical stress-strain curve of steel at elevated temperatures
is shown in Figure 6.
The stress-strain relationship at elevated temperature
does not exhibit a distinctive yield plateau. Therefore,
the yield stress, or 0.2% proof stress, which is conventional
design strength for steel at ambient temperature, loses
its relevance because of the nonlinearity of the stress
strain curve. Since fire is considered to be an accidental
situation, large plastic strains are allowed. Hence, aneffective yield stress is used, which is attainable when
the strain is considerably larger than the elastic limit at
normal temperatures. Eurocode 3: Part 1-2 (2001) adopts
a yield strain of 2% to define the effective yield
stress. The temperature dependence of the proportional
limit, the effective yield strength as well as the elastic
modulus recommended by the code is shown in Figure 7.
Creep may be of importance in a fire situation where
a cross section is subjected to high temperature (above
400C) and high stress for a long period of time. The
stress-strain curves given in the Eurocode code arebased on measurements at constant temperature within a
period of time to allow creep to take place in the tests.
Therefore, creep effect is implicitly included in the
effective yield strength used for design. In other words,
when the design is based upon code values, creep does
not need to be considered explicitly. If the temperature
and load history is such that a structural component
remains at high temperature or is highly stressed for
only a short period, the prediction using the code values
should yield conservative results.
6. NONLINEAR ANALYSIS ATELEVATED TEMPERATUREModern design standards such as Eurocodes provide
sufficient guidance to assess the fire performance of
individual members in a fire compartment of a building
framework. In the case of a braced frame in which each
storey comprises a separate fire compartment with
sufficient fire resistance, the effective buckling length of
a column may be used to compute the limit load of the
frame. However, guidance is not given for sway frames
in which storey buckling and overall stability may
dominate the design of individual member. Wang et al.(1995) provide simplified methods to analyse the
performance of steel frames. They study the effect of
continuity on the fire resistance of columns in both sway
and non-sway steel frame and suggested some restraint y,
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
318 Advances in Structural Engineering Vol. 7 No. 4 2004
Strain x
fy, h effective yield strength;
fp, h proportional limit;
Ea, h slope of the linear elastic range;
xp, h strain at the proportional limit;
xy, h yield strain;
x t, h limiting strain for yield strength;
x u, h Ultimate strain;
x u, hx t, hxy, hxp, h
fy, h
fp, h
Ea, h= tan a
a
Stress q
Figure 6. Stress-strain relationship of steel at elevated temperature according to European Committee for Standardisation (2001)
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stiffness values at the end of the column due to the
continuity of the sub-frame from the parametric study.
General commercial programs such as ABAQUS,
ANSYS, NASTRAN, may be used for analysing
structures exposed to fires. They offer the advantages of
full validation, powerful ability to model different kinds
of problems and availability of further developmentso that they can almost suffice all needs. But these
programs are rather inconvenient to use for being both
time-consuming and complicated to operate since they
are general purpose program not specifically written to
perform analysis of structures under fire condition
which is highly non-linear and transient.
One powerful tool for analyzing large-scale steel
structures exposed to fire is to adopt a second order
plastic hinge-based analysis (Liew et al. 1998, 2002). In
this approach, it is assumed that cross section is compact
and the full plastic capacity can be achieved. At elevated
temperature the plastic strength surface should follow
the effective yield strength and its temperature reduction
curve for yield, as illustrated in Figure 7. The elastic
modulus also degrades at elevated temperature following
the temperature degradation curve for the slope of linear
elastic range as in Figure 7. Other fire effects
include thermal expansion and thermal bowing. Further
improvement to this model is to model the gradual
plastification of members cross section using a two-
surface plastic hinge method, which captures the gradual
yielding of cross sections at elevated temperature (Ma
and Liew 2004; Liew et al. 2000).
The two-surface plastic hinge model, which is
formulated based on the bounding surface plasticity
concept, represents the inelastic cross section behaviour
by considering the interaction of axial force and bi-axial
bending. The initial yield surface is assumed to be a
scaled down version of the bounding surface that is
fixed in size and translates without rotation in a stress-resultant space. The gradual translation of the initial
yield surface towards the bounding surface provides a
smooth transition from initial yield to full plastification
of cross section. Moreover, the element displacement
fields are derived from the exact solution of the fourth
order differential equation for a beam-column subjected
to end forces (Liew et al. 2000), hence it is accurate
enough to use only one beam-column element to model
the stability behaviour of column member.
At elevated temperature, the yield surface and the
bounding surface have to contract in size in order to
satisfy the yield condition. The degradation of the yield
strength is based on the effective strength concept. At
high temperature, the stress-strain relationship of steel
is highly nonlinear and does not exhibit a distinct yield
plateau. The idea of the effective strength is introduced
to define a yield plateau at a relatively high strain level.
For the two-surface plasticity model, the size of the
bounding surface corresponding to full cross-sectional
plastification, follows the reduction curve for effective
yield strength in Eurocode 3: Part1-2 (2001), as illustrated
in Figure 8. The size of the initial yield surface is
assumed to degrade proportional to the bounding surface.
kE,
ky,
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 319
Reduction factor, k
0 200 400 600 800 1000 1200
0.2
0
0.4
0.6
0.8
1.0
Temperature [C]
Proportional limitkp,h= fp,h/fy
Slope of linear elastic rangekE,h= Ea,h/Ea
Design strength for satisfying
deformation criteriakx,h= fx,h/fy
Effective yield strengthky,h= fy,h/fy
Figure 7. Reduction factor for steel according to Eurocode 3: Part 1-2 (2001)
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However, it can be observed from Figure 8 that the
initial yield strength decreases at a faster rate than the
effective yield strength; therefore, the size of the initial
yield surface may be over predicted at higher temperature.
In practice, this will not have any significant effect on
the inelastic behaviour of members in fire.
The verification of the two-surface plasticity model at
ambient and elevated temperature is reported in Liew
et al. (1998) and Ma and Liew (2004). Verification studies
have been carried out on both components and frames
over a wide range of parameters including uniformly
heated members, three-side heated members with
concrete slab acting as heat sink, members with passive
fire protection and 2-D frames. Several examples are
given in the next section to illustrate the application of
the plasticity model and to study the accuracy of the
model in modelling the inelastic behaviour of frame
structures.
7. COMPARISON OF PLASTICHINGE METHOD WITH SPREAD-OF-PLASTICITY ANALYSISFigures 9 to 11 show a simply supported beam, a single
storey braced frame and a multi storey braced frame
subjected to fire. The main purposed of the study is to
compare the results obtained from fire analyses based on
the plastic hinge (P-Hinge) method and the Spread of
plasticity (S-Plastic) methods.
All the structural models are subject to ISO
standard fire. For the simply supported beam (model 1),
the member cross section is exposed to 4-side fire
(Figure 9). The temperature is assumed to be uniform
over the cross section and along the length. The second
and the third models are based on the portal frame
shown in Figure 10. In model 2, the frame members are
exposed to fire from all sides without fire protection
while in model 3, the beam is protected by concrete slab,
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
320 Advances in Structural Engineering Vol. 7 No. 4 2004
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 200 400 600 800 1000 1200
Temperature [C]
Strengthdegradation
Ratio
effective yieldstrength
initial yield strength
bounding surface(200C)
initial yield surface(200C)
bounding surface(700C)
initial yield surface(700C)
Figure 8. Size of yield and bounding surface at elevated temperature according to Eurocode 3
q = 15 KN/m
Uy
Ux
254 146 UB
4.5 m
Figure 9. Model 1: simply supported beam (4-side heated)
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and the beam section is 3-side heated. Model 4 is a
3-bay, 3-storey rigid frame (Figure 11), in which the
lower left corner compartment is subject to fire. S275
steel with yield strength of 275 N/mm2 is used for all the
structural members.
For model 1, only vertical deflection of the beam is
compared. For the other models, the comparison is made
both on the mid-span deflection of the beam and the
lateral deflection at the top of the heated column. The
results are shown in Figures 12 to 15. In all figures, solid
lines represent the vertical deflection of the beam, and the
dashed line means the lateral deflection of the column.
The comparison of the results indicates that the
plastic hinge method gives satisfactory results before
the formulation the first plastic hinge in the structure. If
the failure is not due to the formation of plastic hinge
mechanism, then, the plastic hinge method shows a greater
stiffness reduction than the spread-of-plasticity method
(Figures 12 and 13).
If a collapse mechanism occurs (Figures 14 and 15),
the plastic hinge method shows collapse with rush out
of deformation while the spread-of-plasticity analysis
shows ability to sustain further load with moderate
deformation. Hence the plastic hinge method may be
used to predict the collapse of structures. But it may
underestimate the post-collapse stiffness of the
structures.
For steel structures under fire attack, it is possible to
allow the structure to undergo large deformation as long
as the structure maintains stable. Therefore, when post-
collapse behaviour is needed, the spread-of-plasticity
method should be used.
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 321
Ux Uy
P = 500 kN P = 500 kNq = 25.4 kN/m
Beam section: 305*165UB40
Column section: 203*203UB52S275 steel
5.5 m
3.5 m
Columns are 4-side heated
Figure 10. Rigid portal frame: Model 2: beam is 3-side heated; Model 3: beam is 4-side heated
P = 75.5 kN P = 151 kN P = 75.5 kNP = 151 kN
5.5 m 5.5 m 5.5 m
3m
3m
3m
Beam section:305*165UB40
Column section:203*203UB52
U.D.L = 25.4 kN/m over all beams
Ux
S275 steel
Uy
Figure 11. Model4: three-bay, three-storey rigid frame
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8. VERIFICATION OF NUMERICALMETHODSVerification studies are important to ensure the validity of
any analytical or numerical methods. Ma and Liew (2004)
established the accuracy of their proposed advanced
analysis method against experimental results for both
individual members and complete frames exposed to fire.
8.1. Uniformly Heated MembersCritical temperatures from the advanced analysis are
compared with those in BS5950: Part 8 (BSI 1990) for
beams under uniform distributed loads and columns
under axial loads in Table 1. Critical temperature for
beams is taken at a mid-span deflection of L/20 and
critical temperature for columns is taken at the failure
of the column symbolized by a sudden increase of
lateral deflection. The results agree well with each
other.
8.2. Three-side Heated BeamsEighteen UK standard fire tests on unprotected simply
supported steel beams supporting concrete slabs without
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
322 Advances in Structural Engineering Vol. 7 No. 4 2004
1600
1400
1200
1000
800
600
400
200
00 2 4 6 8 10
Time (minute)
Formulation of the plastic hinge
at the mid of the beam
PHinge
SPlasticity
uy(mm)
12 14 16
Figure 13. Deformation of structural model 2
700
100
0
1000
P-HingeS-Plasticity
Solid line: Uy
Dash line: Ux
Time (minute)
Deformation(
mm)
5 10 15 20 25
600
500
400
300
200
Figure 12. Deformation of structural model 1
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composite action are simulated. The test descriptions
and data are available in Wainman (1988). Table 2
summarizes the measured and calculated critical time
and temperature for each test. In general, the agreement
is good except for a few cases (such as Test 14). The
discrepancy is possibly resulted from the assumed steel
strength degradation at elevated temperatures due to
lack of material test data. Figure 16 plots the temperature
and the mid-span deflection predictions against
experimental results for test 11.
8.3. Two-dimensional FramesTwo frames (Li et al. 1997; Zhao 1995) have been
studied. The configuration of the frame and the loading
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 323
Solid line: Uy
Dash line: Ux
yielding of the column
P-Hinge
S-Plasticity
Plastic hinge of the beam
350
400
300
250
200
150
100
50
0 5 10
Time (minute)
Deformation(m
m)
15 20 25
0
50
Figure 14. Deformation of structural model 3
Solid line: Uy
Dash line: Ux
P-Hinge
Time (minute)
Deformation(mm)
S-Plasticity
300
250
200
150
100
50
00 2 4 6 8 10 12
Figure 15. Deformation of structural model 4
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is shown in Figures 17 and 18. In both studies, the
measured temperature of each member is used in
the structural analysis. Figures 19 and 20 illustrate
the excellent correlation between the predicted and the
measured displacements.
8.4. Three-dimensional FrameA full scale fire test was carried out on a three-
dimensional steel tubular frame in SINTEF. The test
details and the verification procedures can be found in
Skallerud and Amdahl (2002). The proposed advanced
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
324 Advances in Structural Engineering Vol. 7 No. 4 2004
Table 2. Critical time and temperature of UK standard fire tests
Critical Time (min) Critical Temperature (C)
Test No Load Ratio Test Analysis Error % Test Analysis Error %
Test 2 0.50 22.5 20.7 8.0 660 693 5.0
Test 3 0.57 22.0 20.6 6.4 634 682 7.6Test 4 0.36 29.0 28.2 2.8 701 745 6.3
Test 5 0.61 26.7 22.9 14.2 647 694 7.3
Test 6 0.37 22.8 25.9 13.6 737 734 0.4
Test 7 0.36 22.3 24.2 8.5 731 743 1.6
Test 8 0.36 21.3 24.4 14.6 705 742 5.2
Test 9 0.37 24.2 26.4 9.1 714 734 2.8
Test 10 0.49 20.5 21.0 2.4 655 709 8.2
Test 11 0.50 21.4 20.8 2.8 683 706 3.4
Test 12 0.53 28.4 29.3 3.2 681 680 0.1
Test 13 0.40 25.1 24.3 3.2 727 736 1.2
Test 14 0.25 26.4 33.2 25.8 745 791 6.2
Test 89 0.50 20.0 22.4 12.0 651 692 6.3
Test 90 0.65 20.7 19.0 8.2 630 640 1.6
Test 91 0.34 23.0 29.5 28.3 705 742 5.2
Test 92 0.05 117.0 109.0 6.8 1061 1046 1.4
Test 93 0.09 75.0 56.4 24.8 977 932 4.6
Table 1. Critical temperature of uniformly heated members
Simply Supported BeamCritical Temperature (C) at load ratio R1
in Bending 0.2 0.3 0.4 0.5 0.6 0.74-side BS5950 715 660 620 585 555 520
heated Analysis 725 671 629 591 559 527
% difference 1.4 1.7 1.5 1.0 0.7 1.3
Critical Temperature (C) at load ratio R2
Column in Compression 0.2 0.3 0.4 0.5 0.6 0.74-side BS5950 710 655 615 580 540 510
heated Analysis 723 678 641 608 564 529
70 % difference 1.9 3.5 4.2 4.8 4.5 3.8
4-side BS5950 635 635 590 545 510 460
heated Analysis 662 649 611 568 529 478
>70 % difference 4.2 2.2 3.5 4.2 3.8 3.9
R1 = Mf/Mc R2 = F/Agpy + Mx/Mcx + My/Mcy
: slenderness ratio Mf: applied mid-span moment at fire
Mc: moment capacity at ambient temperature F: axial force
Ag: cross-section areapy: yield strength
Mx and My: applied major and minor axis moment at fire
Mcx and Mcy: major and minor axis moment capacity at ambient temperature
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analysis is used for the verification. It has been found
that the correlation between simulation and test results
with respect to the mechanical response was extremely
good. The primary collapse load obtained was almost
perfectly predicted.
9. FIRE ANALYSIS OF ANOFFICE BUILDINGThis section presents a performance-based approach for
analysing a six-storey building frame subject to various
scenarios of fire attack. Advanced analysis method (Ma
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 325
Time (min)
Test (deflection)
Analysis (deflection)
Test (temperature)
Analysis (temperature)
Mid-Span
Deflection(m)
0.20
0.16
0.12
0.08
0.04
0.00
LowerFlan
geTemperature
800
600
400
200
0
0 10 20 30 40 50
Figure 16. Test and analysis results for test 11
30 30 30 30 30 30 30 kN
540 540540 540 540 540
4.2
55
4.5
7.2
column crosssection
beam crosssection
A B
100
100
100
1400mm
Figure 17. Lis frame
beam & columncross-section
82 kN 82 kN
9.45 kN
1500 mm
1500mm
DC
6.0
100
4.5
56
Figure 18. Zhaos frame
010
0
Horizontaldisplacement
(mm)
Time (min)
Node B,Analysis
Node A,Analysis
Node B, Test
Node A, Test
10
20
10 20 30
Figure 19. Analysis and test results (Lis frame)
Analysis
Test20
10
0
0 20 3010
Horizontaldisplacement at D
Vertical displacement
at CDisplacement(mm)
Time (min)
Figure 20. Analysis and test results (Zhaos frame)
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and Liew 2004) is used to propose a much reduced fire
protection plan for beams and columns and prove that
the design can satisfy the performance criteria of fire
safety. The building is classified as office building as
shown in Figure 21.
9.1. Limit States DesignThe frame is designed for the strength limit state at
ambient temperature according to Eurocode 3 with the
following actions:
Permanent Dead load (Gk,1) 3.6 kN/m2
actions Gk:
Permanent imposed 1.9 kN/m2
load (Gk,2)
Variable Variable imposed 1.6 kN/m2
actions Qk: load (Qk,1)
Wind load (Qk,2) 593 kN (in
Y-direction)The beam and column sizes are indicated in
Figure 21. A36 steel (design strength of 250 N/mm2) is
used in all sections. Plastic hinge analysis method is
adopted. Each beam is modelled using 4 elements and
each column using 1 element. Wind load is simulated
by applying a point load in Y-direction at every beam-
column joint of the front elevation.
At the fire limit state, which is treated as accidental
loads in Eurocode 3 Part 1-2 (2001), the design effect of
the actions is expressed as:
Efi,d,t = Gk+ 1Qk,1 + 2Qk,2 (15)
Where 1, 2 are factors due to the probability of loadsacting individually or in combination. Depending upon
which variable load is the dominant action, two load
combinations are possible under fire limit state:
Load combination 1:
Efi,d,t = Gk,1 + Gk,2 + 0.5Qk,1 + NL (Notional Load)
Load combination 2:
Efi,d,t = Gk,1 + Gk,2 + 0.3Qk,1 + 0.5Qk,2
In load combination 1, the notional load is taken as
0.5% of the factored gravity load at each storey, applied
in Y-direction and is distributed to the beam-column
joints as point load. In both cases, the structure is subjected
to gravity load or the combination of gravity load and
wind load first, followed by fire.
9.2. Fire ModellingParametric fire recommended in Eurocode 1 Part 1-2
(2001), is used to simulate the fire in the compartment
by considering the type of building, floor layout,
realistic fire load and possible fire fighting measures.
Fire load density per floor area qf,k = 420 MJ/m2 is
adopted for common office building. The design fire
load qf,d is defined as:
qf,d = qf,k. m. q1. q2 . n (16)
where m is the combustion factor and is assumed as
0.8; q1 is the partial factor taking into account thefire activation risk due to the size of the compartment.
For floor area from 25 m2
up to 250 m2
, q1 is equal to
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
326 Advances in Structural Engineering Vol. 7 No. 4 2004
Z
7.315 m 7.315 m
1 2 3
X
Y
7.315m
W12 26 W12 26
W12 26 W12 26
W1253
W1287
W1253
PLAN
W12x87
W1287
W12120
X
W
1060
H=6x3.658m=2
1.948m
1 2 3
W1060
FRONT ELEVATION
Figure 21. Six-storey building frame
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1.5 (in this case the floor area Af is 53.5 m2). q2 is 1.0
for occupancies such as office, residence and hotel. It is
assumed that no automatic fire suppression and
detection system is installed but an off site fire brigade
is available from which n is calculated as 0.78. Thedesign fire load qf,d is thus computed as 393 MJ/m
2,
which is equivalent to 98 MJ/m
2
per total area (qt,d). Thesurrounding surfaces of the compartment are assumed to
be normal concrete with b value of 1900 J/m2s1/2K.
Assuming an opening factor OF = 0.4, the temperature
time curve is plotted as shown in Figure 22. It can be
seen from Figure 22 that the fire curve with opening
factor OF = 0.04 are below the standard ISO 834 fire
curve, providing the possibility of reducing passive fire
protections. Two compartments are considered asshown in Figure 23. The columns in compartment 1 are
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 327
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120
ISO 834
OF = 0.04
Time (Min)
Temperature (C)
Figure 22. Parametric time-temperature curves for six-storey office building frame
Firecompartment 1
Firecompartment 2
1
4
5
2
7Z
X
Y
9
40
42
43
41
Elementnumber
Figure 23. Fire compartments in 6-storey space frame
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most heavily loaded and the size of columns reduces
from the 4th storey onwards.
9.3. Fire at the First Storey CompartmentIf all the beams and columns in the lower floor fire
compartment are unprotected, it is found that load
combination 2 is more severe as the structure fails at a
critical time of 33.7 minutes while it can survive the fire
under load combination 1. The deformed shape of the
structure under fire for each load combination is shown
in Figure 24.
Under load combination 1, as the beams expand
under fire, column heads are forced to open up in both
X and Y directions. When the frame is subjected to load
combination 2, the effect of wind load in Y-direction
becomes pronounced, causing the frame to deform in a
twisting mode. Despite the expansion of the heated
beams, all columns (1, 2, 4 and 5) sway to the same
direction as the wind load. The center of gravity of the
frame thus shifts to the leeward columns (4 and 5),
producing large axial force in the columns (Figure 25).
It is the failure of column 4 which triggers the collapse
of the frame under fire.
Load combination 2 is found to be most critical;
therefore subsequent analyses are carried out using only
this load combination.
Since the columns are found to be the critical
members, it is proposed that all the fire affected
columns are fully protected. Second-order plastic hinge
analysis is again carried out on the partly protected
structure, and the displacement of the column head in Y-
direction is found to be greatly reduced (see Figure 25),
in contrast to the runaway deflection of column 4 when
approaching failure for the unprotected columns.
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
328 Advances in Structural Engineering Vol. 7 No. 4 2004
Buckling ofColumn 4
Load Combination 1 (no collapse) Load Combination 2
Z
X
Y
Figure 24. Deformed shapes of 6-storey frame for load combinations 1 and 2
Case 1: Column Unprotected
Case 2: Column Protected
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.000 5 10 15 20
Time (min)
ColumnHeadDeflection(m)
25 30 35
1
4
Figure 25. Column 4 head displacement in the Y-direction
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However, the critical time shows only marginal
improvement, from 33.7 min to 35.5 min. Beam collapse
mechanism forms at beams 7 and 9 (the smallest beams)
in X-direction due to large restraint force from the
supporting columns, causing larger mid-span deflection
as shown in Figure 26.
The next logical step is to provide fire protection to
beams 7 and 9. In this case, the building survives the
entire fire duration with plastic hinges occur at the
beams in Y-direction.
9.4. Fire at the Fourth Storey CompartmentFire is assumed to occur at the 4th storeys compartment
as shown in Figure 23. When all the members are
unprotected, extensive plastic hinges form at the four
columns, triggering the collapse of the frame during the
fire. Although the loads on the fourth storeys columns
are smaller than those on the first storeys columns, the
column size from the fourth storey onward is also smaller.
At a critical time of 33 min, columns experience runaway
deflections in both X and Y directions (Figure 27),
symbolizing the failure of the columns. Figure 28 shows
the axial force in windward and leeward columns. The
shift of the center of gravity due to wind load produces
larger axial force in the leeward column.
If a realistic fire model is considered, it is possible
to reduce the cost of fire protection. In this 6-storey
building frame, columns and beams in X-direction
require passive fire protection from 1st storey to 3rd
storey. But from 3rd storey onwards, only columns
need to be protected while all the beams can be left
unprotected. However if ISO standard curve is used
irrespective of layout of the building, fire loads and
ventilation condition, all the members in the building
need to be fire protected Further study will be carried
out on high-rise buildings where the savings in passive
fire protection may become more significant if a
realistic fire is considered.
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 329
00 5 10 15
Case 1: Column Unprotected
Case 2: Column Protected
20
Beam 7
Beam 9
25 30 35
0.05
0.1
0.15
BeamMid-SpanDeflection(m)
Time (min)
0.25
0.27
9
Figure 26. Mid-span deflection of Beams 7 and 9
Column 42
Deflection in X-direction
35302520
Time (min)
ColumnHeadDeflection(m)
1510500.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.05
0.10
0.15
Column 42
Column 40
Column 40
Deflection in Y-direction
40
42
Figure 27. Column head displacements in X and Y directions (unprotected)
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10. FIRE PROTECTIONFire protection falls into two main categories, prevention
and protection. Preventative measures include control
of flammable inventories, control of ignition sources,
monitoring of environmental conditions leading to
initiation of alarms and automatic process control,
and fire detection systems designed to extinguish fires
immediately on detection. Protection measures fall into
two categories, passive and active. Passive measures
include fire barriers, fire resistant enclosures, fire doors,
fire retardant coatings and fire protective coatings. Active
measures include water and chemical sprays or deluges,foam dispersion and inert gas dispersal.
After the WTC incident, people expect the public
buildings and their work place to be designed to allow
safe evacuation in the event of fire or explosion. Certain
industrial buildings have stringent fire protection
requirements. For examples, oil and gas production
and processing, nuclear related product storage and
processing, chemical process and storage and key
infrastructures and transportation routes are facilities
that attracted greater risks.
From safety and licensing authorities point of view, the
structure must be capable of safe evacuation in the event
of fire. From the owners view point, the fire protection
is often an expensive statutory feature, which requires
initial capital investment. From the operator point of
view, fire protection must be maintained to preserve the
safety margins declared in the safety documentation. The
volume and cost of passive fire protection materials are
often a critical factor for consideration; therefore, there is
a need to balance these conflicting requirements when
specifying fire protection.
Fire protection can be provided as an all
encompassing scheme, or it can be functionally designed
to optimize on cost, weight and maintenance. Researchhas shown that fire can be successfully suppressed using
a properly design and maintained active protection system
without the need of passive fire protection. Evidently
the structural member affected by the fire may not be
reusable, but there is no guarantee that a fire protected
structure could be re-used anyway.
Computer models have been developed to predict
the response of structures considering fire protection
materials. This model will include the basic thermal
transmission phenomena, radiation, conduction and
convection, the temperature dependent properties ofmaterials and the location and nature of fire protection
measures. The resulting thermal histories are then
applied to the structure to predict time to collapse, or
to demonstrate the degree of collapse. From this, the
structure can be economically protected to meet the
safety requirements.
11. INTEGRATED EXPLOSIONAND FIRE ASSESSMENTOF STRUCTURESThe assessment of the response of structures to explosion
is an increasingly important factor in design, particularly
where the storage and processing of explosive materials
is concerned. Many structures are required to be blast
resistant to protect personnel and adjacent facilities, and
to reduce the possibility of escalation of events. These
structures are therefore designed to contain the effects of
explosion or to act as a significant barrier.
There is a great difference in the structural behaviour
of buildings subject to explosion and fire loads. The short
duration of explosion loading implies that the material is
strain-rates dependent, i.e., high strain rate will increase
the yield strength of steel (Izzuddin & Fang 1997). On
Performance Based Fire Safety Design of Structures A Multi-dimensional Integration
330 Advances in Structural Engineering Vol. 7 No. 4 2004
Column 40
00
50
100
150
200
250
300
5 10 15
Time (min)
ColumnAxialFor
ce(kN)
20 25 30 35
Column 42
40
42
Figure 28. Axial force in columns 40 and 42 (unprotected members)
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the other hand, fire loading is associated with elevated
temperatures which cause thermal strains and lead to
significant deterioration in the material properties of steel.
Izzuddin et al. (2000) proposed an integrated analysis
method for explosion and fire analysis of steel structures
incorporating material models which account both for
rate-dependency and thermal property of steel.Liew and Chen (2004) presented a numerical
approach for inelastic transient analysis of steel frame
structures subjected to explosion loads followed by
fire. The proposed transient inelastic analysis can be
used effectively to solve explosion and thermal response
problems, taking account of geometric and material non-
linearities. To achieve both computational accuracy and
efficiency, an analysis procedure has been proposed in
which fire can be treated as a separate event after the
occurrence of an explosion. The fire resistance of the
structure can be evaluated by analyzing the deformed
geometry of the structure caused by the explosion. Theapproximate fire analysis method does not require time
domain solutions but it predicts higher fire resistance
than the strict inelastic transient analysis. Nevertheless,
it offers an alternate means to evaluate the performance
of structures subjected to combined scenarios of explosion
and fire at a much reduced computational cost.
Hand calculation procedure and computational
techniques have been developed with the aim of predicting
how a structure will respond under the interaction of blast
and fire. The followings summarized some of the works
that are being investigated using the explosion responsetechnologies developed.
Pseudo-dynamic or pseudo-static methods these
are the simplest to apply since they take the
explosion overpressure as a blanket loading, and
are usually combined with dynamic amplification
factors. The methods can assess both elastic and
inelastic responses and can be applied to complex
structures.
Single Degree of Freedom Method this is a
dynamic analysis technique, which predicts the
response of a structure by reducing the structure
to a simplified spring/mass system. The method
is effective for simple structures that behave in a
similar manner as to a spring/mass system. The
method can assess both linear and non-linear
responses and can be applied to simulate the
response behaviour of more complex structures.
Finite Element Analysis they can be used
effectively to solve explosion response problems,
taking account of geometric and material non-
linearities. In term of computation time usage,
balance has to be sought since there is a fine line
between a model which is detailed enough to
predict the response, and coarse enough not to
run for impracticable lengths of time. Evidently,
with the continued increase in the speed and
capacity of computers, this problem will be less
critical. The model detail is a matter to be
addressed by the analysts carrying out the work
as is the choice of solution method. The twomost common time domain solutions, implicit
integration and explicit integration can both be
used, each having their own pros and cons.
Significant experience has been gained in the
assessment of structures subjected to explosion loading
using both hand and FEA based methods. Combining
the structural response analysis with the explosion
prediction analysis, it is possible to predict and hence
optimize structural resistance.
12. CONCLUSIONSThe difference in perspective between architect andengineer is noticeable in the design and construction
process. In the conventional approach, the architect
would specify the fire designs based on prescriptive
code requirements and the engineer would design the
structures with fire protection to achieve a certain fire
rating. It becomes apparent in the recent years that
the structural engineers should directly involve in fire
engineering rather than the traditional approach of the
architect specifying the fire designs. In a performance
based design approach, the first step is to understand
what level of performance is expected, then to design tothese levels and followed by predicting the performance
that will be achieved, and finally to be able to assure the
reliability and robustness of the design in the occurrence
of an extreme event.
To carry out a quantitative assessment on the
performance of a building in fire requires the knowledge
of fire science, material properties at elevated temperature,
occupant behaviour and evacuation procedure during an
emergency situation, heat transient and structural response
phenomena, and fire protection etc. All these would
require a multi-dimensional integration approach, as
described in this paper, for performance-based design of
structures.
Fire may be treated as a building load, consistent with
the treatment of other loads in building design such that
it can be integrated with structural design in various load
combinations. Design fire scenarios can be prescribed
for standard building forms and further examined for
more complex systems. Structural design should also
consider the integration between evacuees and fire-
fighter interactions. Proper fire model with interaction
with the active and passive protection measures should
be developed, and relationship between emergency
J. Y. Richard Liew
Advances in Structural Engineering Vol. 7 No. 4 2004 331
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response and fire resistance should be established so
that appropriate performance-based method can be
developed to predict the building response to extreme
events. The examples given in this paper illustrated that
saving in passive fire protection could be substantial for
high-rise and large building framework if realistic
natural fires, instead of the conventional standard fire,were considered in design.
Improved understanding of the real behaviour of
natural fire in tall buildings opens new ways of integrating
fire safety and structural design. Prescriptive codes
without considering the systems limit states behaviour,
are often quite approximate in nature. With the advance in
computing technologies, there is an increasing demand for
robust and efficient nonlinear analysis methods for
performance-based design of structures subject to fire and
explosion. Some of the works mentioned in this paper are
a step towards this development.
ACKOWLEDGEMENTSThe author would like to acknowledge the contributions
made by Dr H Chen, Dr L K Tang, Ms K Y Ma, and
Ms H X Yu for their research work on steel structures
in fire in the Department of Civil Engineering at the
National University of Singapore. The work is funded
by research grants (R264000138112) made available by
the National University of Singapore.
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J. Y. Richard Liew
Jat-Yuen Richard Liew is an associate professor and the director of the centre forconstruction materials and technology in the National University of Singapore (NUS). Hereceived his B.Eng and M.Eng degrees (Civil Engineering) from NUS and his Ph.D degreefrom Purdue University in 1992. His research interests include deployable structures, steel-concrete composite systems and fire safety design of buildings. Arising from theseworks, he has generated some 150 technical publications. These include technical articles
in journals, presentations, reports, books, and patents. He interacts closely with the steelindustry in the Asian region as a technical advisor in the areas of steel and compositestructures. He has also seen his R&D brought from the laboratory to full-scale applications.The latter include projects in airport structures, high-rise buildings, large-span andprestressed structures. He is a registered professional engineer in Singapore and achartered engineer in U.K.