18 Finite Element Modelling Reinforced...

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


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Geometria Armatura del Telaio – Vista 1



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Geometria Armatura del Telaio – Particolare 1 Geometria Armatura del Telaio – Particolare 2


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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


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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


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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”


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La struttura è stata modellata con ETABS e ABAQUS e SISMICAD.

Modello – ETABS


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Modello – SISMICAD


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Modello – SISMICAD – Elementi Finiti


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Armatura Platea Armatura Pilastri

Armatura Travi Armatua CompletaModello – Abaqus – Armatua


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Modello – Abaqus – Struttura Ca


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Modello – Abaqus – Struttura Ca + Armatura


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Modello Elemeti Finiti – AbaqusElelemti Calcetruzzo: Linear hexahedron, type C3D8RH

Elementi Armatura: Linear line, type T3D2H


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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


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Deformata 1° Modo

Etabs Sismicad Abaqus

Deformata 2° Modo


Deformata 3° Modo



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Deformata 4° Modo


Deformata 5° Modo


Deformata 6° Modo


- 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+


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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+


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Alcuni risultati ottenuti da Abaqus .

Analisi Pushover – X+:

Deformata


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Struttura Calcestruzzo Armatura

Armatura - Particolare Armatura - Particolare

Abaqus – AC YIELD – Zone Plastiche


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Struttura Calcestruzzo - Particolare Armatura - Particolare

Abaqus – PEEQMAX - Maximum equivalent plastic strain


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Struttura Calcestruzzo - Particolare Armatura – Particolare

Abaqus – MISES Mises equivalent stress


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ABQUS - Analisi Pushover – Y+:

Deformata


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Armatura - Particolare Armatura - Particolare

Abaqus – AC YIELD – Zone Plastiche


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Struttura Calcestruzzo - Particolare Armatura - Particolare

Abaqus – PEEQMAX - Maximum equivalent plastic strain


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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


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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]




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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]



-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



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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]



-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]




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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


-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]




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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]



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


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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


-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



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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]



-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]




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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


-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]




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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]



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


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Friuli X

Etabs – Cerniere Plastiche Abaqus - plastic strain


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Friuli Y

Etabs – Cerniere Plastiche Abaqus - plastic strain


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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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