2a-B Fire Models

Chap.
II Evaluating fire development

in buildings
1
2016/2017
University of Liege
J-M Franssen & T. Gernay
2. Fire development in buildings
Evaluating the fire action: objectives
List the different models for building fires and the associated input data
Use the adequate type of fire model for a given problem
Estimate the values of the input data required in the models
Assess the variation of temperature in a building with time and (possibly) space
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Evaluating the fire action: what is at stake?

Fire generates a temperature increase of the gas present in the vicinity of the structural
elements
This temperature increase weakens the materials that constitute the structure (1), and
creates thermal expansion (2)
To evaluate the response of the structure in case of fire, the first step consists in
characterizing the fire action, i.e. the temperature increase
In all generality, one aims at determining the transient temperature field
= (x,y,z,t)
In practice, one can use models of different sophistication levels, depending on the
applications
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Evaluating the fire action: what is at stake?

The action of the fire on a structure can be represented using models
- Prescrip ve approach standardized, nominal re
Objective: standard representation, useful for comparison and classification
Criterion for fire resistance: ensure the required function

during the prescribed duration
t
- Performance-based approach natural re

Objective: realistic representation of the temperature evolution, based on physics
Criterion for fire resistance: ensure the required function

during the whole fire duration (incl. decay and extinction)
t
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Different models for fire

The choice of the model depends on the objectives, hypotheses and available data
Nominal temperature-time curves
Standard fire curve (ISO834)
External fire curve
Hydrocarbon curve
Natural fire models
Simplified fire models
- Compartment re parametric re
- Localized re Heskestadt or Hasemi
Advanced fire models
- Two-Zone- or One-Zone Fire or a combination
- CFD Computational Fluid Dynamics
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Different models: hypotheses and required data
*) Nominal temperature-time curve
Standard fire curve, external fire curve &
hydrocarbon curve
No data required
*) Simplified fire models

Localized fire
Full compartment fire
- HESKESTADT
- HASEMI
- Parametric fire
(t) uniform
In the compartment
(x, y, z, t)
*) Advanced fire models
Rate of heat release

Fire surface
Fire load density
Boundary properties
Area of openings
Ceiling height
+
- One-Zone model
- Two-Zone model
- Combination Two-Zone and One-Zone
Exact geometry
- CFD
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Standard fire curve (ISO834)
= 20 + 345 log (8 t + 1)
with t the time in min
[C]
1200
1110
1006
1000
945
1049
The ISO curve
* Is applied to the whole compartment even if it is large
842
800
600
ISO
ISO
ISO
400
ISO
ISO
ISO
ISO
ISO
* Never cools down/decreases

* Does not consider the PRE-FLASHOVER PHASE
200
* Does not depend on the fire load and the ventilation conditions
0
0
30
60
90
120
180
Temps [min]
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Temperature
Pre- Flashover
Post- Flashover
1000-1200C
Flashover
Natural fire curve
ISO834 standard fire curve
Time
Ignition
heating
cooling .
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Gas temperature (C)

1200
Hydrocarbon Fire
1000
Standard Fire
800
External Fire
600
400
200
0
1200
2400
Time (s)
3600
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Natural fire concept
hydrocarbon curve
No data required

Localized fire
- HESKESTADT
- HASEMI
- Parametric fire
(t) uniform
In the compartment
(x, y, z, t)

Fire surface
Fire load density
Boundary properties
Area of openings
Ceiling height
+
- One-Zone model
- Two-Zone model
Exact geometry
- CFD
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Assumptions of nominal curves fall short notably when considering fires with:
Cooling down phases
[C]
1200
1000
800
600
400
200
0
30
60
90
120
180
Time [min]
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Assumptions of nominal curves fall short notably when considering fires with:
Localized development
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Natural fire concept is implemented in:

EN 1991-1-2
Some National Annexes
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University of Liege
Inputs for natural fire model

List of physical parameters required for a natural fire model
Properties of boundary of enclosure
Area of openings
Ceiling height
Geometry
Fire surface
Rate of Heat Release (RHR)
Fire load density
Fire
Rate of heat release (RHR): rate at which heat (energy) is generated by the fire (in W)
Fire load density (qf): sum of thermal energies which are released by combustion of
all combustible materials in a space (building contents and construction elements),
per unit area
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Characteristics of the fire compartment
Definition of the compartment

according to national regulations
Material properties for the

boundary of enclosure: c, ,
Definition of the openings
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Characteristics of the fire compartment
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Characteristics of the fire: fire load
The fire load is rarely known in a deterministic way.
In theory, it can be calculated by summing all the energy able to be released in the
compartment in case of fire:
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Deterministic calculation of the fire load
Table: Net calorific value of some

combustible materials Hu [MJ/kg]
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More often, the fire load is calculated in a statistical way
Statistical information is given for specific building types
Table in MJ/m (based on a Gumbel type I distribution)
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More often, the fire load is calculated in a statistical way
Which value to take?
Distribution of fire load (MJ/m) in

(a) Government buildings
(b) Private offices
(adapted from Culver, 1978)
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Fire load density: characteristic value (qfk) and design value (qfd)
The design value (to be used in the calculations) is calculated by multiplying the
characteristic value (80% fractile) by a series of factors:
q f ,d = q1 . q 2 . ni . m . q f ,k
The factors allow taking into account the fire risk, using a semi-probabilistic approach
q1 takes into account the fire activation risk due to the size of the compartment
q2 takes into account the fire activation risk due to the type of occupancy
n =
n takes into account the different active fire fighting measures
m is the combustion factor (assumed as 0.8 for cellulosic materials)
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Principle: semi-probabilistic approach to fire risk
q f ,d = q1 . q 2 . ni . m . q f ,k
The Eurocode approach is based on a target value = acceptable probability of failure

Pf (failure probability) Pt (target probability)
EN 1990: Pt = 1.3 x 10-6 per year
for a building, for ultimate limit state in normal conditions
Pf (failure probability) = Pfi (probability of fire) x Pf,fire (probability of failure if fire)
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Consider the case of structural failures due to snow in a big country
N = 107 buildings
Pf = 10-6 per year
10 buildings failure due to snow per year, deemed acceptable
Pf = Psnow x Pf,snow = 1 x 10-6
100
10-6
Psnow is close to 1 and cannot be modified

Pf,snow = 1 x 10-6 must be ensured by design
deniQon of safety factors on the loads and materials such that Pf,snow = 1 x 10-6
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Now, consider the case of structural failures due to fire in the same country
N = 107 buildings
Pf = 10-6 per year
10 buildings failure due to fire per year, deemed acceptable
Pf = Pfi x Pf,fi = 1 x 10-6
10-4 10-2
Not all buildings will catch fire! Pfi = 10-4 and can be modified by different measures
Pf,fi = 1 x 10-2 must be ensured by design
safety factors on the loads and materials much less severe because such that Pf,fi = 1 x 10-2
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Now, compare 3 building compartments identical except for fire protection
Case 1
Case 2
Case 3
No active system
Fire alarm
Fire alarm + sprinklers
Pfi
Pfi
Pfi
Pf,fi
Pf,fi
Pf,fi
qfd
qfd
qfd
All 3 have the same failure probability Pf
Considering a higher design fire load decreases the probability of failure in case of fire
Decreasing the Pfi by adding fire protection systems, allows accepting a higher Pf,fi,
therefore designing with a lower qfd
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Probability distribution
Why a higher design fire load decreases the probability of failure in case of fire
The fire load in the compartment is a random parameter
The value that is selected influences the design fire
The design fire influences the amount of fire protection
Case 3
Case 2 Case 1
Temperature [C]
Fire load q [MJ/m]
Design fire
Case 3
Case 2
Case 1
time [sec]
26
In reality, if a fire occurs, the fire load / fire will be

whatever it is and the most protected structure has
the least chance to fail (lower Pf)
Case 1
Case 2
Case 3
If sprinklers are installed in a compartment, it is allowed to reduce the fire load used in the
calculation for designing the structure, based on the target failure probability approach of EN
2016/2017
University of Liege

Characteristics of the fire for different building types
The characteristic value of fire load is the 80% fractile (EN 1991-1-2)
RHRf: maximum RHR produced by 1 m of fire in case of fuel controlled conditions
Occupancy
Fire growth rate
RHRf
[kW/m]
Fire load qfk

80% fractile
[MJ/m]
Dwelling
Medium
250
948
Hotel (room)
Medium
250
377
Library
Fast
500
1824
Office
Medium
250
511
School
Medium
250
347
Fast
250
730
Shopping centre
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Characteristics of the fire: RHR
The fire load defines the available energy for the fire
The RHR defines the evolution of gas temperature
Sequence of a typical fire:
Starts small, localized source
Rising phase in t (hyp.: diameter of the source increases at constant rate)
Stationary phase, either fuel controlled or ventilation controlled
Decay phase, with linear decrease of the RHR
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Rate of heat release curve (RHR)
Steady-state phase and decay phase
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RHR [MW]
Medium (FGR)
RHR [MW]
RHR [MW]
Fire A
Growth
Rate = FGR
x RHR
fi
Decay phase
1
75'' 150''
70% (qf,d 1Afi)0 0

0
Slow (FGR)FIRE
LOCALISED
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COMPARTMENT FIRE
Fast (FGR)
(FGR)
29
A f x RHR
10 Ultra8
Fast
9 7
8
Growing
Steady
state phase
Decay Phase
300''
5
5
tdecay
University of Liege
600''
10
15
10
20
15
t [min]
25t [min]30
20
Time [min]
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Natural fire concept Simplified fire models
hydrocarbon curve
No data required

Localized fire
- HESKESTADT
- HASEMI
- Parametric fire
(t) uniform
In the compartment
(x, y, z, t)

Fire surface
Fire load density
Boundary properties
Area of openings
Ceiling height
+
- One-Zone model
- Two-Zone model
Exact geometry
- CFD
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Natural fire model - Simplified

Localized fire VS Full compartment fire
Localized fire

(t) uniform in the compartment
(x, y, z, t)
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Full compartment fire: e.g. here a real fire in an office building
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Full compartment fire: calculation
No spa!al varia!on in temperature = (t)
Annex A of EN 1991-1-2 Parametric Eurocode fire
Temperature [C]
1100
Iso-Curve
1000
O = 0.04 m
900
O = 0.06 m
800
O = 0.10 m
O = 0.14 m
700
O = 0.20 m
600
500
For a given b, qfd, At & Af
400
300
200
100
time [min]
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20
30
40
50
60
70
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80
90
100
110 120

Input data:
- Fire load density qf,d
- Opening factor
O = Av h / At
- Wall factor
b = c
Temperature = (t)
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Applicability limits of the model:
- Afloor 500 m
- No horizontal opening
- H4m
- Design fire load density, qf,d, between 50 and 1000 [MJ/m]
- Opening factor, O, between 0.02 and 0.20 [m1/2]
- Wall factor, b, between 100 and 2200 [J/ms1/2K]
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Localized fire: e.g. here in a test
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Localized fire: calculation
Spa!al varia!on of the temperature = (x,y,z,t)
Annex C of EN 1992-1-2 Equations to calculate the thermal action of a localized fire
The equations to adopt depend on the relative height of the flame to the ceiling
If the flame is not impacting the ceiling (Lf < H),
or in open air Heskestadt method
If the flame is impacting the ceiling (Lf > H)
Hasemi method
with H the distance between the fire source
and the ceiling [m]
The flame lengths Lf of a localized fire is given by:

Lf = -1,02 D + 0,0148 Q2/5
[m]
with D the diameter of the fire [m]

with Q the RHR of the fire [W]
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Localized fire: Heskestadt method (Lf < H)
Spa!al varia!on of the temperature = (x,y,z,t)
Flame not impacting the ceiling, or fire in open air
Temperature (z) in the plume along the symmetrical vertical flame axis:
(z) = 20 + 0,25 Qc2/3 (z-z0) -5/3 900
[C]
with Qc the convective part of the RHR [W]

with z the height along the flame axis [m]
Virtual origin z0 of the axis:
z0 = -1,02 D + 0,00524 Q2/5
[m]
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Localized fire: Hasemi method (Lf > H)
Spatial variation of the temperature = (x,y,z,t)
Flame axis
Flame impacting the ceiling
Lh
Concrete slab
beam
Hasemi gives the equations to calculate the

heat flux received by the fire-exposed unit
surface area at the level of the ceiling:
h [W/m]
40
h is function of:
r: Horizontal distance between the fire vertical axis and
the point along the ceiling where the flux is calculated
Lh: Horizontal flame length
H: distance between the fire source and the ceiling
D: Diameter of the fire
Q: RHR of the fire
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= Temperature
at beam level
D
x

Localized fire: Limits of applicability
Spatial variation of the temperature = (x,y,z,t)
The Heskestadt and Hasemi methods are valid if:
The diameter of the fire is limited by D 10 m
The RHR of the fire is limited by Q 50 MW
Note: the Hasemi method can be employed in case

of several separate localized fires,
simply by summing the heat fluxes h due to each fire
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Localized fire: Heat flux calculation
EN 1991-1-2
Formula to calculate the heat flux from a localized fire to a structural member
Net heat flux hnet on the fire exposed surfaces:
hnet = hnet,c + hnet,r
[W/m]
Net convective heat flux hnet,c:

hnet,c = c (g - m)
[W/m]
with c the coeff. of heat transfer by convection [W/mK]

with g the gas temperature in the vicinity of the member [C]
with m the surface temperature of the member [C]
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Localized fire: Heat flux calculation
EN 1991-1-2
Formula to calculate the heat flux from a localized fire to a structural member
Net radiative heat flux hnet,r:
hnet,r = m f [(r + 273)4 (m + 273) 4]
[W/m]
with the configuration factor [-]

with m the surface emissivity of the member [-]
with f the emissivity of the fire [-]
with the Stefan Boltzmann constant [=5.67 x 10-8 W/mK4]
with r the effective radiation temperature of the fire environment [C]
with m the surface temperature of the member [C]
Note:
These formula for hnet are not specific to localized fire

For any time-temperature curve (fire), the thermal actions are then
calculated using the net heat flux hnet to the surface of the member
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Natural fire concept Advanced fire models
hydrocarbon curve
No data required

Localized fire
- HESKESTADT
- HASEMI
- Parametric fire
(t) uniform
In the compartment
(x, y, z, t)

Fire surface
Fire load density
Boundary properties
Area of openings
Ceiling height
+
- One-Zone model
- Two-Zone model
Exact geometry
- CFD
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Natural fire model - advanced

OZone software
Combination of Two-Zone and One-Zone fires
Start:
Localized fire
OZone model
Stratification (2 zones)
Z
QC
ZS
Upper layer
mU , TU, VU,
EU, U
m OUT,U
QR
ZP
Q
m IN,L
mL , TL, V L,
EL, L
p
mp
Lower layer
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m IN,L

OZone software
Criteria for flash-over (transition to full compartment fire)
2 1 zone: if the following criteria are reached
Tsmoke > 500 oC
Combustible material is in the smoke and Tsmoke > 300 oC
Localized fire > 25 % of the area of the compartment
Smoke > 80 % of the height of the compartment
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OZone software
Combination of Two-Zone and One-Zone fires
OZone model
Z
QC
QR
mOUT,L
p = f(Z)
m, T, V,
E, (Z)
mOUT
ZP
mIN,L
Fire: RHR,
combustion products
0
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QC+R,O

OZone software
Validation of the software
Localized fire - 39 tests:
VTT: salle (8 tests)
VTT: room (21 tests)
DSTV: room (10 tests)
Generalized fire - 71 tests:
CTICM: room, wood (36 tests)
CTICM: room, furniture and paper (10 tests)
BRE: deep compartment (9 tests)
CTICM: hotel (3 tests)
CTICM: school (1 tests)
BRE: NFSC2 series (8 tests)
VTT: timber structure (4 tests)
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OZone software
Validation of the software based on fire tests in compartments fire load
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OZone software
Validation of the software based on fire tests in compartments exterior flames
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OZone software
Validation of the software based on fire tests in compartments after the test
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OZone software
Validation of the software based on fire tests in compartments
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OZone software
Validation of the software based on fire tests in compartments
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OZone software
Utilization
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OZone software
UQlizaQon compartment definition
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OZone software
UQlizaQon compartment definition
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OZone software
UQlizaQon fire definition
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OZone software
Utilization definition of criteria to shift from 2 zones to 1 zone
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OZone software
UQlizaQon results
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Measured temperatures compared to OZone results
Temperatures calculated with OZone [C]
1400
1300
1200
1100
1000
900
800
700
y = 1.0955x - 102.13
600
500
R2 = 0.9348
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400
Temperatures measured during the tests [C]

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Comparison BRE Test 4: Measures vs OZone Design fire
1400
OZone Office Fast

OZone Office Medium
Test Average
Test Max
Test Min
1300
1200
Gas Temp [C]
1100
1000
900
800
qf,d =511MJ/m2
RHRf = 250kW/m2
700
600
500
400
300
200
100
0
0
600
1200
1800
2400
3000
3600
4200
4800
5400
6000
6600
7200
Time [sec]
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Computational Fluid Dynamics (CFD)
- Allows studying fluid flows and their effects
- Solve numerically the equations governing the fluid (e.g. Navier-Stokes)
- Based on a discretization of the domain of resolution (finite volumes method, finite
elements method, finite difference method, etc.)
- Powerful and versatile method: allows computing all characteristics of the fluids
(speed, pressure, etc.) in every points of the domain, for multiple types of application
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FDS software
Computational Fluid Dynamics (CFD)
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FDS software
Definition of the mesh and boundary conditions
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FDS software
Results: gas temperature
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CFD Computational Fluid Dynamics
Video Bosphore
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University of Liege

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Chap.

II Evaluating fire development

J-M Franssen & T. Gernay

2. Fire development in buildings

Evaluating the fire action: objectives

J-M Franssen & T. Gernay

2. Fire development in buildings

Evaluating the fire action: what is at stake?

J-M Franssen & T. Gernay

2. Fire development in buildings

Evaluating the fire action: what is at stake?

Criterion for fire resistance: ensure the required function

- Performance-based approach natural re

Criterion for fire resistance: ensure the required function

J-M Franssen & T. Gernay

2. Fire development in buildings

Different models for fire

J-M Franssen & T. Gernay

2. Fire development in buildings

Different models for fire

*) Simplified fire models

*) Advanced fire models

Rate of heat release

J-M Franssen & T. Gernay

2. Fire development in buildings

Nominal temperature-time curves

with t the time in min

* Never cools down/decreases

J-M Franssen & T. Gernay

2. Fire development in buildings

Nominal temperature-time curves

Natural fire curve

ISO834 standard fire curve

J-M Franssen & T. Gernay

2. Fire development in buildings

Nominal temperature-time curves

Gas temperature (C)

J-M Franssen & T. Gernay

2. Fire development in buildings

Different models for fire

*) Simplified fire models

*) Advanced fire models

Rate of heat release

J-M Franssen & T. Gernay

2. Fire development in buildings

Different models for fire

J-M Franssen & T. Gernay

2. Fire development in buildings

Different models for fire

Natural fire concept is implemented in:

J-M Franssen & T. Gernay

2. Fire development in buildings

Inputs for natural fire model

J-M Franssen & T. Gernay

2. Fire development in buildings

Inputs for natural fire model

Definition of the compartment

Material properties for the