NO1 Top No1 Amil Baba In Azad Kashmir, Kashmir Black Magic Specialist Expert ...
Analisis dinamico de un portico
1. 2018
INGENIERIA ANTISISMICA
UNIVERSIDAD NACIONAL
“SANTIAGO ANTUNEZ DE MAYOLO”
FACULTAD DE INGENIERIA CIVIL
TRABAJO ESCALONADO
“ANALISIS DINAMICO DE UN EDIFICIO
UBICADO EN LA CIUDAD DE HUARAZ”
ALUMNO:
- ALBA ROSALES ARTHUR
FIC- UNASAM
HUARAZ - 2018
DOCENTE:
- ING. ITA ROBLES LUIS.
2. ANÁLISIS SÍSMICO DE EDIFICIOS USANDO EL MÉTODO ESTÁTICO
1. Coordenadas Globales de la Estructura total:
PRIMER NIVEI
AZOTEA
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3. 2. Calcular la matriz de rigidez Lateral de cada uno de los porticos :
El Portico en modelo estructural
PÒRTICO 1 PÒRTICO 2 PÒRTICO 3
Calculo de la Matriz de Rigidez Lateral del Portico I
Sabemos : [K]=[A]T[K][A]
[K]: Rigidez Lateral del Portico
[K]: Matriz de Rigidez del Portico
[A]: Matriz de Transformacion
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4. Procedimiento a seguir para el calculo de matriz de rigidez:
N°gdl 10
Grados dinamicos N°gdld 2
Portico 1:
Definicion del Sistema Global de Coordenadas {Q}-{D} :
Definicion del Sistema Local de Coordenadas {q}-{d} :
para 5 y 6
para 1 y 2
para 3y 4
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5. Determnacion de la Matriz de Transformacion [A] :
1° Estado de Deformacion: 2° Estado de Deformacion:
D1=1 , Di=0 D2=1 , Di=0
A11
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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6. 3° Estado de Deformacion:
4° Estado de Deformacion:
D3=1 , Di=0
D4=1 , Di=0
A13
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
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7. 5° Estado de Deformacion: 6° Estado de Deformacion:
D5=1 , Di=0
D6=1 , Di=0
A15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
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8. 7° Estado de Deformacion: 8° Estado de Deformacion:
D7=1 , Di=0
D8=1 , Di=0
A17
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
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9. 9° Estado de Deformacion: 10° Estado de Deformacio
D9=1 , Di=0
D10=1 , Di=0
A19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
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11. Determinacion de la Matriz de Rigidez del elemento en el Sistema Local:
Hallando Modulo de Elasticidad, Inercia y Area:
Placa apoyo A : Fc 210
kg
cm2
b 0.2
m h 0.8
m
E 15100 Fc
10
2.188 10
6
Apa b h
0.16
E Apa
3.501 10
5
Iu
b h
3
12
8.533 10
3
Ik
h b
3
12
5.333 10
4
Iuk 0
6
0.524
rad
Ixx
Iu Ik
( )
2
Iu Ik
( ) cos 2
( )
2
Iuk sin 2
( )
6.533 10
3
Iyy
Iu Ik
( )
2
Iu Ik
( ) cos 2
( )
2
Iuk sin 2
( )
2.533 10
3
E Ixx
1.43 10
4
E Iyy
5.543 10
3
Placa Apoyo B: Fc 210
kg
cm2
b 0.2
m h 2
m
E 15100 Fc
10
2.188 10
6
Apb b h
0.4
E Apb
8.753 10
5
Ipb b
h
3
12
0.133
E Ipb
2.918 10
5
Viga 1: Fc 210
kg
cm2
b 0.25
m h 0.40
m
E 15100 Fc
10
2.188 10
6
Av b h
0.1
E Av
2.188 10
5
Iv b
h
3
12
1.333 10
3
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12. E Iv
2.918 10
3
Para Barra 1 :
0.2
f 1.2
G
E
2 1
( )
9.117 10
5
L 3.5
3 E
Iyy
f
G Apa
L
2
0.011
k1
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
1 10
5
0
0
0
1.485 10
3
2.599 10
3
0
2.599 10
3
6.132 10
3
Para Barra 2 :
L 3.5
3 E
Ipb
f
G Apb
L
2
0.235
k2
E Apb
( )
L
0
0
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
4E Ipb
( ) 1
( )
L 1 4
( )
2.501 10
5
0
0
0
4.208 10
4
7.365 10
4
0
7.365 10
4
2.122 10
5
Para Barra 3 :
L 3
3 E
Iyy
f
G Apa
L
2
0.015
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13. k3
E Apa
( )
L
0
0
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
2E Iyy
( ) 1 2
( )
L 1 4
( )
E Apa
( )
L
0
0
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
2E Iyy
( ) 1 2
( )
L 1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
k3
1.167 10
5
0
0
1.167
10
5
0
0
0
2.323 10
3
3.484
10
3
0
2.323
10
3
3.484
10
3
0
3.484
10
3
7.074 10
3
0
3.484 10
3
3.378 10
3
1.167
10
5
0
0
1.167 10
5
0
0
0
2.323
10
3
3.484 10
3
0
2.323 10
3
3.484 10
3
0
3.484
10
3
3.378 10
3
0
3.484 10
3
7.074 10
3
Para Barra 4 :
L 3
3 E
Ipb
f
G Apb
L
2
0.32
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14. k4
E Apb
( )
L
0
0
E Apb
( )
L
0
0
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
4E Ipb
( ) 1
( )
L 1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
2E Ipb
( ) 1 2
( )
L 1 4
( )
E Apb
( )
L
0
0
E Apb
( )
L
0
0
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
2E Ipb
( ) 1 2
( )
L 1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
4E Ipb
( ) 1
( )
L 1 4
( )
k4
2.918 10
5
0
0
2.918
10
5
0
0
0
5.687 10
4
8.531
10
4
0
5.687
10
4
8.531
10
4
0
8.531
10
4
2.252 10
5
0
8.531 10
4
3.071 10
4
2.918
10
5
0
0
2.918 10
5
0
0
0
5.687
10
4
8.531 10
4
0
5.687 10
4
8.531 10
4
0
8.531
10
4
3.071 10
4
0
8.531 10
4
2.252 10
5
Para Barra 5 :
L 4.29
3 E
Iv
f
G Av
L
2
6.259 10
3
k5
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
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15. k5
432.608
927.945
432.608
927.945
927.945
2.671 10
3
927.945
1.31 10
3
432.608
927.945
432.608
927.945
927.945
1.31 10
3
927.945
2.671 10
3
Para Barra 6 :
L 4.29
3 E
Iv
f
G Av
L
2
6.259 10
3
k6
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
k6
432.608
927.945
432.608
927.945
927.945
2.671 10
3
927.945
1.31 10
3
432.608
927.945
432.608
927.945
927.945
1.31 10
3
927.945
2.671 10
3
Acoplando en un solo Matriz:
i 0 2
j 0 2
K
i j
k1
i j
K
i 3
j 3
k2
i j
i 0 5
j 0 5
K
i 6
j 6
k3
i j
K
i 12
j 12
k4
i j
i 0 3
j 0 3
K
i 18
j 18
k5
i j
K
i 22
j 22
k6
i j
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16. APLICAREMOS LA FORMULA GENERAL DE MATRIZ DE RIGIDEZ Y ASI TENDREMOS MATRIZ DE ROGODEZ
KK A1
T
K
A1
KK
0 1 2 3 4 5 6
0
1
2
3
4
5
6
7
8
5
1.028·10 4
-5.92·10 0 0 0 0 -1.166·10
4
-5.92·10 4
5.92·10 0 0 0 0 8.531·10
0 0 5
5.423·10 -432.608 5
-2.918·10 0 -1.361·10
0 0 -432.608 5
2.172·10 0 5
-1.167·10 1.361·10
0 0 5
-2.918·10 0 5
2.922·10 -432.608
0 0 0 5
-1.167·10 -432.608 5
1.171·10
4
-1.166·10 4
8.531·10 3
-1.361·10 3
1.361·10 0 0 4.424·10
-884.754 3
3.484·10 -927.945 927.945 0 0 2.238·10
4
-8.531·10 4
8.531·10 0 0 3
-1.361·10 3
1.361·10 3.071·10
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17. 9 3
-3.484·10 3
3.484·10 0 0 -927.945 927.945
i 0 1
j 0 1
KLL
i j
KK
i j
KLL
1.028 10
5
5.92
10
4
5.92
10
4
5.92 10
4
i 0 7
j 0 1
KOL
i j
KK
i 2
j
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18. KOL
0
0
0
0
1.166
10
4
884.754
8.531
10
4
3.484
10
3
0
0
0
0
8.531 10
4
3.484 10
3
8.531 10
4
3.484 10
3
i 0 1
j 0 7
KLO
i j
KK
i j 2
KLO
0
0
0
0
0
0
0
0
1.166
10
4
8.531 10
4
884.754
3.484 10
3
8.531
10
4
8.531 10
4
3.484
10
3
3.484 10
3
i 0 7
j 0 7
KOO
i j
KK
i 2
j 2
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20. Definicion del Sistema Local de Coordenadas {q}-{d} :
Determnacion de la Matriz de Transformacion [A] :
Podemos ver que la matriz [A] es la misma del portico 1
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22. Apa b h
0.16
E Apa
3.501 10
5
Iu
b h
3
12
8.533 10
3
Ik
h b
3
12
5.333 10
4
Iuk 0
6
0.524
rad
Ixx
Iu Ik
( )
2
Iu Ik
( ) cos 2
( )
2
Iuk sin 2
( )
6.533 10
3
Iyy
Iu Ik
( )
2
Iu Ik
( ) cos 2
( )
2
Iuk sin 2
( )
2.533 10
3
E Ixx
1.43 10
4
E Iyy
5.543 10
3
Placa Apoyo B: Fc 210
kg
cm2
b 0.2
m h 2
m
E 15100 Fc
10
2.188 10
6
Apb b h
0.4
E Apb
8.753 10
5
Ipb b
h
3
12
0.133
E Ipb
2.918 10
5
Viga 1: Fc 210
kg
cm2
b 0.25
m h 0.40
m
E 15100 Fc
10
2.188 10
6
Av b h
0.1
E Av
2.188 10
5
Iv b
h
3
12
1.333 10
3
E Iv
2.918 10
3
Para Barra 1 :
0.2
f 1.2
G
E
2 1
( )
9.117 10
5
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23. L 3.5
3 E
Iyy
f
G Apa
L
2
0.011
k1
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
1 10
5
0
0
0
1.485 10
3
2.599 10
3
0
2.599 10
3
6.132 10
3
Para Barra 2 :
L 3.5
3 E
Ipb
f
G Apb
L
2
0.235
k2
E Apb
( )
L
0
0
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
4E Ipb
( ) 1
( )
L 1 4
( )
2.501 10
5
0
0
0
4.208 10
4
7.365 10
4
0
7.365 10
4
2.122 10
5
Para Barra 3 :
L 3
3 E
Iyy
f
G Apa
L
2
0.015
k3
E Apa
( )
L
0
0
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
2E Iyy
( ) 1 2
( )
L 1 4
( )
E Apa
( )
L
0
0
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
2E Iyy
( ) 1 2
( )
L 1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
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25. L 4.29
3 E
Iv
f
G Av
L
2
6.259 10
3
k5
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
k5
432.608
927.945
432.608
927.945
927.945
2.671 10
3
927.945
1.31 10
3
432.608
927.945
432.608
927.945
927.945
1.31 10
3
927.945
2.671 10
3
Para Barra 6 :
L 4.29
3 E
Iv
f
G Av
L
2
6.259 10
3
k6
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
k6
432.608
927.945
432.608
927.945
927.945
2.671 10
3
927.945
1.31 10
3
432.608
927.945
432.608
927.945
927.945
1.31 10
3
927.945
2.671 10
3
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26. i 0 2
j 0 2
K
i j
k1
i j
K
i 3
j 3
k2
i j
i 0 5
j 0 5
K
i 6
j 6
k3
i j
K
i 12
j 12
k4
i j
i 0 3
j 0 3
K
i 18
j 18
k5
i j
K
i 22
j 22
k6
i j
KK A1
T
K
A1
KK
0 1 2 3 4 5 6
0
1
2
3
4
5
6
7
8
9
5
1.028·10 4
-5.92·10 0 0 0 0 -1.166·10
4
-5.92·10 4
5.92·10 0 0 0 0 8.531·10
0 0 5
5.423·10 -432.608 5
-2.918·10 0 -1.361·10
0 0 -432.608 5
2.172·10 0 5
-1.167·10 1.361·10
0 0 5
-2.918·10 0 5
2.922·10 -432.608
0 0 0 5
-1.167·10 -432.608 5
1.171·10
4
-1.166·10 4
8.531·10 3
-1.361·10 3
1.361·10 0 0 4.424·10
-884.754 3
3.484·10 -927.945 927.945 0 0 2.238·10
4
-8.531·10 4
8.531·10 0 0 3
-1.361·10 3
1.361·10 3.071·10
3
-3.484·10 3
3.484·10 0 0 -927.945 927.945
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27. i 0 1
j 0 1
KLL
i j
KK
i j
KLL
1.028 10
5
5.92
10
4
5.92
10
4
5.92 10
4
i 0 7
j 0 1
KOL
i j
KK
i 2
j
You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
28. KOL
0
0
0
0
1.166
10
4
884.754
8.531
10
4
3.484
10
3
0
0
0
0
8.531 10
4
3.484 10
3
8.531 10
4
3.484 10
3
i 0 1
j 0 7
KLO
i j
KK
i j 2
KLO
0
0
0
0
0
0
0
0
1.166
10
4
8.531 10
4
884.754
3.484 10
3
8.531
10
4
8.531 10
4
3.484
10
3
3.484 10
3
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30. Definicion del Sistema Local de Coordenadas {q}-{d} :
Determnacion de la Matriz de Transformacion [A] :
Podemos ver que la matriz [A] es la misma del portico 1
A3 A1
0 1 2 3 4 5 6 7 8 9
0
1
2
3
0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0 0 0
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31. A3
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1
0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 -1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0 -1 0
0 0 0 0 0 0 0 0 1 0
Determinacion de la Matriz de Rigidez del elemento en el Sistema Local:
Hallando Modulo de Elasticidad, Inercia y Area:
Placa apoyo A : Fc 210
kg
cm2
b 0.2
m h .8
m
E 15100 Fc
10
2.188 10
6
Apa b h
0.16
E Apa
3.501 10
5
Iu
b h
3
12
8.533 10
3
Ik
h b
3
12
5.333 10
4
Iuk 0
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32. 6
0.524
rad
Ixx
Iu Ik
( )
2
Iu Ik
( ) cos 2
( )
2
Iuk sin 2
( )
6.533 10
3
Iyy
Iu Ik
( )
2
Iu Ik
( ) cos 2
( )
2
Iuk sin 2
( )
2.533 10
3
E Ixx
1.43 10
4
E Iyy
5.543 10
3
Placa Apoyo B: Fc 210
kg
cm2
b 0.2
m h 2
m
E 15100 Fc
10
2.188 10
6
Apb b h
0.4
E Apb
8.753 10
5
Ipb b
h
3
12
0.133
E Ipb
2.918 10
5
Viga 1: Fc 210
kg
cm2
b 0.25
m h 0.40
m
E 15100 Fc
10
2.188 10
6
Av b h
0.1
E Av
2.188 10
5
Iv b
h
3
12
1.333 10
3
E Iv
2.918 10
3
Para Barra 1 :
0.2
f 1.2
G
E
2 1
( )
9.117 10
5
L 3.5
3 E
Iyy
f
G Apa
L
2
0.011
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33. k1
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
1 10
5
0
0
0
1.485 10
3
2.599 10
3
0
2.599 10
3
6.132 10
3
Para Barra 2 :
3.5
3 E
Ipb
f
G Apb
L
2
0.235
k2
E Apb
( )
L
0
0
0
12E Ipb
( )
L
3
1 4
( )
6E Ipb
( )
L
2
1 4
( )
0
6E Ipb
( )
L
2
1 4
( )
4E Ipb
( ) 1
( )
L 1 4
( )
2.501 10
5
0
0
0
4.208 10
4
7.365 10
4
0
7.365 10
4
2.122 10
5
Para Barra 3 :
L 3
3 E
Iyy
f
G Apa
L
2
0.015
k3
E Apa
( )
L
0
0
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
2E Iyy
( ) 1 2
( )
L 1 4
( )
E Apa
( )
L
0
0
E Apa
( )
L
0
0
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
12E Iyy
( )
L
3
1 4
( )
6E Iyy
( )
L
2
1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
2E Iyy
( ) 1 2
( )
L 1 4
( )
0
6E Iyy
( )
L
2
1 4
( )
4E Iyy
( ) 1
( )
L 1 4
( )
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35. L 4.29
3 E
Iv
f
G Av
L
2
6.259 10
3
k5
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
k5
432.608
927.945
432.608
927.945
927.945
2.671 10
3
927.945
1.31 10
3
432.608
927.945
432.608
927.945
927.945
1.31 10
3
927.945
2.671 10
3
Para Barra 6 :
L 4.29
3 E
Iv
f
G Av
L
2
6.259 10
3
k6
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
12E Iv
( )
L
3
1 4
( )
6E Iv
( )
L
2
1 4
( )
6E Iv
( )
L
2
1 4
( )
2E Iv
( ) 1 2
( )
L 1 4
( )
6E Iv
( )
L
2
1 4
( )
4E Iv
( ) 1
( )
L 1 4
( )
k6
432.608
927.945
432.608
927.945
927.945
2.671 10
3
927.945
1.31 10
3
432.608
927.945
432.608
927.945
927.945
1.31 10
3
927.945
2.671 10
3
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36. i 0 2
j 0 2
K
i j
k1
i j
K
i 3
j 3
k2
i j
i 0 5
j 0 5
K
i 6
j 6
k3
i j
K
i 12
j 12
k4
i j
i 0 3
j 0 3
K
i 18
j 18
k5
i j
K
i 22
j 22
k6
i j
You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
37. KK A1
T
K
A1
KK
0 1 2 3 4 5 6
0
1
2
3
4
5
6
7
8
9
5
1.028·10 4
-5.92·10 0 0 0 0 -1.166·10
4
-5.92·10 4
5.92·10 0 0 0 0 8.531·10
0 0 5
5.423·10 -432.608 5
-2.918·10 0 -1.361·10
0 0 -432.608 5
2.172·10 0 5
-1.167·10 1.361·10
0 0 5
-2.918·10 0 5
2.922·10 -432.608
0 0 0 5
-1.167·10 -432.608 5
1.171·10
4
-1.166·10 4
8.531·10 3
-1.361·10 3
1.361·10 0 0 4.424·10
-884.754 3
3.484·10 -927.945 927.945 0 0 2.238·10
4
-8.531·10 4
8.531·10 0 0 3
-1.361·10 3
1.361·10 3.071·10
3
-3.484·10 3
3.484·10 0 0 -927.945 927.945
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38. i 0 1
j 0 1
KLL
i j
KK
i j
KLL
1.028 10
5
5.92
10
4
5.92
10
4
5.92 10
4
i 0 7
j 0 1
KOL
i j
KK
i 2
j
KOL
0
0
0
0
1.166
10
4
884.754
8.531
10
4
3.484
10
3
0
0
0
0
8.531 10
4
3.484 10
3
8.531 10
4
3.484 10
3
i 0 1
j 0 7
KLO
i j
KK
i j 2
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40. KL3 KLL KLO KOO
1
KOL
7.041 10
4
2.678
10
4
2.678
10
4
1.402 10
4
CONDENSACIÓN DINÁMICA
KLE
1
N°porticos
ip
C
T
ip
KLip
Cip
KLip ........... (1)
i 0 1
j 0 1
KLL
i j
KK
i j
i 0 7
j 0 1
I). Calculo del centro de masa:
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41. X
4.5 4
4.5
2
0.5 4
1
4.5
1
3
4.5 4
1
2
4
1
Y
4.5 4
2
0.5 4
1
2
3
4
4.5 4
1
2
4
1
4. Determinar La Matriz de Transformacion de Desplazamiento Para Cada Portico:
Portico 1:
0
r Y 2.067
C1
cos( )
0
0
cos( )
sin( )
0
0
sin( )
r
0
0
r
1
0
0
1
0
0
0
0
2.067
0
0
2.067
Portico 2:
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