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Structures in Fire Structures in Fire
Yesterday, Today and TomorrowYesterday, Today and Tomorrow
Jean-Marc Jean-Marc [email protected]
http://www.structuresinfire.comhttp://www.structuresinfire.com
Mécanique des matériaux& Structures
88thth IAFSS Symposium IAFSS Symposium Beijing, 18-23/9/2005Beijing, 18-23/9/2005
Plan of this presentationPlan of this presentation
• AA A.1A.1 A.2A.2
• BB B.1B.1 B.2B.2
• CC C.1C.1 C.2C.2
• DD D.1D.1 D.2D.2 D.3D.3 D.4D.4
Part 1: Part 1: General considerationsGeneral considerations
……………….Dynamic analyses.Dynamic analyses
Part 2: Part 2: Dynamic analysesDynamic analyses• II• IIII• IIIIII
Various methods for determining the fire resistance.Various methods for determining the fire resistance.
Part 1 of the presentation: General considerationsPart 1 of the presentation: General considerations
1.1. Experimental TestsExperimental Tests
2.2. Tabulated dataTabulated data
3.3. Simple calculation modelsSimple calculation models
4.4. Advanced calculation modelsAdvanced calculation models
Method 1 : Experimental testingMethod 1 : Experimental testing
Testing specimens for material behaviourTesting specimens for material behaviour
Test setup at NIST
Method 1 : Experimental testingMethod 1 : Experimental testing
Testing material behaviourTesting material behaviour Standard fire testsStandard fire tests..
• Circumstancial disadvantages: cost, delays, limited # of facilities.Circumstancial disadvantages: cost, delays, limited # of facilities.
• Real disadvantages: only elements, size of the element, Real disadvantages: only elements, size of the element, boundary conditions, boundary conditions,
variability.variability.
Method 1 : Experimental testingMethod 1 : Experimental testing
Testing material behaviourTesting material behaviour Standard fire testsStandard fire tests Small scale fire testsSmall scale fire tests Steel: OKSteel: OK
Hydral materials: ???Hydral materials: ???
Picture from Nakamura et al.,1rst IAFSS, Gaithersburg, 1985
Method 1 : Experimental testingMethod 1 : Experimental testing
Testing material behaviourTesting material behaviour Standard fire testsStandard fire tests Small scale fire testsSmall scale fire tests Large scale fire tests Large scale fire tests
Rare - Local fires - Observations more than researchRare - Local fires - Observations more than research
Courtesy: T. Lennon - B.R.E.
Experimental testing is used mainly in research.Experimental testing is used mainly in research.
Experimental testing will remain for ever.Experimental testing will remain for ever.Verification of basic hypotheses used in calculation modelsVerification of basic hypotheses used in calculation models Integrity criteria in separating elementsIntegrity criteria in separating elements
Definition: presentation, in simple form, of results obtained by Definition: presentation, in simple form, of results obtained by other methods.other methods.
Standard fire resistance
Minimum dimensions (mm)
Slab thickness hs
Axis-distance a
One way Two way
ly/lx 1.5 1.5 < ly/lx 2
1 2 3 4 5
REI 30 60 10* 10* 10*
REI 60 80 20 10* 15*
REI 90 100 30 15* 20
REI 120 120 40 20 25
REI 180 150 55 30 40
REI 240 175 65 40 50
ly and lx are the spans of a two-way slab where ly is the longer span.
For prestressed slabs the increase of axis distance should be noted.The axis distance a in Column 4 and 5 for two way slabs relate to slabs supported on all four edges. Otherwise, they should be treated as one-way spanning slabs.* Normally the cover required at room temperature will control
Method 2 : Tabulated dataMethod 2 : Tabulated data
Method 2 : Tabulated dataMethod 2 : Tabulated data
• Background: ???Background: ???
• Available for simple Available for simple membersmembers submitted to the submitted to the standard firestandard fire..• Used mainly for masonry, concrete and composite elements, Used mainly for masonry, concrete and composite elements,
not so much for steel.not so much for steel.• Quite valuable for a preliminary design.Quite valuable for a preliminary design.• Interpolation software, please.Interpolation software, please.
Reinforcement ratio = 0.50 ; Eccentricity e 200 mm
Standard fire resistance
Column width bmin / axis distance a
n = 0.15 n = 0.30 n = 0.50 n = 0.70
R30 304050607080
150/25*150/25*150/25*150/25*150/25*150/25*
150/25*150/30:200/25*200/30:250/25*200/35:300/25*250/40:400/25*300/40:500/25*
250/35:300/25*300/35:450/25*400/40:500/25*450/50:550/25*500/40:600/30*550/50:600/40*
500/40:550/25*550/30
550/50:600/40(1)(1)(1)
R 60 304050607080
150/30:200/25*150/35:250/25*200/35:300/25*200/40:500/25*200/40:550/25*250/40:600/25*
200:40:450/25*250:40:500/25*300:45:550/25*400:40:600/30500:40:550/35500:40:600/35
450/50:550/30500/40:550/35500/55:550:40550/50:600/45
600/60(1)
550/50:600/40600/60
(1)(1)(1)(1)
R 90 304050607080
250/40:450/25*200/50:500/25*250/45:550/25*250/50:550/30300/50:550/35350/50:600/35
300/50:500/25350/50:550/35500/45:550/40500/50:550/45550/50:600/45550/60:600/50
500/55:600/40550/60:600/50
600/60600/80
(1)(1)
600/80(1)(1)(1)(1)(1)
* Normally the cover at room conditions will control(1) Requires a width greater than 600 mm.
Method 3 : Simple calculation modelsMethod 3 : Simple calculation models
Definition: Method based on global equilibrium conditions.Definition: Method based on global equilibrium conditions.
• Can be used by hand Can be used by hand • One method for each material/member type.One method for each material/member type.• Not well suited for complex structures.Not well suited for complex structures.
=> Used for real projects.=> Used for real projects.
Method 3 : Simple calculation modelsMethod 3 : Simple calculation models
• Extrapolations of similar methods used at room temperature Extrapolations of similar methods used at room temperature
, ²At high temperature :
8d fi
pl y
q LW f T
Method 4 : Advanced calculation modelsMethod 4 : Advanced calculation models
Definition: Based on principles of structural mechanics or of Definition: Based on principles of structural mechanics or of heat transfer (local equations). heat transfer (local equations).
• Finite differences, finite elements, boundary elements.Finite differences, finite elements, boundary elements.
• Require a computer (numerical calculation models).Require a computer (numerical calculation models).
Method 4 : Advanced calculation modelsMethod 4 : Advanced calculation models
1.1. ''My Ph.D.My Ph.D.' software' software• One author (university)One author (university)
Three different families of software:Three different families of software:Method 4 : Advanced calculation models
1.1. ''My Ph.D.My Ph.D.' software' software• One author (university)One author (university)• Limited field of applicationLimited field of application
Three different families of software:Three different families of software:Method 4 : Advanced calculation models
1.1. ''My Ph.D.My Ph.D.' software' software• One author (university)One author (university)• Limited field of applicationLimited field of application• Limited availabilityLimited availability
Three different families of software:Three different families of software:
This is This is MYMY software !!!software !!!
Method 4 : Advanced calculation models
1.1. ''My Ph.D.My Ph.D.' software' software• One author (university)One author (university)• Limited field of applicationLimited field of application• Limited availabilityLimited availability• Limited durabilityLimited durability
Three different families of software:Three different families of software:
This is This is MYMY software !!!software !!!
Method 4 : Advanced calculation models
Three different families of software:Three different families of software:
1.1. ''My Ph.D.My Ph.D.' software' software2.2. Dedicated software (VULCAN, SAFIR,…)Dedicated software (VULCAN, SAFIR,…)
• From a group (University)From a group (University)
Method 4 : Advanced calculation models
Three different families of software:Three different families of software:
1.1. ''My Ph.D.My Ph.D.' software' software2.2. Dedicated software (VULCAN, SAFIR,…)Dedicated software (VULCAN, SAFIR,…)
• From a group (University)From a group (University)• Wider field of applicationWider field of application
Method 4 : Advanced calculation models
Three different families of software:Three different families of software:
1.1. ''My Ph.D.My Ph.D.' software' software2.2. Dedicated software (VULCAN, SAFIR,…)Dedicated software (VULCAN, SAFIR,…)
• From a group (University)From a group (University)• Wider field of applicationWider field of application• Become available nowBecome available now
$ $ $ $ $$ $ $ $ $
Method 4 : Advanced calculation models
Three different families of software:Three different families of software:
1.1. ''My Ph.D.My Ph.D.' software' software2.2. Dedicated software (VULCAN, SAFIR,…)Dedicated software (VULCAN, SAFIR,…)3.3. Commercial software (ANSYS, ABAQUS,…)Commercial software (ANSYS, ABAQUS,…)
• Widely distributed, used and validatedWidely distributed, used and validated• Price !!!Price !!!• Nice graphicsNice graphics
+ + + or - - -+ + + or - - - ??
Method 4 : Advanced calculation models
YesterdayYesterday Uniform temperatureUniform temperature
TodayToday Non Non uniformuniform temperature temperature
X
Y
Z
Diamond 2004 for SAFIR
FILE: HEB_U
NODES: 28
ELEMENTS: 17
CONTOUR PLOT
TEMPERATURE PLOT
TIME: 500000 sec>Tmax
900.00
800.00
700.00
600.00
500.00
400.00
300.00
200.00
100.00
0.00
<Tmin
X
Y
Z
Diamond 2004 for SAFIR
FILE: HEB_U
NODES: 28
ELEMENTS: 17
CONTOUR PLOT
TEMPERATURE PLOT
TIME: 500000 sec800.00
790.91
781.82
772.73
763.64
754.55
745.45
736.36
727.27
718.18
709.09
700.00
Linear gradientLinear gradient
X
Y
Z
Diamond 2004 for SAFIR
FILE: HEB_R
NODES: 496
ELEMENTS: 405
CONTOUR PLOT
TEMPERATURE PLOT
TIME: 1440 sec756.90
753.93
750.95
747.98
745.01
742.04
739.06
736.09
733.12
730.15
727.17
724.20
X
Y
Z
Diamond 2004 for SAFIR
FILE: span_section
NODES: 720
ELEMENTS: 663
CONTOUR PLOT
TEMPERATURE PLOT
TIME: 3600 sec>Tmax
1000.00
900.00
800.00
700.00
600.00
500.00
400.00
300.00
200.00
100.00
<Tmin
Method 4 : Advanced calculation models
YesterdayYesterday
Single members or 2D framesSingle members or 2D frames
TodayToday
3D analyses3D analyses
Method 4 : Advanced calculation models
XY
Z
Diamond 2004 for SAFIR
FILE: cadre2
NODES: 352
BEAMS: 171
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
DISTRIBUTED LOADS PLOT
Beam Element
F0F0
F0F0 F0
F0
F0F0F0
F0F0
F0F0 F0
F0
F0F0
F0F0F0
F0F0F0F0
F0F0
F0
F0
F0
F0
F0F0F0F0
F0
F0
F0
F0F0
F0F0 F0
F0
F0
F0
F0
F0F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0F0
F0
F0
F0F0
X Y
Z
Diamond 2004 for SAFIR
FILE: cadre2
NODES: 352
BEAMS: 171
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
IMPOSED DOF PLOT
Beam Element
YesterdayYesterday Linear elementsLinear elements
TodayTodayShell elementsShell elements
Method 4 : Advanced calculation models
YesterdayYesterday
One type of F.E.One type of F.E.
TodayToday
Several types of F.E.Several types of F.E.
Method 4 : Advanced calculation models
X Y
Z
5.0 E-01 m
Diamond 2004 for SAFIR
FILE: ParkdeckB
NODES: 547
BEAMS: 251
TRUSSES: 0
SHELLS: 0
SOILS: 0
DISPLACEMENT PLOT ( x 4)
TIME: 2100 sec
YesterdayYesterday
Static analysesStatic analyses
TodayToday
Dynamic analysesDynamic analyses
See part 2 of this presentationSee part 2 of this presentation
Method 4 : Advanced calculation models
TomorrowTomorrow
• C.F.D. - F.E. interconnectionC.F.D. - F.E. interconnection• Spalling of concreteSpalling of concrete• Cooling phase of the fireCooling phase of the fire• Moisture movements (e.g. in wood)Moisture movements (e.g. in wood)• Shear strength of concreteShear strength of concrete• Mechanical properties of gypsumMechanical properties of gypsum• … …
• ConnectionsConnections• Very large modelsVery large models
Diamond 2004 for SAFIR
FILE: a0d
NODES: 9458
ELEMENTS: 6054
SOLIDS PLOT
CONTOUR PLOT
STEELEC3SILCONCEC2
Method 4 : Advanced calculation models
Part 2 of the presentation: Dynamic analysesPart 2 of the presentation: Dynamic analyses
Successive static analyses used Successive static analyses used to load a structure at room temperatureto load a structure at room temperature
Tim e ste p 2
Tim e ste p 1
Tim e ste p 2
Tim e ste p 1
Tim e ste p 3Tim e ste p 2
Successive static analyses used Successive static analyses used to take into account the temperature increaseto take into account the temperature increase
uKF
F
u
1 2 3 4
F
u
1 2 3 4
Normal evolution toward failureNormal evolution toward failure
uKF 40 TTforK
F
1 2
F
u
1 2 3 4
Local or temporary failure at TLocal or temporary failure at T33
Local or temporary failure caused by:Local or temporary failure caused by:
geometrical reasons (buckling of one bar in a geometrical reasons (buckling of one bar in a statically statically indeterminate sytem),indeterminate sytem),
material behaviour (descending branches in material behaviour (descending branches in relationships).relationships).
Various solutions sometimes used:Various solutions sometimes used:
Remove the unstable element from the structure.Remove the unstable element from the structure.
Use « modified » Use « modified » relationships. relationships.
Use non-tangent stiffness matrix.Use non-tangent stiffness matrix.
Use « Riks » type methods (arc-length).Use « Riks » type methods (arc-length).
Solution implemented in SAFIR:Solution implemented in SAFIR: DYNAMIC ANALYSISDYNAMIC ANALYSIS
withwith
andand
1*
1001 uKAFAF
NEWMARK methodNEWMARK method
Case study 1 : 1D axial oscillatorCase study 1 : 1D axial oscillator
20°C, elastic20°C, elastic
Dynamic analysis of a single d.o.f. structure (No damping)
For t > 0, Faxial = 1000 N
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
Time (s)
Ax
ial
forc
e (
N)
No dampingNo damping
Damping = 1.5%Damping = 1.5%
Dynamic analysis of a single d.o.f. structure (Damping = 1.5% of the critical damping)
For t > 0, Faxial = 1000 N)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
Time (s)
Ax
ial
forc
e (
N)
Damping = 50%Damping = 50%
Dynamic analysis of a single d.o.f. structure (Damping = 50% of the critical damping)
For t > 0, Faxial = 1000 N)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
Time (s)
Axi
al f
orc
e (N
)
Case study 2 : 2D snap throughCase study 2 : 2D snap through
20°C, damping = 1.5%20°C, damping = 1.5%
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Time (s)
Ve
rtic
al
po
sit
ion
of
no
de
2 (
m)
ElasticElastic
Displacement (With Damping)
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0 0.05 0.1 0.15 0.2 0.25 0.3
Elasto-plasticElasto-plastic
Case study 3 : EC3 steel, heated bracing in a sway frameCase study 3 : EC3 steel, heated bracing in a sway frame
Evolution of the horizontal displacementEvolution of the horizontal displacement
uu
Evolution of the axial force in the diagonalEvolution of the axial force in the diagonal
-4000
-2000
0
2000
4000
6000
8000
10000
12000
0 400 800 1200 1600 2000 2400 2800 3200 3600
Dynamic analysis Static analysis
NN
Case study 4 : EC3 steel, 1 out of 2 bays heatedCase study 4 : EC3 steel, 1 out of 2 bays heated
F0
F0
F0
F0
F0
F0
X
Y
Z
Diamond 2004 for SAFIR
FILE: Frame stat 2D
NODES: 123
BEAMS: 61
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
IMPOSED DOF PLOT
IPE500.tem
IPE450.tem
IPE500c.tem
IPE450c.tem
-6
-5
-4
-3
-2
-1
0
0 10 20 30
TIME [min.]
VE
RT.
DIS
PL.
[m]
Static Dynamic
F0
F0
F0
F0
F0
F0
X
Y
Z
5.0 E+00 m
Diamond 2004 for SAFIR
FILE: Frame stat 2D
NODES: 123
BEAMS: 61
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
IMPOSED DOF PLOT
DISPLACEMENT PLOT ( x 1)
TIME: 1504 sec
IPE500.tem
IPE450.tem
IPE500c.tem
IPE450c.tem
tt = 25’ = 25’
-6
-5
-4
-3
-2
-1
0
0 10 20 30
TIME [min.]
VE
RT.
DIS
PL.
[m]
Static Dynamic
F0
F0
F0
F0
F0
F0
X
Y
Z
5.0 E+00 m
Diamond 2004 for SAFIR
FILE: Frame stat 2D
NODES: 123
BEAMS: 61
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
IMPOSED DOF PLOT
DISPLACEMENT PLOT ( x 1)
TIME: 1593.5 sec
IPE500.tem
IPE450.tem
IPE500c.tem
IPE450c.tem
tt = 26’30’’ = 26’30’’
-6.5
-5.5
-4.5
-3.5
-2.5
-1.5
-0.5
0.5
0 10 20 30
TIME [min.]
VE
RT.
DIS
PL.
[m]
Static Dynamic
X
Y
Z
5.0 E+00 m
Diamond 2004 for SAFIR
FILE: Frame dyn 2D
NODES: 123
BEAMS: 61
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
DISPLACEMENT PLOT ( x 1)
TIME: 1590.542 sec
IPE500.tem
IPE450.tem
IPE500c.tem
IPE450c.tem
tt = 26’34’’ = 26’34’’
Case study 5 : The same, now in 3D, with heated purlinsCase study 5 : The same, now in 3D, with heated purlins
3D frame (no amplification in the deformation)3D frame (no amplification in the deformation)
Case study 6 : Continuous reinforced concrete beamCase study 6 : Continuous reinforced concrete beam
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
X
Y
Z
Diamond 2004 for SAFIR
FILE: poutre32_new
NODES: 57
BEAMS: 28
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
IMPOSED DOF PLOT
DISTRIBUTED LOADS PLOT
Beam Element
X
Y
Z
5.0 E+05 Nm
Diamond 2004 for SAFIR
FILE: poutre32_new
NODES: 57
BEAMS: 28
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
BENDING MOMENT PLOT
TIME: 30 sec
t = 0’30’’t = 0’30’’X
Y
Z
5.0 E+05 Nm
Diamond 2004 for SAFIR
FILE: poutre32_new
NODES: 57
BEAMS: 28
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
BENDING MOMENT PLOT
TIME: 2609.531 sec
t = 43’29’’t = 43’29’’
X
Y
Z
5.0 E+05 Nm
Diamond 2004 for SAFIR
FILE: poutre32_new
NODES: 57
BEAMS: 28
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLOT
BENDING MOMENT PLOT
TIME: 2611.562 sec
t = 43’31’’t = 43’31’’
Case study 7 : Composite Steel-Concrete bridge Case study 7 : Composite Steel-Concrete bridge subjected to a local firesubjected to a local fire
Viaduc of MillauViaduc of MillauCourtesy "Bureau d'Etudes Greisch"Courtesy "Bureau d'Etudes Greisch"
Case study 8 : Lee’s Frame Analysed with Shell F.E. Case study 8 : Lee’s Frame Analysed with Shell F.E. dT/dt = 1°C/sdT/dt = 1°C/s
Case study 9 : Short Cellular Steel beamCase study 9 : Short Cellular Steel beamSymmetry not usedSymmetry not used
F0
F0
F0
F0
F0F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0F0
F0
F0F0
F0F0
F0
F0F0
F0F0
F0
F0F0
F0
F0F0
F0
F0F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0F0
F0
X Y
Z
Diamond 2004 for SAFIR
FILE: acb_hot
NODES: 905
BEAMS: 0
TRUSSES: 0
SHELLS: 608
SOILS: 0
SHELLS PLOT
IMPOSED DOF PLOT
POINT LOADS PLOT
Shell Element
F0
F0
F0
F0
F0F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0F0
F0
F0F0
F0F0
F0
F0F0
F0F0
F0
F0F0
F0
F0F0
F0
F0F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0F0
F0
X Y
Z
5.0 E-01 m
Diamond 2004 for SAFIR
FILE: acb_hot
NODES: 905
BEAMS: 0
TRUSSES: 0
SHELLS: 608
SOILS: 0
IMPOSED DOF PLOT
POINT LOADS PLOT
DISPLACEMENT PLOT ( x 1)
TIME: 648.4375 sec
F0
F0
F0
F0
F0F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0F0
F0
F0F0
F0F0
F0
F0F0
F0F0
F0
F0F0
F0
F0F0
F0
F0F0
F0
F0
F0F0
F0
F0
F0
F0F0
F0
F0F0
F0F0
F0X Y
Z
5.0 E-01 m
Diamond 2004 for SAFIR
FILE: acb_dyn_hot
NODES: 905
BEAMS: 0
TRUSSES: 0
SHELLS: 608
SOILS: 0
IMPOSED DOF PLOT
POINT LOADS PLOT
DISPLACEMENT PLOT ( x 1)
TIME: 651.1728 sec
Case study 10 : Reinforced concrete flat slab (20°C)Case study 10 : Reinforced concrete flat slab (20°C)
F0F0F0F0
F0F0F0F0F0F0F0F0
F0F0
F0F0 F0
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F0F0 F0
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F0F0 F0
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F0F0 F0
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F0 F0F0F0 F0F0F0 F0
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F0F0 F0
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F0F0F0F0F0 F0 F0F0F0 F0F0 F0F0F0 F0 F0
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F0F0 F0
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F0F0F0F0F0 F0 F0 F0F0F0 F0F0 F0F0 F0F0F0 F0 F0 F0
F0F0F0F0
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F0 F0 F0
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F0 F0F0F0 F0
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F0 F0 F0
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Diamond 2004 for SAFIR
FILE: p-dyn2d
NODES: 6614
BEAMS: 0
TRUSSES: 0
SHELLS: 6245
SOILS: 0
SHELLS PLOT
IMPOSED DOF PLOT
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Courtesy "Batiserf, Grenoble"Courtesy "Batiserf, Grenoble"
F0F0F0F0
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F0F0F0F0F0 F0 F0 F0F0F0 F0F0 F0F0 F0F0F0 F0 F0 F0
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F0 F0 F0
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F0 F0F0F0 F0
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F0 F0 F0
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5.0 E-01 m
Diamond 2004 for SAFIR
FILE: p0pure4
NODES: 6614
BEAMS: 0
TRUSSES: 0
SHELLS: 6245
SOILS: 0
IMPOSED DOF PLOT
DISPLACEMENT PLOT ( x 20)
TIME: 9.8304 sec
Case study 11 : Reinforced concrete flat slab (20°C)Case study 11 : Reinforced concrete flat slab (20°C)
ConclusionsConclusions
The behaThe beha viour of the structure is viour of the structure is oneone aspect of FSE. aspect of FSE.
Spectacular developments have been made during the last Spectacular developments have been made during the last 20 years.20 years.
Dynamic analyses are feasible and are a must.Dynamic analyses are feasible and are a must.
There are still some problems to be solved.There are still some problems to be solved.
Thank you and …... Fly high!Thank you and …... Fly high!