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)