18 finite element modelling reinforced...
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18 Finite Element Modelling Reinforced Concrete
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Finite Element Modelling Reinforced Concrete – TELAIO 3D
Si vuole analizzare il comportamento di un semplice telaio in cemento armato le cui caratteristiche
geometriche sono di seguito riportate:
Geometria del Telaio – Vista 1
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Geometria del Telaio – Vista 2
Geometria del Telaio – Vista 3
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Geometria Armatura del Telaio – Vista 1
Geometria Armatura del Telaio – Vista 2
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Geometria Armatura del Telaio – Vista 3
Geometria Armatura del Telaio – Particolare 1 Geometria Armatura del Telaio – Particolare 2
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Le proprietà dei materiali:
Calcestruzzo C25/30Peso specifico 25Modulo Elasticità 31476000
Coeff. Poisson 0,2
Strain Stress (KN/m2)1 -0,006 -11732,12 -0,005 -14879,73 -0,003306 -19861,774 -0,001613 -250005 -0,001128 -23522,136 -0,000644 -17332,927 -0,000159 -50008 0 0
-30000
-25000
-20000
-15000
-10000
-5000
0-0,007 -0,006 -0,005 -0,004 -0,003 -0,002 -0,001 0
C25/30
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Acciaio B450CPeso specifico 78Modulo Elasticità 210000000Coeff. Poisson 0,1
Strain Stress (KN/m2)1 -0,703286 02 -0,675 -5940003 -0,3125 -590849,944 -0,095 -569363,085 -0,002357 -4950006 0 07 0,002357 4950008 0,095 569363,089 0,3125 590849,94
10 0,675 59400011 0,703286 0
-800000
-600000
-400000
-200000
0
200000
400000
600000
800000
-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8
B450C
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Travi:
Sez. 0,3 m x 0,5m - Ferri Longitudinali: 3+3 Φ14 – Staffe Φ8/10”
Pilastri:
Sez. 0,3 m x 0,5m - Ferri Longitudinali:Φ14 – Staffe Φ8/10”
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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La struttura è stata modellata con ETABS e ABAQUS e SISMICAD.
Modello – ETABS
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Modello – SISMICAD
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Modello – SISMICAD – Elementi Finiti
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Armatura Platea Armatura Pilastri
Armatura Travi Armatua CompletaModello – Abaqus – Armatua
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Modello – Abaqus – Struttura Ca
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Modello – Abaqus – Struttura Ca + Armatura
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Modello Elemeti Finiti – AbaqusElelemti Calcetruzzo: Linear hexahedron, type C3D8RH
Elementi Armatura: Linear line, type T3D2H
- Finite Element Modelling Reinforced Concrete – TELAIO 3D-
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Le analisi svolte sono:
· Analisi Modale (ETABS – SISMICAD - ABAQUS);
· Analisi Statica Non Lineare (Pushover) (ETABS – SISMICAD - ABAQUS) ;
· Analisi Dinamica non Lineare (ETABS - ABAQUS);
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Modale
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Analisi Modale:
EtabsModo Periodo Massa X Massa Y Massa Z
1 0.39256729 0 0.849113547 02 0.284343767 0 0.001112084 03 0.273195106 0.834839588 0 04 0.125170786 0 0.10408539 05 0.083849567 0.11268195 0 06 0.073933538 0 0.025597948 07 0.047278087 0.031260576 0 08 0.021404514 0.000158488 0 09 0.006694042 0.010888987 0 0
Sismicad
Abaqus
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Modale
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Deformata 1° Modo
Etabs Sismicad Abaqus
Deformata 2° Modo
Etabs Sismicad Abaqus
Deformata 3° Modo
Etabs Sismicad Abaqus
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Modale
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Deformata 4° Modo
Etabs Sismicad Abaqus
Deformata 5° Modo
Etabs Sismicad Abaqus
Deformata 6° Modo
Etabs Sismicad Abaqus
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Confronto fra le curve di capacità ottenute da Etabs e Sismicad.
0
100
200
300
400
500
600
700
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45
Base
For
ce[K
N]
Monitored Displ [m]
Curve di Capacità
ETABS-Push X+ PETABS-Push Y+ SISMICAD-Push X+ SISMICAD-Push Y+
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Curve di capacità ottenute da Abaqus:
0
500
1000
1500
2000
2500
-1,E-02 0,E+00 1,E-02 2,E-02 3,E-02 4,E-02 5,E-02 6,E-02 7,E-02 8,E-02 9,E-02 1,E-01
Caric
o [K
N]
Monitored Displ [m]
Curve di Capacità - Abaqus
Push X+ Push Y+
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Alcuni risultati ottenuti da Abaqus .
Analisi Pushover – X+:
Deformata
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Struttura Calcestruzzo Armatura
Armatura - Particolare Armatura - Particolare
Abaqus – AC YIELD – Zone Plastiche
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Struttura Calcestruzzo Armatura
Struttura Calcestruzzo - Particolare Armatura - Particolare
Abaqus – PEEQMAX - Maximum equivalent plastic strain
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Struttura Calcestruzzo Armatura
Struttura Calcestruzzo - Particolare Armatura – Particolare
Abaqus – MISES Mises equivalent stress
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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ABQUS - Analisi Pushover – Y+:
Deformata
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Struttura Calcestruzzo Armatura
Armatura - Particolare Armatura - Particolare
Abaqus – AC YIELD – Zone Plastiche
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Struttura Calcestruzzo Armatura
Struttura Calcestruzzo - Particolare Armatura - Particolare
Abaqus – PEEQMAX - Maximum equivalent plastic strain
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Pushover
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Struttura Calcestruzzo Armatura
Struttura Calcestruzzo - Particolare Armatura – Particolare
Abaqus – MISES Mises equivalent stress
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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Per l’analisi dinamica si è preso in considerazione l’evento del Friuli registrato il 6 Maggio 1976:
Considerato agente nella direzione X e Y.
Lo smorzamento è assunto proporzionale alla massa ed alla rigidezza del sistema attraverso la relazione:
ove αR e βR sono i coefficienti di Rayleigh che controllano lo smorzamento viscoso. Essi possono
essere determinati attraverso la seguente relazione:
Si è assunto, considerando uno smorzamento del 5% :
-6,00
-4,00
-2,00
0,00
2,00
4,00
6,00
0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00 18,00 20,00
Acce
lera
zion
e [m
/s2]
Time[s]
Friuli
Friuli
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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Alcuni risultati delle analisi:
-2,00E-02
-1,50E-02
-1,00E-02
-5,00E-03
0,00E+00
5,00E-03
1,00E-02
1,50E-02
2,00E-02
0 2 4 6 8 10 12 14 16 18 20
Spos
tam
ento
[m]
Time [sec]
Time History Plot - Spostamento - Friuli X+ - Livello 01
ETABS-Liv_01 ABAQS-Liv_01
-2,00E-02
-1,50E-02
-1,00E-02
-5,00E-03
0,00E+00
5,00E-03
1,00E-02
1,50E-02
2,00E-02
0 2 4 6 8 10 12 14 16 18 20
Spos
tam
ento
[m]
Time [sec]
Time History Plot - Spostamento - Friuli X+ - Livello 02
ETABS-Liv_02 ABAQS-Liv_02
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-2,00E-02
-1,50E-02
-1,00E-02
-5,00E-03
0,00E+00
5,00E-03
1,00E-02
1,50E-02
2,00E-02
0 2 4 6 8 10 12 14 16 18 20
Spos
tam
ento
[m]
Time [sec]
Time History Plot - Spostamento - Friuli X+ - Livello 03
ETABS-Liv_03 ABAQS-Liv_02
-5,00E-01
-4,00E-01
-3,00E-01
-2,00E-01
-1,00E-01
0,00E+00
1,00E-01
2,00E-01
3,00E-01
4,00E-01
5,00E-01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Velocità - Friuli X+ - Livello 01
ETABS-Liv_01 ABAQS-Liv_01
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-5,00E-01
-4,00E-01
-3,00E-01
-2,00E-01
-1,00E-01
0,00E+00
1,00E-01
2,00E-01
3,00E-01
4,00E-01
5,00E-01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Velocità - Friuli X+ - Livello 02
ETABS-Liv_02 ABAQS-Liv_02
-5,00E-01
-4,00E-01
-3,00E-01
-2,00E-01
-1,00E-01
0,00E+00
1,00E-01
2,00E-01
3,00E-01
4,00E-01
5,00E-01
0 2 4 6 8 10 12 14 16 18 20
SVel
ocità
[m/s
ec]
Time [sec]
Time History Plot - Velocità - Friuli X+ - Livello 03
ETABS-Liv_03 ABAQS-Liv_03
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-1,50E+01
-1,00E+01
-5,00E+00
0,00E+00
5,00E+00
1,00E+01
1,50E+01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Accelerazione - Friuli X+ - Livello 01
ETABS-Liv_01 ABAQS-Liv_01
-1,50E+01
-1,00E+01
-5,00E+00
0,00E+00
5,00E+00
1,00E+01
1,50E+01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Accelerazione - Friuli X+ - Livello 02
ETABS-Liv_02 ABAQS-Liv_02
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-1,50E+01
-1,00E+01
-5,00E+00
0,00E+00
5,00E+00
1,00E+01
1,50E+01
0 2 4 6 8 10 12 14 16 18 20
SVel
ocità
[m/s
ec]
Time [sec]
Time History Plot - Accelerazione - Friuli X+ - Livello 03
ETABS-Liv_03 ABAQS-Liv_03
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6 8 10 12 14 16 18 20
Hyst
erer
etic
Dam
ping
[kN
-m ]
Time [sec]
Hystereretic Damping - Friuli X+
Etabs Abaqus
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-4,00E-02
-3,00E-02
-2,00E-02
-1,00E-02
0,00E+00
1,00E-02
2,00E-02
3,00E-02
4,00E-02
0 2 4 6 8 10 12 14 16 18 20
Spos
tam
ento
[m]
Time [sec]
Time History Plot - Spostamento - Friuli Y+ - Livello 03
ETABS-Liv_03 ABAQS-Liv_02
-8,00E-01
-6,00E-01
-4,00E-01
-2,00E-01
0,00E+00
2,00E-01
4,00E-01
6,00E-01
8,00E-01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Velocità - Friuli Y+ - Livello 01
ETABS-Liv_01 ABAQS-Liv_01
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-8,00E-01
-6,00E-01
-4,00E-01
-2,00E-01
0,00E+00
2,00E-01
4,00E-01
6,00E-01
8,00E-01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Velocità - Friuli Y+ - Livello 02
ETABS-Liv_02 ABAQS-Liv_02
-8,00E-01
-6,00E-01
-4,00E-01
-2,00E-01
0,00E+00
2,00E-01
4,00E-01
6,00E-01
8,00E-01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Velocità - Friuli Y+ - Livello 03
ETABS-Liv_03 ABAQS-Liv_03
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-1,50E+01
-1,00E+01
-5,00E+00
0,00E+00
5,00E+00
1,00E+01
1,50E+01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Accelerazione - Friuli Y+ - Livello 01
ETABS-Liv_01 ABAQS-Liv_01
-1,50E+01
-1,00E+01
-5,00E+00
0,00E+00
5,00E+00
1,00E+01
1,50E+01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Accelerazione - Friuli Y+ - Livello 02
ETABS-Liv_02 ABAQS-Liv_02
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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-1,50E+01
-1,00E+01
-5,00E+00
0,00E+00
5,00E+00
1,00E+01
1,50E+01
0 2 4 6 8 10 12 14 16 18 20
Velo
cità
[m/s
ec]
Time [sec]
Time History Plot - Accelerazione - Friuli Y+ - Livello 03
ETABS-Liv_03 ABAQS-Liv_03
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10 12 14 16 18 20
Hyst
erer
etic
Dam
ping
[kN
-m ]
Time [sec]
Hystereretic Damping - Friuli Y+
Etabs Abaqus
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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Friuli X
Etabs – Cerniere Plastiche Abaqus - plastic strain
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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Friuli Y
Etabs – Cerniere Plastiche Abaqus - plastic strain
- Finite Element Modelling Reinforced Concrete – TELAIO 3D- Analisi Dinamica non Lineare
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Abaqus – Friuli X - Plastic strain Abaqus – Friuli Y - Plastic strain
Abaqus – Friuli X – Stress Max Abaqus – Friuli Y – Stress Max
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