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Matriz de Rigidez Muro Inclinado Vargas
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Matriz de Rigidez Muro Inclinado Vargas
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Iván Vargas Sanchez
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ANALISIS ESTRUCTURAL POR EL METODO DE RIGIDEZ PARA PÓRTICOS CONDICIONES GENERALES: ALTURA PI SO TECHO:
VI GAS:
1º NI VEL:
2.85 m
PERALTE(h):
2º NI VEL:
2.6 m
L=
ESPESOR DE MURO(t):
h=
0.532
Zona Sísmica 3
h=
0.443
≥ℎ/20
h= b=
t>
0.14
t=
0.15
1
ℎ= ℎ=/10 ℎ= ℎ=/12
5.32 m
0.5 m 0.3 m
2
3
C
C
ESPESOR DE ALIGERADO(e): ALIGERADO(e): Lmax:
5.05
m
=
e=
B
B
0.2 0.202
e=
0.20 m.
A
A
aprox. 1
2
3
METRADO DE CARGAS EJE 2-2
TRAMO A-B PRIMER PISO
SEGUNDO PISO
CARGAS MUERTAS:
CARGAS MUERTAS:
ALI GERADO(e=0.20m):
ALI GERADO(e=0.20m):
peso propio:
300 kg/m2
peso propio:
300 kg/m2
piso terminado:
100 kg/m2
piso terminado:
100 kg/m2
carga total: carga repartida:
400 kg/m2 1730 kg/m
PESO DEL MURO(t=0.15m): peso propio:
carga total: carga repartida: PESO DEL MURO(t=0.15m):
1800 kg/m3
peso propio:
1800 kg/m3
h=
2.60
h=
0.00
t=
0.15
t=
0
carga repartida:
702 kg/m
PESO DE LA VI GA: p. concreto armado:
400 kg/m2 1730 kg/m
carga repartida:
0 k g/ m
PESO DE LA VI GA: 2400 kg/m3
p. concreto armado:
h=
0.5 m
h=
0.5 m
b=
0.3 m
b=
0.3 m
2400 kg/m3
carga repartida:
360 kg/m
carga repartida:
360 kg/m
TOTAL CARGA MUERTA(CM):
2792 2792 kg/m kg/m
TOTAL CARGA MUERTA(CM):
2090 kg/m
2.8 Tn/m
2.1 Tn/m
CARGAS VI VAS:
CARGAS VI VAS:
ALI GERADO(e=0.20m):
ALI GERADO(e=0.20m):
carga viva
200 kg/m2
carga viva
tabiquería móvil
100 kg/m2
tabiquería móvil
carga total:
300 kg/m2
4.40Tn/m
carga total :
0 kg / m 2 200 kg/m2
carga repartida:
1297.5 kg/m
carga repartida:
865 kg/m
TOTAL CARGA VIVA(CV):
1297. 1297.55 kg/m kg/m
TOTAL CARGA VIVA(CV):
865 865 kg/m kg/m
1.3 Tn/m
CARGA ULTIMA
6.11 Tn/m
4.40Tn/m
200 kg/m2
6.11Tn/m
4.40Tn/m
0.9 Tn/m
CARGA ULTIMA
4.40 Tn/m
TRAMO B-C PRIMER PISO
SEGUNDO PISO
CARGAS MUERT AS:
CARGAS MU ERTAS:
ALI GERADO(e=0.20m):
ALI GERADO(e=0.20m):
peso propio:
300 kg/m2
peso propio:
300 kg/m2
piso terminado:
100 kg/m2
piso terminado:
100 kg/m2
carga total: carga repartida:
400 kg/m2 1730 kg/m
PESO DE LA VI GA: p. concreto armado:
carga total : carga repartida:
400 kg/m2 1730 kg/m
PESO DE LA VI GA: 2400 kg/m3
p. concreto armado:
h=
0.5 m
h=
0.5 m
b=
0.3 m
b=
0.3 m
11.44Tn
9.91Tn-m
carga repartida:
360 kg/m
carga repartida:
360 kg/m
TOTAL CARGA MUERTA(CM):
2090 2090 kg/m kg/m
TOTAL CARGA MUERTA(CM):
2090 2090 kg/m kg/m
2.1 Tn/m CARGAS VI VAS:
15.89Tn
tabiquería móvil carga total:
13.77Tn-m
ALI GERADO(e=0.20m): 200 kg/m2 0 kg/m2 200 kg/m2
carga viva tabiquería móvil carga total :
200 kg/m2 0 kg / m 2 200 kg/m2
carga repartida:
865 kg/m
carga repartida:
865 kg/m
TOTAL CARGA VIVA(CV):
865 865 kg/m g/m
TOTAL CARGA VIVA(CV):
865 865 kg/m kg/m
0.9 Tn/m
7.81Tn
5.29Tn-m
23.7Tn
4.62Tn-m
7.81Tn
2.1 Tn/m CARGAS VI VAS:
ALI GERADO(e=0.20m): carga viva
19.25Tn
2400 kg/m3
0.9 Tn/m
9.15Tn-m
4.62Tn-m
CARGAS VI VAS:
CARGAS VI VAS:
ALI GERADO(e=0.20m):
ALI GERADO(e=0.20m):
carga viva
200 kg/m2
carga viva
tabiquería móvil
100 kg/m2
tabiquería móvil
carga total:
300 kg/m2
4.40Tn/m
carga total :
0 kg / m 2 200 kg/m2
carga repartida:
1297.5 kg/m
carga repartida:
865 kg/m
TOTAL CARGA VIVA(CV):
1297. 1297.55 kg/m kg/m
TOTAL CARGA VIVA(CV):
865 865 kg/m kg/m
1.3 Tn/m
CARGA ULTIMA
6.11 Tn/m
4.40Tn/m
200 kg/m2
6.11Tn/m
4.40Tn/m
0.9 Tn/m
CARGA ULTIMA
4.40 Tn/m
TRAMO B-C PRIMER PISO
SEGUNDO PISO
CARGAS MUERT AS:
CARGAS MU ERTAS:
ALI GERADO(e=0.20m):
ALI GERADO(e=0.20m):
peso propio:
300 kg/m2
peso propio:
300 kg/m2
piso terminado:
100 kg/m2
piso terminado:
100 kg/m2
carga total: carga repartida:
400 kg/m2 1730 kg/m
PESO DE LA VI GA: p. concreto armado:
carga total : carga repartida:
400 kg/m2 1730 kg/m
PESO DE LA VI GA: 2400 kg/m3
p. concreto armado:
h=
0.5 m
h=
0.5 m
b=
0.3 m
b=
0.3 m
11.44Tn
9.91Tn-m
carga repartida:
360 kg/m
carga repartida:
360 kg/m
TOTAL CARGA MUERTA(CM):
2090 2090 kg/m kg/m
TOTAL CARGA MUERTA(CM):
2090 2090 kg/m kg/m
2.1 Tn/m CARGAS VI VAS:
15.89Tn
tabiquería móvil carga total:
13.77Tn-m
ALI GERADO(e=0.20m): 200 kg/m2 0 kg/m2 200 kg/m2
carga viva tabiquería móvil carga total :
200 kg/m2 0 kg / m 2 200 kg/m2
carga repartida:
865 kg/m
carga repartida:
865 kg/m
TOTAL CARGA VIVA(CV):
865 865 kg/m g/m
TOTAL CARGA VIVA(CV):
865 865 kg/m kg/m
0.9 Tn/m
7.81Tn
5.29Tn-m
23.7Tn
4.62Tn-m
7.81Tn
2.1 Tn/m CARGAS VI VAS:
ALI GERADO(e=0.20m): carga viva
19.25Tn
2400 kg/m3
0.9 Tn/m
9.15Tn-m
4.62Tn-m
CARGA ULTIMA
4.40 Tn/m
CARGA ULTIMA
4.40 Tn/m
5
2
8
1
4
7
1
2
3
DATOS DE LA ESTRUCTURA VIGAS 280 2509980.1 0.15 0.003125
f'c E A I
Kg/cm2 Tn/m2 m2 m4
f'c E A I
6 3
COLUMNA 280 2509980.08 0.075 0.00625
Kg/cm2 Tn/m2 m2 m4
4 11 10
15
19
1. Matriz en cordenadas locales de la barra 1
K1
5.2 2509980.1 0.15 0.003125
=
7
m Tn/m2 m2 m4 72403.2715 0
0 669.4089
0 1740.4633
-72403.2715 0
0 -669.4089
0 1740.4633
0
1740.4633
6033.6060
0
-1740.4633
3016.8030
-72403.2715 0 0
0 -669.4089 1740.4633
0 -1740.4633 3016.8030
72403.2715 0 0
0 669.4089 -1740.4633
0 -1740.4633 6033.6060
10
26
23
24
16
18 9
20 21
17
13
6
8
Longitud = E = A= I =
5 14
12
BARRA 1
9
22
27
25
2. Matriz de transformación .
x y
0 1 0
= = =
T
T
T
=
=
1 0
0 1
0 0
0 0
0 0
0 0
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
1 0
0 1
0 0
0 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
1 0
0 1
3. Determinamos matriz de rigidez en coordenadas globales
K
=
72403.2715 0.0000 0.0000
0.0000 669.4089 1740.4633
0.0000 1740.4633 6033.6060
-72403.2715 0.0000 0.0000
0.0000 -669.4089 -1740.4633
0.0000 1740.4633 3016.8030
-72403.2715 0.0000 0.0000
0.0000 -669.4089 1740.4633
0.0000 -1740.4633 3016.8030
72403.2715 0.0000 0.0000
0.0000 669.4089 -1740.4633
0.0000 -1740.4633 6033.6060
1 72403.2715 0.0000
2 0.0000 669.4089
3 0.0000 1740.4633
4 -72403.2715 0.0000
5 0.0000 -669.4089
6 0.0000 1740.4633
1 2
0.0000
1740.4633
6033.6060
0.0000
-1740.4633
3016.8030
3
-72403.2715 0.0000
0.0000 -669.4089
0.0000 -1740.4633
72403.2715 0.0000
0.0000 669.4089
0.0000 -1740.4633
4 5
0.0000
1740.4633
3016.8030
0.0000
-1740.4633
6033.6060
6
BARRA 2
1. Matriz en cordenadas locales de la barra 1 Longitud = E =
5.2 m 2509980.1 Tn/m2
A= I =
0.15 m2 0.003125 m4
K2
=
72403.2715 0
0 669.4089
0 1740.4633
-72403.2715 0
0 -669.4089
0 1740.4633
0
1740.4633
6033.6060
0
-1740.4633
3016.8030
-72403.2715 0
0 -669.4089
0 -1740.4633
72403.2715 0
0 669.4089
0 -1740.4633
0
1740.4633
3016.8030
0
-1740.4633
6033.6060
1 0
0 1
0 0
0 0
0 0
0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
0 0 0
0
0
0
0
0
1
1
0
0
0
0
0
0 0
1 0
0 1
0 0
0 0
0 0
0 0
0 0
0 0
1 0
0 1
0 0
0
0
0
0
0
1
2. Matriz de transformación
x y
0 1 0
= = =
T
T
T
=
=
3. Determinamos matriz de rigidez en coordenadas globales
K
=
72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000
0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633
0.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030
-72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000
0.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633
0.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060
4 72403.2715 0.0000 0.0000
5 0.0000 669.4089 1740.4633
6 0.0000 1740.4633 6033.6060
7 -72403.2715 0.0000 0.0000
8 0.0000 -669.4089 -1740.4633
9 0.0000 1740.4633 3016.8030
4 5 6
-72403.2715 0.0000 0.0000
0.0000 -669.4089 1740.4633
0.0000 -1740.4633 3016.8030
72403.2715 0.0000 0.0000
0.0000 669.4089 -1740.4633
0.0000 -1740.4633 6033.6060
7 8 9
BARRA 3
1. Matriz en cordenadas locales de la barra 1 Longitud = E = A= I =
K3
3.55 2509980.1 0.075 0.00625
=
m Tn/m2 m2 m4 53027.7482 0
0 4207.7166
0 7468.6969
-53027.7482 0
0 -4207.7166
0 7468.6969
0
7468.6969
17675.9161
0
-7468.6969
8837.9580
-53027.7482 0 0
0 -4207.7166 7468.6969
0 -7468.6969 8837.9580
53027.7482 0 0
0 4207.7166 -7468.6969
0 -7468.6969 17675.9161
2. Matr z de transformac n x y
1.5707796 1.669E-05 1
= = =
T
=
TT
=
1.66941E-05
1
0
-1
1.66941E-05
0
0
0
0
0 0 0 0
0 0 0 0
1 0 0 0
0 1.66941E-05 -1 0
0
0 0 1 1.66941E-05 0
0 0 0 0 1
1.66941E-05 1 0
-1 1.66941E-05 0
0 0 1
0 0 0
0 0 0
0 0 0
0
0
0
1.66941E-05
-1
0
0 0
0 0
0 0
1 0
1.66941E-05 0
0 1
3. Determinamos matriz de rigidez en coordenadas globales
K
=
0.8853 53027.7482 0.0000
-4207.7166 0.0702 7468.6969
-7468.6969 0.1247 17675.9161
-0.8853 -53027.7482 0.0000
4207.7166 -0.0702 -7468.6969
-7468.6969 0.1247 8837.9580
-0.8853 -53027.7482 0.0000
4207.7166 -0.0702 7468.6969
7468.6969 -0.1247 8837.9580
0.8853 53027.7482 0.0000
-4207.7166 0.0702 -7468.6969
7468.6969 -0.1247 17675.9161
10
11
12
1
2
3
4207.7166 0.8150 -7468.6969
0.8150 53027.7481 0.1247
-7468.6969 0.1247 17675.9161
-4207.7166 -0.8150 7468.6969
-0.8150 -53027.7481 -0.1247
-7468.6969 0.1247 8837.9580
10 11 12
-4207.7166 -0.8150 -7468.6969
-0.8150 -53027.7481 0.1247
7468.6969 -0.1247 8837.9580
4207.7166 0.8150 7468.6969
0.8150 53027.7481 -0.1247
7468.6969 -0.1247 17675.9161
1 2 3
BARRA 4
1. Matriz en cordenadas locales de la barra 1 Longitud = E = A=
3.55 m 2509980.1 Tn/m2 0.075 m2
I =
0.00625 m4
K4
=
53027.7482
0
0
4207.7166
7468.6969
0
-4207.7166
7468.6969
0
7468.6969
17675.9161
0
-53027.7482 0
-7468.6969
0
8837.9580
0
-53027.7482
0
0
53027.7482
0
0
0 0
-4207.7166 7468.6969
-7468.6969 8837.9580
0 0
4207.7166 -7468.6969
-7468.6969 17675.9161
1.66941E-05 -1
1 1.66941E-05
0 0
0 0
0 0
0 0
0 0 0 0
0 0 0 0
1 0 0 0
0 1.66941E-05 -1 0
0 1 1.66941E-05 0
0 0 0 1
1.66941E-05 1
-1 1.66941E-05
0 0
0 0
0 0
0
0
1
0
0
0
0
0
0
1.66941E-05
-1
0
0 0
0 0
0 0
1 0
1.66941E-05 0
0 1
2. Matriz de transformación
x y
1.5707796
= = =
1.669E-05 1
T
=
TT
=
0 0
3. Determinamos matriz de rigidez en coordenadas globales
K
=
0.8853 53027.7482 0.0000 -0.8853 -53027.7482 0.0000
-4207.7166 0.0702 7468.6969 4207.7166 -0.0702 7468.6969
-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580
-0.8853 -53027.7482 0.0000 0.8853 53027.7482 0.0000
4207.7166 -0.0702 -7468.6969 -4207.7166 0.0702 -7468.6969
-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161
13 4207.7166 0.8150 -7468.6969
14 0.8150 53027.7481 0.1247
15 -7468.6969 0.1247 17675.9161
4 -4207.7166 -0.8150 7468.6969
5 -0.8150 -53027.7481 -0.1247
6 -7468.6969 0.1247 8837.9580
13 14 15
-4207.7166 -0.8150 -7468.6969
-0.8150 -53027.7481 0.1247
7468.6969 -0.1247 8837.9580
4207.7166 0.8150 7468.6969
0.8150 53027.7481 -0.1247
7468.6969 -0.1247 17675.9161
4 5 6
BARRA 5
1. Matriz en cordenadas locales de la barra 1 Longitud = E = A= I =
K5
3.55 2509980.1 0.075 0.00625
=
m Tn/m2 m2 m4 53027.7482 0
0 4207.7166
0 7468.6969
-53027.7482 0
0 -4207.7166
0 7468.6969
0
7468.6969
17675.9161
0
-7468.6969
8837.9580
-53027.7482 0 0
0 -4207.7166 7468.6969
0 -7468.6969 8837.9580
53027.7482 0 0
0 4207.7166 -7468.6969
0 -7468.6969 17675.9161
2. Matr z de transformac n x y
1.5707796 1.669E-05 1
= = =
T
=
TT
=
1.66941E-05
1
0
-1
1.66941E-05
0
0
0
0
0 0 0 0
0 0 0 0
1 0 0 0
0 1.66941E-05 -1 0
0
0 0 1 1.66941E-05 0
0 0 0 0 1
1.66941E-05 1 0
-1 1.66941E-05 0
0 0 1
0 0 0
0 0 0
0 0 0
0
0
0
1.66941E-05
-1
0
0 0
0 0
0 0
1 0
1.66941E-05 0
0 1
3. Determinamos matriz de rigidez en coordenadas globales
K
=
0.8853 53027.7482 0.0000
-4207.7166 0.0702 7468.6969
-7468.6969 0.1247 17675.9161
-0.8853 -53027.7482 0.0000
4207.7166 -0.0702 -7468.6969
-7468.6969 0.1247 8837.9580
-0.8853 -53027.7482 0.0000
4207.7166 -0.0702 7468.6969
7468.6969 -0.1247 8837.9580
0.8853 53027.7482 0.0000
-4207.7166 0.0702 -7468.6969
7468.6969 -0.1247 17675.9161
16
17
18
7
8
9
4207.7166 0.8150 -7468.6969
0.8150 53027.7481 0.1247
-7468.6969 0.1247 17675.9161
-4207.7166 -0.8150 7468.6969
-0.8150 -53027.7481 -0.1247
-7468.6969 0.1247 8837.9580
16 17 18
-4207.7166 -0.8150 -7468.6969
-0.8150 -53027.7481 0.1247
7468.6969 -0.1247 8837.9580
4207.7166 0.8150 7468.6969
0.8150 53027.7481 -0.1247
7468.6969 -0.1247 17675.9161
7 8 9
BARRA 6
1. Matriz en cordenadas locales de la barra 1 Longitud =
5.2 m
E = A= I =
2509980.1 Tn/m2 0.15 m2 0.003125 m4
K6
=
72403.2715 0
0 669.4089
0 1740.4633
-72403.2715 0
0 -669.4089
0 1740.4633
0
1740.4633
6033.6060
0
-1740.4633
3016.8030
-72403.2715
0
0
72403.2715
0
0
0 0
-669.4089 1740.4633
-1740.4633 3016.8030
0 0
669.4089 -1740.4633
-1740.4633 6033.6060
1 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 1 0
0 0 0 1
1 0 0
0 1 0
0 0 1
0 0 0
0 0 0
0 0 0
0
0
0
1
0
0
0 0
0 0
0 0
0 0
1 0
0 1
2. Matriz de transformación
x y
0 1 0
= = =
T
=
TT
=
3. Determinamos matriz de rigidez en coordenadas globales
K
=
72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000
0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633
0.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030
-72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000
0.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633
0.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060
10 72403.2715 0.0000 0.0000
11 0.0000 669.4089 1740.4633
12 0.0000 1740.4633 6033.6060
13 -72403.2715 0.0000 0.0000
14 0.0000 -669.4089 -1740.4633
15 0.0000 1740.4633 3016.8030
10 11 12
-72403.2715 0.0000 0.0000
0.0000 -669.4089 1740.4633
0.0000 -1740.4633 3016.8030
72403.2715 0.0000 0.0000
0.0000 669.4089 -1740.4633
0.0000 -1740.4633 6033.6060
13 14 15
BARRA 7
1. Matriz en cordenadas locales de la barra 1 Longitud = E = A= I =
K7
5.2 2509980.1 0.15 0.003125
=
m Tn/m2 m2 m4 72403.2715 0
0 669.4089
0 1740.4633
-72403.2715 0
0 -669.4089
0 1740.4633
0
1740.4633
6033.6060
0
-1740.4633
3016.8030
-72403.2715 0 0
0 -669.4089 1740.4633
0 -1740.4633 3016.8030
72403.2715 0 0
0 669.4089 -1740.4633
0 -1740.4633 6033.6060
2. Matr z de transformac n x y
0 1 0
= = =
T
TT
=
=
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
1 0 0
0 1 0
0 0 1
1
0
0
0
0
0
0 0
1 0
0 1
0 0
0 0
0 0
0 0
0 0
0 0
1 0
0 1
0 0
0
0
0
0
0
1
3. Determinamos matriz de rigidez en coordenadas globales
K
=
72403.2715 0.0000
0.0000 669.4089
0.0000 1740.4633
-72403.2715 0.0000
0.0000 -669.4089
0.0000 1740.4633
0.0000 -72403.2715 0.0000
1740.4633 0.0000 -669.4089
6033.6060 0.0000 -1740.4633
0.0000 72403.2715 0.0000
-1740.4633 0.0000 669.4089
3016.8030 0.0000 -1740.4633
0.0000
1740.4633
3016.8030
0.0000
-1740.4633
6033.6060
13
14
15
16
17
18
72403.2715 0.0000 0.0000
0.0000 669.4089 1740.4633
0.0000 1740.4633 6033.6060
-72403.2715 0.0000 0.0000
0.0000 -669.4089 -1740.4633
0.0000 1740.4633 3016.8030
13 14 15
-72403.2715 0.0000
0.0000 -669.4089
0.0000 -1740.4633
72403.2715 0.0000
0.0000 669.4089
0.0000 -1740.4633
16 17
0.0000
1740.4633
3016.8030
0.0000
-1740.4633
6033.6060
18
BARRA 8
1. Matriz en cordenadas locales de la barra 1 Longitud =
3.55 m
E = A= I =
2509980.1 Tn/m2 0.075 m2 0.00625 m4
K8
=
53027.7482 0
0 4207.7166
0 7468.6969
-53027.7482 0
0 -4207.7166
0 7468.6969
0
7468.6969
17675.9161
0
-7468.6969
8837.9580
-53027.7482 0
0 -4207.7166
0 -7468.6969
53027.7482 0
0 4207.7166
0 -7468.6969
0
7468.6969
8837.9580
0
-7468.6969
17675.9161
1.66941E-05 -1
1 1.66941E-05
0 0
0 0
0 0
0 0
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
1.66941E-05 -1 0
1 1.66941E-05 0
0 0 1
1.66941E-05 1 0
-1 1.66941E-05 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0
0 0
0 0
1.66941E-05 1
-1 1.66941E-05
0 0
0
0
0
0
0
1
2. Matriz de transformación
x y
1.5707796 1.669E-05
= = =
1
T
TT
=
=
3. Determinamos matriz de rigidez en coordenadas globales
K
=
0.8853 53027.7482 0.0000 -0.8853
-4207.7166 0.0702 7468.6969 4207.7166
-7468.6969 0.1247 17675.9161 7468.6969
-0.8853 -53027.7482 0.0000 0.8853
4207.7166 -0.0702 -7468.6969 -4207.7166
-7468.6969 0.1247 8837.9580 7468.6969
-53027.7482 0.0000
-0.0702 7468.6969
-0.1247 8837.9580
53027.7482 0.0000
0.0702 -7468.6969
-0.1247 17675.9161
19 4207.7166 0.8150 -7468.6969
20 0.8150 53027.7481 0.1247
21 -7468.6969 0.1247 17675.9161
10 -4207.7166 -0.8150 7468.6969
11 -0.8150 -53027.7481 -0.1247
12 -7468.6969 0.1247 8837.9580
19 20 21
-4207.7166
-0.8150
7468.6969
4207.7166
0.8150
7468.6969
10
-0.8150 -7468.6969
-53027.7481 0.1247
-0.1247 8837.9580
0.8150 7468.6969
53027.7481 -0.1247
-0.1247 17675.9161
11 12
BARRA 9
1. Matriz en cordenadas locales de la barra 1 Longitud = E = A= I =
3.55 2509980.1 0.075 0.00625
K9
m Tn/m2 m2 m4
=
53027.7482 0
0 4207.7166
0 7468.6969
-53027.7482 0
0 -4207.7166
0 7468.6969
0
7468.6969
17675.9161
0
-7468.6969
8837.9580
-53027.7482 0 0
0 -4207.7166 7468.6969
0 -7468.6969 8837.9580
53027.7482 0 0
0 4207.7166 -7468.6969
0 -7468.6969 17675.9161
1.66941E-05
1
0
-1
1.66941E-05
0
0
0
0
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
1.66941E-05 -1 0
1 1.66941E-05 0
0 0 1
2. Matriz de transformación x y
1.5707796
= = =
1.669E-05 1
T
TT
=
=
0
0
0
0
1.66941E-05
-1
0
0
0
1 0
1.66941E-05 0
0 1
0 0
0 0
0 0
0 0 0
0 0 0
0 0 0
1.66941E-05 1 0
-1 1.66941E-05 0
0 0 1
-7468.6969 0.1247 17675.9161 7468.6969 -0.1247
-0.8853 -53027.7482 0.0000 0.8853 53027.7482
4207.7166 -0.0702 -7468.6969 -4207.7166 0.0702
-7468.6969 0.1247 8837.9580 7468.6969 -0.1247
3. Determinamos matriz de rigidez en coordenadas globales
K
BARRA 10
=
0.8853 53027.7482 0.0000 -0.8853 -53027.7482
-4207.7166 0.0702 7468.6969 4207.7166 -0.0702
0.0000
7468.6969
8837.9580
0.0000
-7468.6969
17675.9161
22 4207.7166
23 0.8150
24 -7468.6969
13 -4207.7166
14 -0.8150
15 -7468.6969
22
0.8150 -7468.6969
53027.7481 0.1247
0.1247 17675.9161
-0.8150 7468.6969
-53027.7481 -0.1247
0.1247 8837.9580
23 24
-4207.7166 -0.8150
-0.8150 -53027.7481
7468.6969 -0.1247
4207.7166 0.8150
0.8150 53027.7481
7468.6969 -0.1247
13 14
-7468.6969
0.1247
8837.9580
7468.6969
-0.1247
17675.9161
15
1. Matriz en cordenadas locales de la barra 1 Longitud = E =
3.55 m 2509980.1 Tn/m2
A= I =
0.075 m2 0.00625 m4
K10
=
53027.7482 0
0 4207.7166
0 7468.6969
-53027.7482 0
0 -4207.7166
0 7468.6969
0
7468.6969
17675.9161
0
-7468.6969
8837.9580
-53027.7482 0 0
0 -4207.7166 7468.6969
0 -7468.6969 8837.9580
53027.7482 0 0
0 4207.7166 -7468.6969
0 -7468.6969 17675.9161
1.66941E-05 -1
1 1.66941E-05
0 0
0 0
0 0
0 0
0 0 0
0 0 0
1 0 0
0 1.66941E-05 -1
0 1 1.66941E-05
0 0 0
0
0
0
0
0
1
2. Matriz de transformación
x y
1.5707796 1.669E-05 1
= = =
T
TT
=
=
1.66941E-05
-1
0
0
0
1 0
1.66941E-05 0
0 1
0 0
0 0
0 0
0 0 0
0 0 0
0 0 0
1.66941E-05 1 0
0
-1 1.66941E-05 0
0 0 1
3. Determinamos matriz de rigidez en coordenadas globales
K
=
0.8853 53027.7482 0.0000 -0.8853 -53027.7482
-4207.7166 0.0702 7468.6969 4207.7166 -0.0702
-7468.6969 0.1247 17675.9161 7468.6969 -0.1247
-0.8853 -53027.7482 0.0000 0.8853 53027.7482
4207.7166 -0.0702 -7468.6969 -4207.7166 0.0702
-7468.6969 0.1247 8837.9580 7468.6969 -0.1247
0.0000
7468.6969
8837.9580
0.0000
-7468.6969
17675.9161
25 4207.7166
26 0.8150
27 -7468.6969
16 -4207.7166
17 -0.8150
18 -7468.6969
25
0.8150 -7468.6969
53027.7481 0.1247
0.1247 17675.9161
-0.8150 7468.6969
-53027.7481 -0.1247
0.1247 8837.9580
26 27
-4207.7166
-0.8150
7468.6969
4207.7166
0.8150
7468.6969
16
-0.8150 -7468.6969
-53027.7481 0.1247
-0.1247 8837.9580
0.8150 7468.6969
53027.7481 -0.1247
-0.1247 17675.9161
17 18
MATRIZ DE RIGIDEZ DE TODA LA ESTRUCTURA
K
=
1
2
3
4
1 2
76610.98812 0.81500624
0.81500624 53697.15709
7468.696923 1740.338575
-72403.27153 0
0 -669.4089453
0 1740.46326
3 4 5 6 7 8 9 10 11
7468.696923 -72403.27153 0 0 0 0 0 -4207.716591 -0.81500624
1740.338575 0 -669.4089453 1740.463258 0 0 0 -0.81500624 -53027.74815
23709.52201 0 -1740.463258 3016.80298 0 0 0 -7468.696923 0.124683135
0 149014.2596 0.81500624 7468.696923 -72403.27153 0 0 0 0
-1740.463258 0.81500624 54366.56604 -0.124683135 0 -669.4089453 1740.463258 0 0
5
3016.80298 0 7468.69692 -72403.2715 -0.1246831 0 29743.128 0 0 76610.9881 -1740.4633 0.81500624 3016.80298 7468.69692 0 0 0 0
6
7
12
7468.696923
-0.124683135
8837.958027
0
0
0
0
0
0
0
1740.46326
41385.4381
13 14
0 0
0 0
0 0
-4207.716591 -0.81500624
-0.81500624 -53027.74815
-7468.6969 0.12468314
0 0
0 0
0 0
-72403.272 0
0 -669.40895
0 -1740.4633
15 16
0 0
0 0
0 0
7468.696923 0
-0.124683135 0
8837.95803 0
0 -4207.71659
0 -0.8150062
0 -7468.6969
0 0
1740.46326 0
3016.80298 0
17 18
0 0
0 0
0 0
0 0
0 0
0 0
-0.81500624 7468.69692
-53027.748 -0.1246831
0.12468314 8837.95803
0 0
0 0
0 0
19 20
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
-4207.7166 - 0.8150062
-0.8150062 -53027.748
-7468.6969 0.12468314
0 0
0 0
0 0
0 0
0 0
21 22 23
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
7468.69692 0 0
-0.1246831 0 0
8837.95803 0 0
0 - 4207.7166 -0.8150062
0 -0.8150062 -53027.748
0 -7468.6969 0.12468314
0 0 0
0 0 0
24 25 26
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
7468.69692 0 0
-0.1246831 0 0
8837.95803 0 0
0 -4207.7166 -0.8150062
0 -0.8150062 -53027.748
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7468.69692
-0.1246831
0 0
8
9
0 0
0 0
0 0 0 0 -669.40895 1740.46326 -1740.4633 3016.80298 0.81500624 7468.69692 53697.1571 -1740.5879 -1740.5879 23709.522 0 0 0 0
10 -4207.7166 -0.8150062
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-0.8150062 -53027.748
7468.69692 -0.1246831
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
-7468.6969 0.12468314 0 0 0 0 0 0 0 0 0 0 0 0 80818.7047 1.63001248 1.63001248 106724.905
8837.95803 0 0 0 0 0 0 0 1740.46326
0 -4207.7166 -0.8150062 -7468.6969 0 0 0 -72403.272 0
0 -0.8150062 -53027.748 0.12468314 0 0 0 0 -669.40895
0 7468.69692 -0.1246831 8837.95803 0 0 0 0 1740.46326
0 0 0 0 -4207.7166 -0.8150062 -7468.6969 0 0
0 0 0 0 -0.8150062 -53027.748 0.12468314 0 0
0 0 0 0 7468.69692 -0.1246831 8837.95803 0 0
0 0 0 0 0 0 0 -4207.7166 -0.8150062
0 0 0 0 0 0 0 -0.8150062 -53027.748
0 0 0 0 0 0 0 7468.69692 -0.1246831
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0
-1740.4633
3016.80298
0
0
0
-7468.6969
0.12468314
8837.95803
0
0
0
0
0
80818.7047 1.63001248
72404.9015 106724.905
0 -1071.0543
0 1740.46326
-72403.272 0
0 -669.40895
0 0
0 0
0 0
-4207.7166 -0.81500624 -0.8150062 -53027.7481
7468.696923 -0.124683135
0 0
0 0
0 0
-1740.4633 -72403.272
43125.9013 0
6033.60596 8415.43318
0 72404.9015
-1740.4633 0
0 0
0 0
0 0
-7468.6969 0
0.12468314 0
8837.958027 0
0 0
0 0
-669.40895 1740.46326
-1738.8332 3016.80298
106055.496 0
669.408945 33611.3688
0 0
0 0
0 0
0 0
0 0
0 0
4207.71659 0.81500624
0.81500624 53027.7481
-7468.6969 0.12468314
0 0
0 0 0
-7468.6969 0 0
0.12468314 0 0
17675.9161 0 0
0 4207.71659 0.81500624
0 -7468.6969 0.12468314
0 0 0
0 0 0
0 0 0
-7468.6969 0 0
0.12468314 0 0
17675.91605 0 0
0 4207.716591 0.81500624
0 0.81500624 53027.7481
8837.95803
0
0
0
0
0
0
-7468.696923
0.12468314
0 -4207.716591
0 -0.81500624
0 0
-0.81500624 -7468.696923
-53027.7481 0.12468314
0 0
0 0
0 0
0 0
0 0.81500624 53027.7481
0 -7468.696923 0.124683135
0 0 0
0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7468.696923 -0.124683135 8837.958027 0 0 0 0 0 0 -7468.696923 0.124683135 17675.91605
CALCULO DE DESPLAZAMI ENTOS
Q=KD
Q1 Q2
0 -11.44
76610.98812 0.81500624
0.81500624 53697.15709
7468.696923 1740.338575
-72403.27153 0
0 -669.4089453
0 1740.46326
0 0
0 0
0 0
-4207.7166 -0.8150062
-0.8150062 -53027.748
7468.69692 -0.1246831
0 0
0 0
0 0
0 0
0 0
0 0
D1 D2
Q3 Q4 Q5 Q6
-9.91 0 -19.25 5.29
7468.696923 -72403.27153 0 0
1740.338575 0 -669.4089453 1740.463258
23709.52201 0 -1740.463258 3016.80298
0 149014.2596 0.81500624 7468.696923
-1740.463258 0.81500624 54366.56604 -0.124683135
3016.80298 7468.69692 -0.1246831 29743.128
0 -72403.2715 0 0
0 0 -669.40895 -1740.4633
0 0 1740.46326 3016.80298
-7468.6969 0 0 0
0.12468314 0 0 0
8837.95803 0 0 0
0 -4207.7166 -0.8150062 -7468.6969
0 -0.8150062 -53027.748 0.12468314
0 7468.69692 -0.1246831 8837.95803
0 0 0 0
0 0 0 0
0 0 0 0
D3 D4 D5 D6
Q7 Q8
0 -7.81
0 0
-72403.27153 0
0 -669.4089453
0 -1740.4633
76610.9881 0.81500624
0.81500624 53697.1571
7468.69692 -1740.5879
0 0
-4207.7166 -0.8150062
-0.8150062 -53027.748
7468.69692 -0.1246831
Q9
4.62
0
0
0
0
1740.463258
3016.80298
7468.69692
-1740.5879
23709.522
0
0
0
0
0
0
-7468.6969
0.12468314
8837.95803
Q10 Q11
0 15.89
-4207.716591 -0.81500624
0 0
-0.81500624 -53027.74815
-7468.696923 0.124683135
0 0
0 0
0 0
0 0
0 0
0 0
80818.7047 1.63001248
1.63001248 106724.905
0 1740.46326
-72403.272 0
0 -669.40895
0 1740.46326
0 0
0 0
0 0
D10 D11
Q12 Q13 Q14 Q15
-13.77 0 -23.7 9.15
7468.696923 0 0 0
-0.124683135 0 0 0
8837.958027 0 0 0
0 -4207.716591 -0.81500624 7468.696923
0 -0.81500624 -53027.74815 -0.124683135
0 -7468.6969 0.12468314 8837.95803
0 0 0 0
0 0 0 0
0 0 0 0
0 -72403.272 0 0
1740.46326 0 -669.40895 1740.46326
41385.4381 0 -1740.4633 3016.80298
0 80818.7047 1.63001248 0
-1740.4633 72404.9015 106724.905 -1740.4633
3016.80298 0 -1071.0543 43125.9013
0 0 1740.46326 6033.60596
0 -72403.272 0 0
0 0 -669.40895 -1740.4633
D12 D13 D14 D15
Q16 Q17
0 -7.81
0 0
0 0
0 0
0 0
0 0
0 0
-4207.71659 -0.81500624
-0.8150062 -53027.748
-7468.6969 0.12468314
0 0
0 0
0 0
0 0
-72403.272 0
0 -669.40895
8415.43318 -1738.8332
72404.9015 106055.496
0 669.408945
D16 D17
Q18
4.62
0
0
0
0
0
0
7468.69692
-0.1246831
8837.95803
0
0
0
0
0
1740.46326
3016.80298
0
33611.3688
D18
=
0 0
0 0
0 0
0 0
0 0
0 0
D7 D8 X
D9
2.28715E-05
-9.5119E-05
0.000117742
-8.27169E-05
0.00082465
-0.000140654
-6.95071E-05
1.58452E-05
-0.000116899
1.5901E-05
3.74461E-05
-4.78186E-06
1.5866E-05
4.80442E-06
-4.06809E-06
1.5857E-05
-4.53522E-06
-1.76209E-06
3.99743E-06
1.87098E-05
-2.27047E-06
4.03122E-06
4.60957E-06
-2.3439E-06
7.245E-06
-4.46162E-06
-3.00083E-0
-8.5183E-05 0.00081928
0.00082992
-5.87606E-06 2.28205E- 05
6.4016E-05 -9.24169E- 05
-8.3049E-05 0.00082611
-2.30369E-05 0.000119821
8.70235E-06 - 8.39803E- 05
-8.2963E-05 0.00082768
2.89172E-05 -0.000142682
1.33071E-05 -7.03663E- 05
-8.46904E-06 0.000332766
-3.27401E-06 1.58143E-05
-1.08338E-07 -0.000115444
-1.11065E-05 0.000333365
-2.55749E-05 0.000125091
1.19675E-05 -0.000110808
-3.21868E-05 0.000435287
2.88498E-05 -0.000140923
1.447 - 0.000165854
-1.0214E-05 -3.227E-05 0.00081231
3.51759E-07 -3.66707E-06 2.27417E-05
3.68567E-06 2.98207E-06 -9.13436E-05
-1.014E-05 -3.3566E-05 0.00081912
2.77828E-05 -1.50359E-05 0.000122696
1.82895E-06 4.54906E-05 -8.32097E-05
-1.0151E-05 -3.2897E-05 0 .0008344
9.58202E-06 1.87047E-05 -0.000145478
-2.43995E-06 3.09099E-06 -7.29504E-05
-2.59664E-06 4.03319E-06 0.000330101
1.86347E-07 -1.93317E-06 1.57587E-05
1.32741E-06 4.91217E-06 -0.000114368
-2.68505E-06 6.06975E-06 0.000330683
9.29964E-06 -1.56025E-05 0.000127955
1.53726E-06 -4.11743E-06 -0.000109774
-9.39557E-06 -5.9173E-06 0.000434672
9.3723E-06 1.75356E-05 -0.000143731
2.97538E-0 5.62406E -0.00016650
-5.7276E-06
-8.29092E-08
1.10085E-06
-5.7667E-06
5.12285E-06
2.24332E-06
-5.7465E-06
3.26765E-05
4.2056E-06
-1.41711E-06
-3.89352E-08
9.48845E-07
-1.36252E-06
4.94256E-06
8.12162E-07
2.12911E-06
1.39544E-05
-0.00013962
-2.10388E-06
-1.61115E-05
6.38193E-05
-5.93789E-05
-1.60434E-06
2.06017E-05
-6.00756E-05
2.03982E-05
2.15105E-05
-4.43511E-05
-1.87912E-05
1.685
0.00040929 1.2383E-05
7.49373E-06 1.87434E-05
-2.48862E-05 -3.15228E-06
-1.53661E-05 -1.21621E-06
0.000246588 3.93657E-06
5.83184E-06 1.87729E-05
-6.40298E-05 -2.15913E-06
0.000240097 3.95229E-06
1.83072E-05 3.20055E-06
-5.82581E-05 -2.1361E-06
0.000257246 6.20738E-06
-2.4151E-05 -3.11567E-06
-8.9582E-0 -2.41794E
-0.00012107
-3.28469E-06
-5.34022E-05
0.00041742 -1.238E-05
7.64169E-06 1.30401E-08
-0.00015852 0.00017589 -1.8759E-08 -0.00015137
-5.15273E-06 8.74473E-06 1.01248E-07 -5.01824E-06
0.00082306
1.85076E-05 -0.00014025 -2.37078E-05 -2.69102E-06
1.82223E-05
0.0004097 1.2373E-05
1.73725E-05 3.26635E-06
2.41014E-06 -0.00012018
-1.33611E-05
-2.7539E-05 2.33048E-06
0.00041805 -1.2394E-05
1.49254E-05 1.08568E-05
1.778E-05 -0.00015991 -1.23066E-05 0.00017842 3.61593E-07 3.9709E-09 1.56146E-05 -0.00015287
-3.63359E-05 0.000130214 4.73215E-06 -4.18614E-05
4.57027E-06 -0.00014285 -2.32089E-05 -2.36479E-06
0.00041156 1.2389E-05
1.2576E-05 -0.00012042
0.000334116
0.000334531
0.000123051
-0.000110472
0.000434995
-0.000138914
-0.000165
3.37637E-
1.66517E-05
8.86565E-06
-5.39221E-05
-2.66676E-06
4.40008E-05
-1.36563E-05
1.4189E-05
-6.51205E-05
1.63259E-05
2.45643
0.00042003 -1.2494E-05
-2.25876E-05 7.98879E-06
-1.44853E-05 -8.75397E-07
0.000242894 -4.36419E-06
5.92678E-06 1.03219E-08
-6.46673E-05 2.05651E-06
0.000249708 -4.39235E-06
1.59222E-05 1.09246E-05
-5.98439E-05 1.90774E-06
0.000265186 -1.01475E-05
-2.18611E-05 7.92346E-06
-9.18707E 3.16493E-
9.14753E-06 -0.00016096 -2.75951E-05 0.00018217 6.04553E-07 8.8041E-08 1.92912E-05 -0.00015587
4.14965E-05 -0.000138968 1.40247E-05 4.68872E-05
1.16694E-05 -5.36761E-06 2.09219E-06 -6.93344E-07
-6.7428E-05 7.12021E-05 4.18578E-07 -6.06366E-05
-3.87676E-06 5.90337E-06 7.44913E-08 -3.40895E-06
2.00173E-05 -2.21112E-05 1.05142E-07 2.09444E-05
-6.78869E-05 7.05258E-05 4.3102E-07 -6.04984E-05
-3.79142E-05 0.000135375 4.7301E-06 -4.39836E-05
4.61192E-05 -2.13675E-05 2.30686E-07 1.82661E-05
-9.87151E-05 0.000175696 3.9288E-06 -9.55833E-05
4.17947E-05 -0.000141284 1.40534E-05 4.73961E-05
-2.19971E-05 1.76145E-06
3.34981E -3.46661 -7.43382E-07 6.36
-0.0030
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17 D18
=
m.
-0.0002
m.
0.0003 -0.0031
rad. m.
-0.0009
m.
0.0005
rad.
-0.0032 -0.0006
m. m.
-0.0004
rad.
-0.0004 0.0000 0.0000
m. m. rad.
-0.0003 -0.0006
m. m.
0.0012
rad.
-0.0036
m.
-0.0004 0.0012
m. rad.
NOTA: los desplazamientos del 19 al 27 son cero
REACCIONES
-0.0030 -0.0002 0.0003 -0.0031
Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27
=
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
-4207.7166 -0.8150062
-0.8150062 -53027.748
-7468.6969 0.12468314
0 0
0 0
0 0
0 0
0 0
0 0
-0.0009 0.0005
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
7468.69692 0 0 0
-0.1246831 0 0 0
8837.95803 0 0 0
0 -4207.7166 -0.8150062 7468.69692
0 -0.8150062 -53027.748 -0.1246831
0 -7468.6969 0.12468314 8837.95803
0 0 0 0
0 0 0 0
0 0 0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
-4207.7166 -0.8150062
-0.8150062 -53027.748
-7468.6969 0.12468314
0.0000 0.0000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7468.69692
-0.1246831
8837.95803
-0.0003
X
-0.0032 -0.0006 -0.0004 -0.0004
-0.0006 0.0012 -0.0036 -0.0004 0.0012
Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27
1.3981 -0.0874 -2.6564 -7.4798 =
32.1473 8.0982 6.0817 22.0601 -16.2396
FUERZAS EN LAS BARRAS
BARRA 1 q1 =k1 TD q1 q2 q3 q4 q5 q6
=
q1 q2 q3 q4 q5 q6
72403.2715 0.0000 0.0000 -72403.2715
0.0000 669.4089 1740.4633 0.0000
0.0000 1740.4633 6033.6060 0.0000
-72403.2715 0.0000 0.0000 72403.2715
0.0000 -669.4089 -1740.4633 0.0000
0.0000 1740.4633 3016.8030 0.0000
0.0000 0.0000
-669.4089 1740.4633
-1740.4633 3016.8030
0.0000 0.0000
669.4089 -1740.4633
-1740.4633 6033.6060
8.620449554 1.846884112 4.396343709 -8.620449554 -1.846884112 5.207453673
=
11.44Tn-m 8.62
Fuerzas Finales q1 q2 q3 q4 q5 q6
8.620449554 13.28688411 =
N= V=
4.396
9.91Tn-m
5.207
(0
9.59
13.29 8.62
4.4 TN/m
8.62
V=
M=
M= M= M maximo =
-14.306 - 4.690 5.761
(x=0) (x =5.2) (x =3.02)
0 1 0 0 0 0
14.31
4.70 x
0 0 1 0 0 0
0 0 669.408945 1740.46326 1740.46326 6033.60596 0 0 -669.40895 -1740.4633 11.44 Tn-m 1740.46326 3016.80298
8.62
14.30634371 -8.620449554 9.593115888 -4.702546327
Corte en la sección
1 0 0 0 0 0 72403.2715 0 0 -72403.2715 0 0
-1.847
1.847
x
9.91Tn-m
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
-72403.272 0 0 72403.2715 0 0
0 - 669.40895 - 1740.4633 0 669.408945 - 1740.4633
0 1740.46326 3016.80298 0 -1740.4633 6033.60596
x
-0.0030 -0.0002 0.0003 -0.0031 -0.0009 0.0005
Diagramas -14.306 9.590
-4.690
-
5.761 -8.620
-13.287
NORMAL
CORTANTE
MOMENTO
BARRA 2 q2 =k2 TD q4 q5 q6 q7 q8 q9
=
q4 q5 q6 q7 q8 q9
72403.2715 0.0000 0.0000 -72403.2715 0.0000
0.0000 669.4089 1740.4633 0.0000 -669.4089
0.0000 1740.4633 6033.6060 0.0000 -1740.4633
-72403.2715 0.0000 0.0000 72403.2715 0.0000
0.0000 -669.4089 -1740.4633 0.0000 669.4089
0.0000 1740.4633 3016.8030 0.0000 -1740.4633
0.0000
1740.4633
3016.8030
0.0000
-1740.4633
6033.6060
7.694856926 -0.077612866 1.261196867 -7.694856926
=
0.077612866 -1.664783772
0.078
0.078
7.694856926 7.732387134 =
1 0 0 0 0
0 1 0 0 0
1.261
0 0 0 0 0
0
0
0
0
1
0 1740.46326 6033.60596 0
-72403.272 0 0 72403.2715
0 - 669.40895 - 1740.4633 0
0 1740.46326 3016.80298 0
- 669.40895 - 1740.4633 1740.46326 3016.80298 7.81 Tn-m
0 0
669.408945 - 1740.4633
- 1740.4633 6033.60596
0 0
x
-0.0031 -0.0009 0.0005 -0.0032 -0.0006 -0.0004
4.62Tn-m
4.62Tn-m
(0
0 0 0 0 1
0 669.408945 1740.46326 0
1.665
Corte en la sección N= V=
0 0 0 1 0
0
7.695
5.881196867 -7.694856926 7.887612866 -6.284783772
0 0 1 0 0
72403.2715 0 0 -72403.2715
7.81Tn-m
7.695 Fuerzas Finales q4 q5 q6 q7 q8 q9
x
7.89
7.73 7.695
4.4 TN/m
5.88
7.695
6.28 x
Diagramas -5.881 7.695
7.890
-1.538
+
0.910 -7.730
NORMAL
CORTANTE
MOMENTO
BARRA 3 q3 =k3 TD q10 q11 q12 q1 q2 q3 q10 q11 q12 q1 q2 q3 Corte en la sección N= V= M=
=
=
53027.7482
0.0000
0.0000
-53027.7482
0.0000
0.0000
0.0000 0.0000 -53027.7482 0.0000 0.0000
4207.7166 7468.6969 0.0000 -4207.7166 7468.6969
7468.6969 17675.9161 0.0000 -7468.6969 8837.9580
0.0000 0.0000 53027.7482 0.0000 0.0000
-4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969
7468.6969 8837.9580 0.0000 -7468.6969 17675.9161
8.62
13.2870 -8.620227741 -16.29546477 -13.28702802 8.620227741 -14.30634371
(0 < x < 2.8) 13.287 8.620 16.295-13.287x 16.295 M= -20.909 M=
13.287 14.306
8.62
(x=0) (x=2.8)
x
16.295
13.287
Diagramas 13.287
8.620
+
+
-20.909 -
+ 16.295
NORMAL
CORTANTE
MOMENTO
x
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 0
0 0 0 0 0 1
0.88525026 -4207.71658 -7468.69692 -0.88525026 4207.71658 -7468.69692
53027.7482 0.07024402 0.12468314 -53027.748 -0.070244 0.12468314
0 7468.69692 17675.9161 0 -7468.6969 8837.95803
-0.8852503 4207.71658 7468.69692 0.88525026 -4207.7166 7468.69692
-53027.748 -0.070244 -0.1246831 53027.7482 0.07024402 -0.1246831
0 7468.69692 8837.95803 0 -7468.6969 17675.9161
-0.0004 x
0.0000 0.0000 -0.0030 -0.0002 0.0003
BARRA 4 q4 =k4 TD q13 q14 q15 q4 q5 q6 q13 q14 q15 q4 q5 q6
53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000
=
0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969
17.3255 0.925881862 4.46553115
=
0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580
-53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000
0.926
-17.32548757 -0.925881862
0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969
0.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161
x
17.325
1.179
-1.178650541
0 -1
1 0
0 0
0 0
0 0
0 0
0 0 0 0
0 0 0 0
1 0 0 0
0 0 -1 0
0 1 0 0
0 0 0 1
0.88525026 -4207.71658 -7468.69692
53027.7482 0.07024402 0.12468314
0 7468.69692 17675.9161
-0.8852503 4207.71658 7468.69692
-53027.748 -0.070244 -0.1246831
0 7468.69692 8837.95803
-0.88525026 4207.71658
-53027.748 -0.070244
0 -7468.6969
0.88525026 -4207.7166
53027.7482 0.07024402
0 -7468.6969
-7468.69692
0.12468314
8837.95803
7468.69692
-0.1246831
17675.9161
x
-0.0003 -0.0006 0.0012 -0.0031 -0.0009 0.0005
(0 < x < 2.8)
Corte en la sección N= V= M=
-17.326
x
-0.926 0.926x-4.466 -4.466 -1.873 M=
0.926
17.326
M=
4.466
Diagramas -17.326
-
-0.926
-1.873
-
-4.466
NORMAL
CORTANTE
MOMENTO
BARRA 5 q5 =k5 TD q16 q17 q18 q7 q8 q9 q16 q17 q18 q7 q8 q9 Corte en la sección N= V= M=
=
53027.7482 0.0000 0.0000
0.0000 4207.7166 7468.6969
0.0000 7468.6969 17675.9161
-53027.7482 0.0000 0.0000
0.0000 -4207.7166 -7468.6969
0.0000 7468.6969 8837.9580
0.0000 -1.0000 0.0000
1.0000 0.0000 0.0000
0.0000 0.0000 1.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
-53027.7482 0.0000
0.0000 -4207.7166
0.0000 -7468.6969
53027.7482 0.0000
0.0000 4207.7166
0.0000 -7468.6969
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 -1.0000
1.0000 0.0000
0.0000 0.0000
-0.0032 -0.0006
0.0000
7468.6969
8837.9580
0.0000
-7468.6969
17675.9161
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0004
7.8875 7.694988602 21.03242576
=
-7.887484407 -7.694988602
7.695
7.888
6.285
6.284783772
(0 < x < 2.8) -7.888 -7.695 7.695x-21.032 M= -21.032 M= 0.514
x
7.695
7.888 21.032
x
0.88525026 -4207.71658
53027.7482 0.07024402
0 7468.69692
-0.8852503 4207.71658
-53027.748 -0.070244
0 7468.69692
-7468.69692
0.12468314
17675.9161
7468.69692
-0.1246831
8837.95803
-0.88525026 4207.71658
-53027.748 -0.070244
0 -7468.6969
0.88525026 -4207.7166
53027.7482 0.07024402
0 -7468.6969
-7468.69692
0.12468314
8837.95803
7468.69692
-0.1246831
17675.9161
x
-0.0036 -0.0004 0.0012
Diagramas -7.888
-7.695
0.514 +
-
-
-21.032
NORMAL
CORTANTE
MOMENTO
BARRA 6 q6 =k6 TD q10 q11 q12 q13 q14 q15
=
q10 q11 q12 q13 q14 q15
=
Fuerzas Finales q10 q11 q12 q13 q14 q15
72403.2715 0.0000
0.0000 669.4089
0.0000 1740.4633
-72403.2715 0.0000
0.0000 -669.4089
0.0000 1740.4633
0.0000
1740.4633
6033.6060
0.0000
-1740.4633
3016.8030
-72403.2715 0.0000 0.0000
0.0000 -669.4089 1740.4633
0.0000 -1740.4633 3016.8030
72403.2715 0.0000 0.0000
0.0000 669.4089 -1740.4633
0.0000 -1740.4633 6033.6060
2.516
15.89Tn-m
2.516
0.0000 0.0000
0.0000 0.0000
0.0000
0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
1.0000 0.0000 0.0000
0.0000 1.0000 0.0000
0.0000 0.0000 1.0000
4.832
8.249 13.77Tn-m
18.41
(0 < x < 5.2) 7.222 6.11x-18.41 - 18.410
7.222
9.090
6.11TN/m
13.37 7.222
(x =0)
13.362 (x=5.2) 18.41x-3.06x^2-18.6 - 18.600 (x =0) M= M= -5.610 (x =5.2) (x =3.01)
0
-72403.272
0
0
669.408945 1740.46326 1740.46326 6033.60596 0 0 - 669.40895 - 1740.4633 1740.46326 3016.80298 15.89 Tn-m
0
0 0 72403.2715 0 0
- 669.40895 - 1740.4633 0 669.408945 - 1740.4633
1740.46326 3016.80298 0 - 1740.4633 6033.60596
7.222
-5.5208
M maximo =
0.0000 0.0000 0.0000
72403.2715
V=
M=
0.0000 0.0000 1.0000
0 0 -72403.2715 0 0
7.2223 13.3743
V=
0.0000 1.0000 0.0000
-7.2223
7.222
Corte en la sección N= V=
1.0000 0.0000 0.0000
2.51569888 4.832462839 7.222322845 -2.51569888 8.249171339
-7.2223 18.4057 18.6025
=
x
18.60
5.52 x
13.77Tn-m
-0.0004 0.0000 x
0.0000 -0.0003 -0.0006 0.0012
Diagramas -18.600 7.222
13.362
-5.610
+
9.090 -18.410
NORMAL
CORTANTE
MOMENTO
BARRA 7 q7 =k7 TD q13 q14 q15 q16 q17 q18
=
q13 q14 q15 q16 q17 q18
=
72403.2715 0.0000 0.0000
0.0000 669.4089 1740.4633
0.0000 1740.4633 6033.6060
-72403.2715 0.0000 0.0000
0.0000 -669.4089 -1740.4633
0.0000 1740.4633 3016.8030
-72403.2715 0.0000 0.0000
0.0000 -669.4089 1740.4633
0.0000 -1740.4633 3016.8030
72403.2715 0.0000 0.0000
0.0000 669.4089 -1740.4633
0.0000 -1740.4633 6033.6060
M= M= M= M maximo =
0.0000 0.0000 0.0000
0.0000 1.0000 0.0000
0.0000 0.0000 1.0000
0 1740.46326
-72403.272 0
0 - 669.40895
0 1740.46326
1740.46326 0 - 669.40895
6033.60596 0 - 1740.4633
0 72403.2715 0
- 1740.4633 0 669.408945
3016.80298 0 - 1740.4633
1740.46326 7.81 3016.80298 Tn-m
0
- 1740.4633
6033.60596
4.057 x
10.458
-4.057
7.81Tn-m 241.0898
10.639 4.62Tn-m
11.87 4.4TN/m
241.0898
- 11.867 (x =0) 3.750 (x =3.55) 11.87x-2.2x^2-15.08 - 15.080 -0.667 0.931
3.75 241.0898
-241.090 4.4x-11.87 V=
0.0000 0.0000 0.0000
1.0000 0.0000 0.0000
0 669.408945
(0 < x < 3.55)
V=
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
72403.2715 0
241.0898 11.8673
N= V=
0.0000 0.0000 1.0000
0.0000 0.0000 0.0000
0 -72403.2715 0
15.0782 -241.0898 3.7527 6.0196
Corte en la sección
0.0000 1.0000 0.0000
0.0000 0.0000 0.0000
241.0898 4.057265577
241.0898
=
1.0000 0.0000 0.0000
10.45816524 -241.0898321 -4.057265577 10.63961576
Fuerzas Finales q13 q14 q15 q16 q17 q18
x
(x =0) (x=3.55) (x=2.7)
15.08 x
6.02
0
4.62Tn-m
x
-0.0003 -0.0006 0.0012 -0.0036 -0.0004 0.0012
Diagramas -15.080 3.750
-0.667
0.931 -241.090
-11.867
NORMAL
CORTANTE
MOMENTO
BARRA 8 q8 =k8 TD q19 q20 q21 q10 q11 q12 q19 q20 q21 q10 q11 q12
Corte en la sección N= V= M=
=
=
53027.7482 0.0000
0.0000 4207.7166
0.0000 7468.6969
-53027.7482 0.0000
0.0000 -4207.7166
0.0000 7468.6969
0.0000
7468.6969
17675.9161
0.0000
-7468.6969
8837.9580
-53027.7482 0.0000
0.0000 -4207.7166
0.0000 -7468.6969
53027.7482 0.0000
0.0000 4207.7166
0.0000 -7468.6969
7468.6969
8837.9580
0.0000
-7468.6969
17675.9161
0.0000
x
0.0000 -1.0000
1.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 -1.0000
1.0000 0.0000
0.0000 0.0000
-0.0004 0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.0874
0.88525026
53027.7482
0
-0.8852503
-53027.748
0
-1.398128169 -2.656356931
1.398
-4207.71658 -7468.69692
0.07024402 0.12468314
7468.69692 17675.9161
4207.71658 7468.69692
-0.070244 -0.1246831
7468.69692 8837.95803
0.087393667 1.398128169 -2.306998068
2.307
-0.88525026 4207.71658 -7468.69692
-53027.748 -0.070244 0.12468314
0 -7468.6969 8837.95803
0.88525026 -4207.7166 7468.69692
53027.7482 0.07024402 -0.1246831
0 -7468.6969 17675.9161
(0 < x < 2.8) 0.087 1.398 2.656 -1.398x M= 2.656 M= -1.258
0.087
x
1.398
0.087 2.656
0 0 x
0
Diagramas 0.087
+
1.398
-1.258
+
2.656
NORMAL
CORTANTE
MOMENTO
53027.7482 0.0000
0.0000 4207.7166
0.0000 7468.6969
-53027.7482 0.0000
0.0000 -4207.7166
0.0000 7468.6969
0.0000
7468.6969
17675.9161
0.0000
-7468.6969
8837.9580
-53027.7482 0.0000 0.0000
0.0000 -4207.7166 7468.6969
0.0000 -7468.6969 8837.9580
53027.7482 0.0000 0.0000
0.0000 4207.7166 -7468.6969
0.0000 -7468.6969 17675.9161
BARRA 9 q9=k9 TD q22 q23 q24 q13 q14 q15 q22 q23 q24 q13 q14 q15
=
=
32.1472 7.480382595 8.098243561 -32.14716634 -7.480382595 18.45711465
7.480 18.457
32.147
X
Corte en la sección N= V= M=
(0 < x < 2.8) -32.147 -7.480 7.48x-8.098 M= -8.098 12.846 M=
7.480
32.147 8.098
x
0.0000 -1.0000
1.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 -1.0000 0.0000
1.0000 0.0000 0.0000
0.0000 0.0000 1.0000
0.88525026 -4207.71658 -7468.69692 -0.88525026 4207.71658 -7468.69692
53027.7482 0.07024402 0.12468314 -53027.748 -0.070244 0.12468314
0 7468.69692 17675.9161 0 -7468.6969 8837.95803
-0.8852503 4207.71658 7468.69692 0.88525026 -4207.7166 7468.69692
-53027.748 -0.070244 -0.1246831 53027.7482 0.07024402 -0.1246831
0 7468.69692 8837.95803 0 -7468.6969 17675.9161
0 0 x
0 -0.0003 -0.0006 0.0012
Diagramas -32.147
-7.480
12.846 +
-
-
-8.098
NORMAL
CORTANTE
MOMENTO
BARRA 10 q10 =k10 TD q25 q26 q27 q16 q17 q18 q25 q26 q27 q16 q17 q18
=
=
53027.7482 0.0000
0.0000 4207.7166
0.0000 7468.6969
-53027.7482 0.0000
0.0000 -4207.7166
0.0000 7468.6969
0.0000
7468.6969
17675.9161
0.0000
-7468.6969
8837.9580
-53027.7482 0.0000 0.0000
0.0000 -4207.7166 7468.6969
0.0000 -7468.6969 8837.9580
53027.7482 0.0000 0.0000
0.0000 4207.7166 -7468.6969
0.0000 -7468.6969 17675.9161
22.0602 -6.081350942 -16.23962015 -22.06022732 6.081350942 -5.349175697
6.081 5.349
22.060
X
Corte en la sección N= V= M=
(0 < x < 2.8) -22.060 6.081 16.239 -6.081x M= 16.239 M= -0.788
6.081
22.060 16.239
x
0.0000 -1.0000
1.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 -1.0000 0.0000
1.0000 0.0000 0.0000
0.0000 0.0000 1.0000
0.88525026 -4207.71658 -7468.69692 -0.88525026 4207.71658 -7468.69692
53027.7482 0.07024402 0.12468314 -53027.748 -0.070244 0.12468314
0 7468.69692 17675.9161 0 -7468.6969 8837.95803
-0.8852503 4207.71658 7468.69692 0.88525026 -4207.7166 7468.69692
-53027.748 -0.070244 -0.1246831 53027.7482 0.07024402 -0.1246831
0 7468.69692 8837.95803 0 -7468.6969 17675.9161
0 0 x
0 -0.0036 -0.0004 0.0012
Diagramas -22.060
6.081
-0.788 -
-
+
+
16.239
NORMAL
CORTANTE
MOMENTO
MATRIZ DE RIGIDEZ DE TODA LA ESTRUCTURA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 2 3 4 5 76610.9881 0.81500624 7468.69692 -72403.272 0 0.81500624 53697.1571 1740.33857 0 -669.40895 7468.69692 1740.33857 23709.522 0 -1740.4633 -72403.272 0 0 149014.26 0.81500624 0 -669.40895 -1740.4633 0.81500624 54366.566 0 1740.46326 3016.80298 7468.69692 -0.1246831 0 0 0 -72403.272 0 0 0 0 0 -669.40895 0 0 0 0 1740.46326 -4207.7166 -0.8150062 -7468.6969 0 0 -0.8150062 -53027.748 0.12468314 0 0 7468.69692 -0.1246831 8837.95803 0 0 0 0 0 -4207.7166 -0.8150062 0 0 0 -0.8150062 -53027.748 0 0 0 7468.69692 -0.1246831 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 7 0 0 1740.46326 0 3016.80298 0 7468.69692 -72403.272 -0.1246831 0 29743.128 0 0 76610.9881 -1740.4633 0.81500624 3016.80298 7468.69692 0 0 0 0 0 0 -7468.6969 0 0.12468314 0 8837.95803 0 0 -4207.7166 0 -0.8150062 0 7468.69692 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 72403.2715 0
6 0 1740.46326
2 3 0 0 669.408945 1740.46326
4 -72403.272 0
5 0 -669.40895
1 2
8 9 10 0 0 -4207.7166 0 0 -0.8150062 0 0 -7468.6969 0 0 0 -669.40895 1740.46326 0 -1740.4633 3016.80298 0 0.81500624 7468.69692 0 53697.1571 -1740.5879 0 -1740.5879 23709.522 0 0 0 80818.7047 0 0 1.63001248 0 0 0 0 0 -72403.272 0 0 0 0 0 0 -0.8150062 -7468.6969 0 -53027.748 0.12468314 0 -0.1246831 8837.95803 0 0 0 -4207.7166 0 0 -0.8150062 0 0 7468.69692 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 -0.8150062 -53027.748 0.12468314 0 0 0 0 0 0 1.63001248 106724.905 1740.46326 0 -669.40895 1740.46326 0 0 0 -0.8150062 -53027.748 -0.1246831 0 0 0 0 0 0
12 7468.69692 -0.1246831 8837.95803 0 0 0 0 0 0 0 1740.46326 41385.4381 0 -1740.4633 3016.80298 0 0 0 -7468.6969 0.12468314 8837.95803 0 0 0 0 0 0
13 0 0 0 -4207.7166 -0.8150062 -7468.6969 0 0 0 -72403.272 0 0 80818.7047 1.63001248 0 0 0 0 0 0 0 -4207.7166 -0.8150062 7468.69692 0 0 0
14 0 0 0 -0.8150062 -53027.748 0.12468314 0 0 0 0 -669.40895 -1740.4633 72404.9015 106724.905 -1740.4633 -72403.272 0 0 0 0 0 -0.8150062 -53027.748 -0.1246831 0 0 0
15 0 0 0 7468.69692 -0.1246831 8837.95803 0 0 0 0 1740.46326 3016.80298 0 -1071.0543 43125.9013 0 -669.40895 1740.46326 0 0 0 -7468.6969 0.12468314 8837.95803 0 0 0
10 11 12 72403.2715 0 0 0 669.408945 1740.46326
13 -72403.272 0
14 0 -669.40895
15 0 1740.46326
10 11
16 0 0 0 0 0 0 -4207.7166 -0.8150062 -7468.6969 0 0 0 0 1740.46326 6033.60596 8415.43318 -1738.8332 3016.80298 0 0 0 0 0 0 -4207.7166 -0.8150062 7468.69692
17 0 0 0 0 0 0 -0.8150062 -53027.748 0.12468314 0 0 0 -72403.272 0 0 72404.9015 106055.496 0 0 0 0 0 0 0 -0.8150062 -53027.748 -0.1246831
18 0 0 0 0 0 0 7468.69692 -0.1246831 8837.95803 0 0 0 0 -669.40895 -1740.4633 0 669.408945 33611.3688 0 0 0 0 0 0 -7468.6969 0.12468314 8837.95803
19 0 0 0 0 0 0 0 0 0 -4207.7166 -0.8150062 -7468.6969 0 0 0 0 0 0 4207.71659 0.81500624 -7468.6969 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 -0.8150062 -53027.748 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.12468314 0 0 0 0 0 0
21 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 0 -0.1246831 0 8837.95803 0 0 -4207.7166 0 -0.8150062 0 -7468.6969 0 0 0 0 0 0 -7468.6969 0 0.12468314 0 17675.9161 0 0 4207.71659 0 0.81500624 0 -7468.6969 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 -0.8150062 -53027.748 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.12468314 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.1246831 8837.95803 0 0 0 0 0 0 -7468.6969 0.12468314 17675.9161 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4207.7166 -0.8150062 -7468.6969 0 0 0 0 0 0 4207.71659 0.81500624 -7468.6969
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.8150062 -53027.748 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.12468314
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.1246831 8837.95803 0 0 0 0 0 0 -7468.6969 0.12468314 17675.9161
K1
0 -72403.272 0 0
1740.46326 6033.60596 0 0 -669.40895 -1740.4633 1740.46326 3016.80298
0 -1740.4633 3016.80298 72403.2715 0 0 0 669.408945 -1740.4633 0 -1740.4633 6033.60596
3 4 5 6
K2
4 72403.2715 0 0 -72403.272 0 0
5 6 0 0 669.408945 1740.46326 1740.46326 6033.60596 0 0 -669.40895 -1740.4633 1740.46326 3016.80298
7 8 9 -72403.272 0 0 0 -669.40895 1740.46326 0 -1740.4633 3016.80298 72403.2715 0 0 0 669.408945 -1740.4633 0 -1740.4633 6033.60596
4 5 6 7 8 9
K3
10 4207.71659 0.81500624 - 7468 .6969 -4207.7166 - 0.8150062 -7468.6969
11 0.81500624 53027.7481 0.1246831 4 -0.8150062 -5302 7.748 0.12468314
12 -7468.6969 0.12468314 176 75.916 1 7468.69692 -0.1246831 8837.95803
1 -4207.7166 -0.8150062 746 8.6969 2 4207.71659 0.8150062 4 7468.69692
2 -0.8150062 -53027.748 - 0.1246831 0.81500624 530 27.748 1 -0.1246831
3 -7468.6969 0.12468314 8837.9 5803 7468.69692 - 0.1246 831 17675.9161
10 11 12 1 2 3
K4
13 4207.71659 0.81500624 - 7468 .6969 -4207.7166 - 0.8150062 -7468.6969
14 0.81500624 53027.7481 0.1246831 4 -0.8150062 -5302 7.748 0.12468314
15 -7468.6969 0.12468314 176 75.916 1 7468.69692 -0.1246831 8837.95803
4 -4207.7166 -0.8150062 746 8.6969 2 4207.71659 0.8150062 4 7468.69692
5 -0.8150062 -53027.748 - 0.1246831 0.81500624 530 27.748 1 -0.1246831
6 -7468.6969 0.12468314 8837.9 5803 7468.69692 - 0.1246 831 17675.9161
13 14 15 4 5 6
K5
16 17 18 7 8 4207.71659 0.81500624 -7468.6969 -4207.7166 -0.8150062 0.81500624 53027.7481 0.12468314 -0.8150062 -53027.748 - 7468 .6969 0.1246831 4 176 75.916 1 746 8.6969 2 - 0.1246831 -4207.7166 -0.8150062 7468.69692 4207.71659 0.81500624 - 0.8150062 -5302 7.748 -0.1246831 0.8150062 4 530 27.748 1 -7468.6969 0.12468314 8837.95803 7468.69692 -0.1246831
9 -7468.6969 0.12468314 8837.9 5803 7468.69692 - 0.1246 831 17675.9161
16 17 18 7 8 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 2 3 4 5 6 72403.2715 0 0 -72403.272 0 0 0 669.408945 1740.46326 0 -669.40895 1740.46326 0 1740.46326 6033.60596 0 -1740.4633 3016.80298 -72403.272 0 0 72403.2715 0 0 0 -669.40895 -1740.4633 0 669.408945 -1740.4633 0 1740.46326 3016.80298 0 -1740.4633 6033.60596
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
0 -72403.272 0 0
1740.46326 6033.60596 0 0 -669.40895 -1740.4633 1740.46326 3016.80298
0 -1740.4633 3016.80298 72403.2715 0 0 0 669.408945 -1740.4633 0 -1740.4633 6033.60596
12 13 14 15
16 -72403.272 0 0 72403.2715 0 0
13 14 15 16 17 18
K6
13 14 15 72403.2715 0 0 0 669.408945 1740.46326 0 1740.46326 6033.60596 -72403.272 0 0 0 -669.40895 -1740.4633 0 1740.46326 3016.80298
K7
19 4207.71659 0.81500624 - 7468.6 969 -4207.7166 - 0.8150 062 -7468.6969
20 0.81500624 53027.7481 0.1246 8314 -0.8150062 -5 3027.748 0.12468314
21 -7468.6969 0.12468314 17675.9161 7468.69692 -0 .1246 831 8837.95803
10 11 12 -4207.7166 -0.8150062 -7468.6969 -0.8150062 -53027.748 0.12468314 7468.6 9692 - 0.1246 831 883 7.9580 3 4207.71659 0.81500624 7468.69692 0.8150 0624 53027.7481 - 0.1246831 7468.69692 -0.1246831 17675.9161
19 20 21 10 11 12
K8
22 4207.71659 0.81500624 - 7468.6 969 -4207.7166 - 0.8150 062 -7468.6969
23 0.81500624 53027.7481 0.1246 8314 -0.8150062 -5 3027.748 0.12468314
24 -7468.6969 0.12468314 17675.9161 7468.69692 -0 .1246 831 8837.95803
13 14 -4207.7166 -0.8150062 -0.8150062 -53027.748 7468.6 9692 - 0.1246 831 4207.71659 0.81500624 0.8150 0624 53027.7481 7468.69692 -0.1246831
15 -7468.6969 0.12468314 883 7.9580 3 7468.69692 - 0.1246831 17675.9161
22 23 24 13 14 15
K9
25 4207.71659 0.81500624 - 7468.6 969 -4207.7166 - 0.8150 062 -7468.6969
26 0.81500624 53027.7481 0.1246 8314 -0.8150062 -5 3027.748 0.12468314
27 -7468.6969 0.12468314 17675.9161 7468.69692 -0 .1246 831 8837.95803
16 17 18 -4207.7166 -0.8150062 -7468.6969 -0.8150062 -53027.748 0.12468314 7468.6 9692 - 0.1246 831 883 7.9580 3 4207.71659 0.81500624 7468.69692 0.8150 0624 53027.7481 - 0.1246831 7468.69692 -0.1246831 17675.9161
25 26 27 16 17 18
8
9
10
11
12
17 18 0 0 -669.40895 1740.46326 -1740.4633 3016.80298 0 0 669.408945 -1740.4633 -1740.4633 6033.60596
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
4207.71659 0.81500624 7468.69692 0.81500624 53027.7481 -0.1246831 7468.69692 -0.1246831 17675.9161 4207.71659 0.81500624 7468.69692 0.81500624 53027.7481 -0.1246831 7468.69692 -0.1246831 17675.9161
-4207.7166 -0.8150062 7468.69692 -0.8150062 -53027.748 -0.1246831 -7468.6969 0.12468314 8837.95803 4207.71659 0.81500624 7468.69692 0.81500624 53027.7481 -0.1246831 7468.69692 -0.1246831 17675.9161
-4207.7166 -0.8150062 7468.69692 -0.8150062 -53027.748 -0.1246831 -7468.6969 0.12468314 8837.95803 4207.71659 0.81500624 7468.69692 0.81500624 53027.7481 -0.1246831 7468.69692 -0.1246831 17675.9161
-4207.7166 -0.8150062 7468.69692
-0.8150062 -7468.6969 -53027.748 0.12468314 -0.1246831 8837.95803
2
3
1 2 3 4207.71659 0.81500624 7468.69692 0.81500624 53027.7481 -0.1246831 7468.69692 -0.1246831 17675.9161
4
5
6
7
8
9
4
5
6
7
8
9
10
11
12
10 11 12 -4207.7166 -0.8150062 7468.69692 -0.8150062 -53027.748 -0.1246831 -7468.6969 0.12468314 8837.95803
72403.2715 0 0 -72403.272 0 0 0 669.408945 1740.46326 0 -669.40895 1740.46326 0 1740.46326 6033.60596 0 -1740.4633 3016.80298 -72403.272 0 0 72403.2715 0 0 0 -669.40895 -1740.4633 0 669.408945 -1740.4633 0 1740.46326 3016.80298 0 -1740.4633 6033.60596 -4207.7166 -0.8150062 7468.69692
-0.8150062 -7468.6969 -53027.748 0.12468314 -0.1246831 8837.95803
-4207.7166 -0.8150062 7468.69692 -0.8150062 -53027.748 -0.1246831 -7468.6969 0.12468314 8837.95803 4207.71659 0.81500624 -7468.6969 0.81500624 53027.7481 0.12468314 -7468.6969 0.12468314 17675.9161
-4207.7166 -0.8150062 7468.69692
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
7
K5
-0.8150062 -7468.6969 -53027.748 0.12468314 -0.1246831 8837.95803
4207.71659 0.81500624 -7468.6969 0.81500624 53027.7481 0.12468314 -7468.6969 0.12468314 17675.9161
13
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-4207.7166 -0.8150062 7468.69692 16
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-0.8150062 -7468.6969 -53027.748 0.12468314 -0.1246831 8837.95803 17 18 17
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19
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4207.71659 0.81500624 -7468.6969 0.81500624 53027.7481 0.12468314 -7468.6969 0.12468314 17675.9161 25 26 27 25
26
27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
-4207.7166 -0.8150062 7468.69692 -0.8150062 -53027.748 -0.1246831 -7468.6969 0.12468314 8837.95803 -4207.7166 -0.8150062 7468.69692 -0.8150062 -53027.748 -0.1246831 -7468.6969 0.12468314 8837.95803 4207.71659 0.81500624 -7468.6969 0.81500624 53027.7481 0.12468314 -7468.6969 0.12468314 17675.9161
-4207.7166 -0.8150062 7468.69692
-0.8150062 -7468.6969 -53027.748 0.12468314 -0.1246831 8837.95803
4207.71659 0.81500624 -7468.6969 0.81500624 53027.7481 0.12468314 -7468.6969 0.12468314 17675.9161 -4207.7166 -0.8150062 7468.69692
-0.8150062 -7468.6969 -53027.748 0.12468314 -0.1246831 8837.95803
4207.71659 0.81500624 -7468.6969 0.81500624 53027.7481 0.12468314 -7468.6969 0.12468314 17675.9161
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4207.71659 0.81500624 7468.69692 0.81500624 53027.7481 -0.1246831 7468.69692 -0.1246831 17675.9161
72403.2715 0 0 -72403.272 0 0 0 669.408945 1740.46326 0 -669.40895 1740.46326 0 1740.46326 6033.60596 0 -1740.4633 3016.80298 -72403.272 0 0 72403.2715 0 0 0 -669.40895 -1740.4633 0 669.408945 -1740.4633 0 1740.46326 3016.80298 0 -1740.4633 6033.60596
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