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FIRE
Advanced models
SUSCOS
107/07/2013
Jean-Marc
Franssen
Three steps Three steps
in the structural fire design:in the structural fire design:
1.1.Define the fireDefine the fire ((not part of Structural Fire Engineeringnot part of Structural Fire Engineering))..
2.2.Calculate the temperatures in the structure.Calculate the temperatures in the structure.
3.3.Calculate the mechanical behaviour.Calculate the mechanical behaviour.
3
Step 1Step 1
Define the fire that will then be taken as a Define the fire that will then be taken as a
data by the SFE software, such as SAFIR, data by the SFE software, such as SAFIR,
VULCAIN, ABAQUS or ANSYS,VULCAIN, ABAQUS or ANSYS,
4
Option 1: a design fire TOption 1: a design fire Tgg = f(t)= f(t)
�� Either Either
•• ISO 834, ISO 834,
•• hydrocarbon curve of Eurocode 1,hydrocarbon curve of Eurocode 1,
•• external fire curve of Eurocode 1,external fire curve of Eurocode 1,
•• ASTM E119.ASTM E119.
�� or choose your own timeor choose your own time--temperature curve temperature curve
(from zone modelling, for example) and describe it (from zone modelling, for example) and describe it
point by point in a text file.point by point in a text file.
( ) ( )4 4
g S g Sq h T T T Tσ ε• = − + −Heat flux linked to a Tg-t curve:
5
Example of a tool for determining
Temperature-time curve:
Software OZone
6
Fire phases and associated modelFire phases and associated model
The compartment.The compartment.
7
Fire phases and associated modelFire phases and associated model
The fire starts. The fire starts.
8
Fire phases and associated modelFire phases and associated model
Stratification in 2 zones.Stratification in 2 zones.
9
Qmp
H
ZS
ZP
0
Lower layer
Upper layer
mOUT,U
mIN,L
mIN,L
QC
QR
mU , TU, VU,
EU, ρU
mL , TL, VL,
EL, ρL
p
Z
Fire phases and associated modelFire phases and associated model
2 zones model. 2 zones model.
10
Fire phases and associated modelFire phases and associated model
Flash over. Flash over.
11
H
ZP
0
mOUT
mOUT,L
mIN,L
QC
QR m, T, V,
E, ρ(Z)
p = f(Z)
Fire: RHR,
combustion products
QC+R,O
Z
Fire phases and associated modelFire phases and associated model
1 zone model. 1 zone model.
12
Result to be used by SFE : the timeResult to be used by SFE : the time--temperature curvetemperature curve
0
100
200
300
400
500
600
700
800
900
1000
0 10 20 30 40 50 60 70
Time [min]
Temperature [°C]
One Zone Model
Combination
OPENING of Vertical Vents
(back tu fuel bed controlled fire)
Begining of Ventilation
controlled fire
External Flaming Combustion Model
Influence of windows breakage on zone temperatures
13
Option 2: a flux at the boundaryOption 2: a flux at the boundary
( )q f t• =
f(t) is described point by point in a text file.
Note: If the flux is positive, the temperature keeps
on rising to infinite values.
=> It is possible (and advised) to combine a flux
with a Tg-t condition, with Tg = 20°C.
14
Option 3: a flux defined Option 3: a flux defined
��by the local fire model of EN 1991by the local fire model of EN 1991--11--2 ,2 ,
��from the results of a CFD analysisfrom the results of a CFD analysis
This is a more complex technique, then a timeThis is a more complex technique, then a time--
temperature curvetemperature curve
15
Steps 2 & 3Steps 2 & 3
Thermal & mechanical calculationsThermal & mechanical calculations
16
Link between thermal and mechanical analysesLink between thermal and mechanical analyses
The type of model used for the thermal analysis depends The type of model used for the thermal analysis depends
on the type of model that will be used in the subsequent on the type of model that will be used in the subsequent
mechanical analysis.mechanical analysis.
17
Temperature fieldTemperature field Mechanical modelMechanical model
3D F.E.Simple calculation
model or 3D F.E.
2D F.E.2D F.E. Beam F.E. (2D or 3D)Beam F.E. (2D or 3D)
1D F.E. Shell F.E. (3D)
Simple calculation
modelTruss F.E. (2D or 3D)
=>
=>=>
=>
=>
Link between thermal and mechanical analysesLink between thermal and mechanical analyses
This
presentation
18
General principle of a mechanical analysis based on
beam F.E. elements.
19
20
Apply boundary conditions
(supports) and loads.
Then let the heating go.
Step 2.Step 2. Thermal Calculation Thermal Calculation --
discretisationdiscretisation of the structureof the structure
2D2D3D3D
Example
A concrete beam
2D thermal model – meshing of the section,
usually with 3 or 4 node linear elementsNote: the temperature is represented here by the vertical
elevation.
T
Y
Z
23
T
Y
Z
The temperature varies linearly along the edges of
the elements => C0 continuity for the temperature
field
24
Not correct Correct
4
4
4
4 3
3
3
25
111 1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
111 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
1
1 111 1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
111
1 1X
Y
Z
Step 2.Step 2. Thermal response : Thermal response :
discretisation of the structurediscretisation of the structure
True sectionTrue section MatchingMatching Discretised sectionDiscretised section
⇒⇒The discretised section The discretised section
is an approximation of the real sectionis an approximation of the real section
27
≠≠≠≠ ≠≠≠≠
Same section.
Different discretisations.
⇒Different results
Note: the results tend toward the true solution
when the size of the elements tends toward 0
28
Example of a very simple discretisationExample of a very simple discretisation
¼¼ of a 30 x 30 cmof a 30 x 30 cm²² reinforced concrete sectionreinforced concrete section
29
0.0
0.5
1.0
1.5
2.0
2.5
0 200 400 600 800 1000
Temperature [°C]
Thermal conductivity [W/mK]
Heating
Cooling
Non linear thermal properties are used.Non linear thermal properties are used.
Here, thermal conductivity of concreteHere, thermal conductivity of concrete(non reversible during cooling).(non reversible during cooling).
The local equilibrium equation for conduction isThe local equilibrium equation for conduction is
It is transformed in an element equilibrium It is transformed in an element equilibrium
equation.equation.
02
2
2
2
=+
∂∂
+∂∂
Qy
Tk
x
Tk
[ ]{ } { }qTK =
=
4
3
2
1
4
3
2
1
4,4
4,33,3
4,23,22,2
4,13,12,11,1
q
q
q
q
T
T
T
T
kSym
kk
kkk
kkkk
31
Integration of the thermal properties on the surface:
Numerical method of Gauss
NG = 1
NG = 2
NG = 3
32
The transient temperature distribution is evaluated.The transient temperature distribution is evaluated.
Here under a natural fire (peak temperature after 3600 sec)Here under a natural fire (peak temperature after 3600 sec)..
33
Concrete Filled Steel SectionConcrete Filled Steel Section
((courtesy N.R.Ccourtesy N.R.C. Ottawa. Ottawa))
TT prestressed beam
35
36
Radiation in the cavities is taken into accountConcrete hollow core slab
37
T.G.V. railway station in Liege (T.G.V. railway station in Liege (courtesy Bureau Greischcourtesy Bureau Greisch).).
Main steel beam with concrete slab.Main steel beam with concrete slab.
38
Old floor system; steel I beams and precast voussoirs
Courtesy: Lenz Weber, Frankfurt
39Steel H section in a steel tube filled with concrete
40
Window frame (courtesy: Permasteelisa)
41
Composite steel-concrete columns (1/2)
Courtesy: Technum
42
Composite beam partly heated
Steel column
through a
concrete slab
3D examples3D examples
43
Composite steelComposite steel--concrete concrete jointjoint
DiscretisationDiscretisation
44
Composite steelComposite steel--concrete concrete jointjoint
TemperatureTemperaturess on the surfaceon the surface
45
Composite steelComposite steel--concrete concrete jointjointTemperatureTemperaturess on the steel elementson the steel elements (concrete is transparent)(concrete is transparent)
46
Composite steel-concrete joint
Temperatures on the concrete elements (steel transparent)
47
Project Team EN 1994-1-2 (Eurocode 4)
Steel stud on a thick plate (axi-symetric problem)
48
Concrete beam (Concrete beam (courtesy courtesy Halfkann & KirchnerHalfkann & Kirchner))
Transmission of the shear force around the holesTransmission of the shear force around the holes
Step 2.Step 2. Thermal response : limitationsThermal response : limitations
• Free water – the evaporation is taken into account,
but not the migration.
• Perfect conductive contact between the materials.
• Fixed geometry (spalling! Can eventualy be taken
into account, but not predicted).
• No influence of the structural analysis on the
thermal analysis (in concrete, no influence of
cracking on the thermal conductivity).
50
Step 2.Step 2. Thermal response : limitationsThermal response : limitations
Linear elements.Consequence: possible skin effects (spatial oscillations)
A wall (uniaxial heat flow)
T
Exact solution
51
Step 2.Step 2. Thermal response : limitationsThermal response : limitations
Linear elements.Consequence: possible skin effects (spatial oscillations)
T
Exact solution
One finite element
F.E solution
Cooling ?!?!?
52
Step 2.Step 2. Thermal response : limitationsThermal response : limitations
Linear elements.Consequence: possible skin effects (spatial oscillations)
T
Exact solution
Two finite elements
F.E solution
53
Step 2.Step 2. Thermal response : limitationsThermal response : limitations
Linear elements.Consequence: possible skin effects (spatial oscillations)
T
Exact solution
Three finite elements
F.E solution
54
Step 2.Step 2. Thermal response : limitationsThermal response : limitations
Linear elements.Consequence: possible skin effects (spatial oscillations)
Solution:
The mesh must not be too crude
in the zones
and in the direction
of non linear temperature gradients.
Step 3.Step 3. Mechanical calculation Mechanical calculation --
discretisationdiscretisation
TrussTruss BeamBeam
SolidSolid ShellShell
6
6
6
3
3
3 3
3
33
3
3
7
7
1
6
6
66
Discretisation of the 2D beamDiscretisation of the 2D beam
Y
X1
2
3
Node
x
y
Discretisation of the beamDiscretisation of the beam
Node 1 Node 2
x
y
z
Node 2 Node 1
x
y
z
The local equilibrium equation is :The local equilibrium equation is :
The element equilibrium equation is :The element equilibrium equation is :
[ ]{ } { }PuK =
=
7
6
2
1
7
6
2
1
7,7
7,66,6
5,5
4,4
3,3
2,2
7,13,12,11,1
p
p
p
p
u
u
u
u
kSym
kk
k
k
k
k
kkkk
........xy
yx
∂
∂+
∂∂ σσ
( )
( )
, ,
, ,
V
V
Nodal forces f x y z dV
Stiffness E f x y z dV
σ=
=
∫
∫
( )
( )
, ,
, ,
V
V
Nodal forces f x y z dV
Stiffness E f x y z dV
σ=
=
∫
∫
( )
( )
( )
( )
0
0
, ,
, ,
, ,
, ,
V
L
S
V
L
S
Nodal forces f x y z dV
f x y z dS dL
Stiffness E f x y z dV
E f x y z dS dL
σ
σ
=
=
=
=
∫
∫ ∫
∫
∫ ∫
( )
( )
( )
( )
( )
( )
0
1
0
1
, ,
, ,
, ,
, ,
, ,
, ,
V
L
S
NG
i
i S
V
L
S
NG
i
i S
Nodal forces f x y z dV
f x y z dS dL
f x y z dS
Stiffness E f x y z dV
E f x y z dS dL
E f x y z dS
σ
σ
ω σ
ω
=
=
=
=
=
=
=
=
∫
∫ ∫
∑ ∫
∫
∫ ∫
∑ ∫
Integrations on the surface are made NG times,
using the discretisation of the thermal analysis
Results:
• Displacements at the nodes
•M, N, V, σ, εm, Et: at the Gaussian integration points
O.21 L
O.11 L
NG = 2
NG = 3
P
M (exact solution)
1 finite element
The maximum moment "seen" by the F.E.
model is smaller than the maximum moment
=> The load capacity is overestimated.
P
M (exact solution)
2 finite elements
P
M (exact solution)
2 finite elements
Conclusions: Beam F.E. not too long in the zones
of peaks in the bending moment diagram
U.D.L.
Conclusions: Beam F.E. not too long in the zones
of peaks in the bending moment diagram
Conclusions: Beam F.E. not too long in the zones
of peaks in the bending moment diagram
How long is too long ?
Lbeam ≥ Dbeam
15% 20%
StressStress--strain relationship in steelstrain relationship in steel
0
2
4
6
8
10
12
14
16
18
20
0 200 400 600 800 1000 1200
Temperature [°C] ==>
Thermal expansion [mm/m]
Thermal expansionThermal expansion in steelin steel
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Stress Related Strain [%]
Stress / Peak Stress at 20°C
20°C100°C
200°C
300°C
400°C
500°C
600°C
StressStress--Strain relationship in concreteStrain relationship in concrete
Thermal Thermal expansionexpansion of concreteof concrete
Non reversible during coolingNon reversible during cooling
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0 200 400 600 800 1000 1200
Température [°C]
Thermal strain Tmax = 1000
Tmax = 800
Tmax = 600
Tmax = 400
Tmax = 200
EC2
2D steel frame2D steel frame (courtesy Vila Real & Piloto)(courtesy Vila Real & Piloto)
Support conditions and loadingSupport conditions and loading
Fire in this
compartment
2D steel frame2D steel frame (courtesy Vila Real & Piloto)(courtesy Vila Real & Piloto)
Evolution of the displacementsEvolution of the displacements
2D steel frame2D steel frame (courtesy Vila Real & Piloto)(courtesy Vila Real & Piloto)
Axial forcesAxial forces
2D steel frame2D steel frame (courtesy Vila Real & Piloto)(courtesy Vila Real & Piloto)
Axial forcesAxial forces
Fina Chemicals in Feluy (Fina Chemicals in Feluy (Bureau Tecnimont Bureau Tecnimont –– MilanMilan))
Bldg extrusion polypropylBldg extrusion polypropylèènene
Mechanical analyses are nowadays performed in
dynamic mode, in order to reduce problems of
local and temporary failure.
COMEBACK 0.0001
time
seconds
COMEBACK procedure stops when the time step
becomes smaller than [0.0001] seconds
BIG QUESTION
How is failure defined/considered in the general
calculation model?
ANSWER
Failure is not considered in the general calculation
model (because the notion of failure is totally
arbitrary and can only be defined by a human
beeing, with different criteria for different
structures, different situations, …).
So, what do I do, practically?
Build your model and run SAFIR.
Two possibilities:
1) SAFIR does not run
=> check the model for• Material properties (fy or E too small or = 0
• Boundary conditions
• Mechanism in structures (axial rotation in diagonals)
• Isolated nodes (nodes not linked to any element)
• Load level (load is too big)
• Time step (too big)
• Etc
2) SAFIR runs (and it will run as far as possible).
=> examine the results
Examine the results
1) The displacements are too big (for me). => I
decide that fire resistance is lost when the
displacements reach my limit.
• Horizontal displacement at a support leads to
loss of support of the beam.
• Beam of a frame deflects into the ground.
• Cantiliver beam is transformed into a cable
hanging on the support.
• etc.
Examine the results
1) The displacements are too big (for me
2) The displacements are not too big. => Look for a
vertical asymptote in the displacement curve of
(at least) one degree of freedom.
This is good indication of (run away) failure.
Note: there are some exceptions if the load
bearing mode is changing, e.g. snap through,
concrete slab going from bending into membrane
action, etc. For these case, there is a post-critical
behaviour after the vertical asymptote.
Examine the results
1) The displ. are too big (for me).
2) The displ. are not too big, with a vertical
asymptote.
3) The displ. are not too big, No vertical asymptote.
This is a good indication of numerical failure
(prematurely lack of convergence)
Note: there is one exception if the failure mode is
really fragile (STEEL IN DESCENDING BRANCH)
=> Do a dynamic calculation
=> Increase the mass
=> Reduce the time step
=> Try with another material (just to know)
=> Try without thermal expansion (just to know)
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