Matriz de Rigidez Muro Inclinado Vargas

ANALISIS ESTRUCTURAL POR EL METODO DE RIGIDEZ PARA PÓRTICOS

CONDICIONES GENERALES:

ALTURA PISO TECHO: VIGAS:

1º NIVEL: 2.85 m PERALTE(h):

2º NIVEL: 2.6 m L= 5.32 m

ESPESOR DE MURO(t): h= 0.532

Zona Sísmica 3 h= 0.443

h= 0.5 m

b= 0.3 m

t> 0.14

t= 0.15

ESPESOR DE ALIGERADO(e):

Lmax: 5.05 m

e= 0.202

e= 0.20 m.

aprox.

METRADO DE CARGASEJE 2-2

TRAMO A-BPRIMER PISO SEGUNDO PISO

CARGAS MUERTAS: CARGAS MUERTAS:

ALIGERADO(e=0.20m): ALIGERADO(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: 400 kg/m2 carga total: 400 kg/m2

carga repartida: 1730 kg/m carga repartida: 1730 kg/m

PESO DEL MURO(t=0.15m): PESO DEL MURO(t=0.15m):


h= 2.60 h= 0.00

t= 0.15 t= 0


PESO DE LA VIGA: PESO DE LA VIGA:

p. concreto armado: 2400 kg/m3 p. concreto armado: 2400 kg/m3

h= 0.5 m h= 0.5 m

b= 0.3 m b= 0.3 m


2792 kg/m 2090 kg/mTOTAL CARGA MUERTA(CM):

TOTAL CARGA MUERTA(CM):

𝑡≥ℎ/20

𝑒=𝐿𝑚𝑎𝑥/25

ℎ=𝐿/10 𝑦 ℎ=𝐿/12

𝑡≥ℎ/20

𝑒=𝐿𝑚𝑎𝑥/25

ℎ=𝐿/10 𝑦 ℎ=𝐿/12

1 2 3

A

B

C

A

B

C

1 2 3

2.8 Tn/m 2.1 Tn/m

CARGAS VIVAS: CARGAS VIVAS:


carga viva 200 kg/m2 carga viva 200 kg/m2

tabiquería móvil 100 kg/m2 tabiquería móvil 0 kg/m2


carga repartida: 1297.5 kg/m carga repartida: 865 kg/m

1297.5 kg/m 865 kg/m

1.3 Tn/m 0.9 Tn/m

CARGA ULTIMA 6.11 Tn/m CARGA ULTIMA 4.40 Tn/m

TRAMO B-CPRIMER PISO SEGUNDO PISO

CARGAS MUERTAS: CARGAS MUERTAS:



piso terminado: 100 kg/m2 piso terminado: 100 kg/m2



PESO DE LA VIGA: PESO DE LA VIGA:

p. concreto armado: 2400 kg/m3 p. concreto armado: 2400 kg/m3

h= 0.5 m h= 0.5 m

b= 0.3 m b= 0.3 m


2090 kg/m 2090 kg/m

2.1 Tn/m 2.1 Tn/m

CARGAS VIVAS: CARGAS VIVAS:


carga viva 200 kg/m2 carga viva 200 kg/m2

tabiquería móvil 0 kg/m2 tabiquería móvil 0 kg/m2



865 kg/m 865 kg/m

0.9 Tn/m 0.9 Tn/m

TOTAL CARGA VIVA(CV):






4.40Tn/m

6.11Tn/m

4.40Tn/m

4.40Tn/m

11.44Tn

9.91Tn-m 5.29Tn-m

15.89Tn

19.25Tn 7.81Tn

4.62Tn-m

7.81Tn

4.62Tn-m9.15Tn-m

23.7Tn

13.77Tn-m

CARGA ULTIMA 4.40 Tn/m CARGA ULTIMA 4.40 Tn/m

DATOS DE LA ESTRUCTURAVIGAS COLUMNA

f'c 280 Kg/cm2 f'c 280 Kg/cm2E 2509980.08 Tn/m2 E 2509980.079602 Tn/m2A 0.15 m2 A 0.075 m2I 0.003125 m4 I 0.00625 m4

BARRA 1

1. Matriz en cordenadas locales de la barra 1

Longitud = 5.2 mE = 2509980.08 Tn/m2A = 0.15 m2I = 0.003125 m4

72403.2715 0 0 -72403.2715 0 00 669.4089 1740.4633 0 -669.4089 1740.4633

K1 = 0 1740.4633 6033.6060 0 -1740.4633 3016.8030-72403.2715 0 0 72403.2715 0 0

0 -669.4089 -1740.4633 0 669.4089 -1740.46330 1740.4633 3016.8030 0 -1740.4633 6033.6060

9

7

84

5

6

1

2

3

10

11

12

13

14

15 16

17

18

19

20

2122

23

24 25

26

27

8

1 2

76

3 4 5

9 10

2. Matriz de transformación.

010

1 0 0 0 0 00 1 0 0 0 0

T = 0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 0

= 0 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

3. Determinamos matriz de rigidez en coordenadas globales

72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.00000.0000 669.4089 1740.4633 0.0000 -669.4089 1740.46330.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030

-72403.2715 0.0000 0.0000 72403.2715 0.0000 0.00000.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.46330.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060

1 2 3 4 5 672403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 1

0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 20.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 3

K = -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 40.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 50.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 6

BARRA 2



72403.2715 0 0 -72403.2715 0 00 669.4089 1740.4633 0 -669.4089 1740.4633

K2 = 0 1740.4633 6033.6060 0 -1740.4633 3016.8030-72403.2715 0 0 72403.2715 0 0

0 -669.4089 -1740.4633 0 669.4089 -1740.46330 1740.4633 3016.8030 0 -1740.4633 6033.6060

2. Matriz de transformación

010

1 0 0 0 0 00 1 0 0 0 0

T = 0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 0

= 0 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

TT

TT

𝜽 = x = y =

𝜽 = x = y =


72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.00000.0000 669.4089 1740.4633 0.0000 -669.4089 1740.46330.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030

-72403.2715 0.0000 0.0000 72403.2715 0.0000 0.00000.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.46330.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060

4 5 6 7 8 972403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 4

0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 50.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 6

K = -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 70.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 80.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 9

BARRA 3



53027.7482 0 0 -53027.7482 0 00 4207.7166 7468.6969 0 -4207.7166 7468.6969

K3 = 0 7468.6969 17675.9161 0 -7468.6969 8837.9580-53027.7482 0 0 53027.7482 0 0

0 -4207.7166 -7468.6969 0 4207.7166 -7468.69690 7468.6969 8837.9580 0 -7468.6969 17675.9161


1.570779631.6694E-05

1

1.66940949E-05 0.999999999861 0 0 0 0-0.999999999861 1.66940949E-05 0 0 0 0

T = 0 0 1 0 0 00 0 0 1.66940949E-05 0.999999999861 00 0 0 -0.999999999861 1.66940949E-05 00 0 0 0 0 1

1.66940949E-05 -0.999999999861 0 0 0 00.999999999861 1.66940949E-05 0 0 0 0

0 0 1 0 0 0

= 0 0 0 1.66940949E-05 -0.999999999861 00 0 0 0.999999999861 1.66940949E-05 00 0 0 0 0 1


0.8853 -4207.7166 -7468.6969 -0.8853 4207.7166 -7468.696953027.7482 0.0702 0.1247 -53027.7482 -0.0702 0.1247

0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580-0.8853 4207.7166 7468.6969 0.8853 -4207.7166 7468.6969

-53027.7482 -0.0702 -0.1247 53027.7482 0.0702 -0.12470.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161

10 11 12 1 2 34207.7166 0.8150 -7468.6969 -4207.7166 -0.8150 -7468.6969 10

0.8150 53027.7481 0.1247 -0.8150 -53027.7481 0.1247 11-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580 12

K = -4207.7166 -0.8150 7468.6969 4207.7166 0.8150 7468.6969 1-0.8150 -53027.7481 -0.1247 0.8150 53027.7481 -0.1247 2

-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161 3

TT

𝜽 = x = y =

BARRA 4



53027.7482 0 0 -53027.7482 0 00 4207.7166 7468.6969 0 -4207.7166 7468.6969

K4 = 0 7468.6969 17675.9161 0 -7468.6969 8837.9580-53027.7482 0 0 53027.7482 0 0

0 -4207.7166 -7468.6969 0 4207.7166 -7468.69690 7468.6969 8837.9580 0 -7468.6969 17675.9161


1.570779631.6694E-05

1

1.66940949E-05 0.999999999861 0 0 0 0-0.999999999861 1.66940949E-05 0 0 0 0

T = 0 0 1 0 0 00 0 0 1.66940949E-05 0.999999999861 00 0 0 -0.999999999861 1.66940949E-05 00 0 0 0 0 1

1.66940949E-05 -0.999999999861 0 0 0 00.999999999861 1.66940949E-05 0 0 0 0

0 0 1 0 0 0

= 0 0 0 1.66940949E-05 -0.999999999861 00 0 0 0.999999999861 1.66940949E-05 00 0 0 0 0 1

TT

𝜽 = x = y =


0.8853 -4207.7166 -7468.6969 -0.8853 4207.7166 -7468.696953027.7482 0.0702 0.1247 -53027.7482 -0.0702 0.1247

0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580-0.8853 4207.7166 7468.6969 0.8853 -4207.7166 7468.6969

-53027.7482 -0.0702 -0.1247 53027.7482 0.0702 -0.12470.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161

13 14 15 4 5 64207.7166 0.8150 -7468.6969 -4207.7166 -0.8150 -7468.6969 13

0.8150 53027.7481 0.1247 -0.8150 -53027.7481 0.1247 14-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580 15

K = -4207.7166 -0.8150 7468.6969 4207.7166 0.8150 7468.6969 4-0.8150 -53027.7481 -0.1247 0.8150 53027.7481 -0.1247 5

-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161 6

BARRA 5



53027.7482 0 0 -53027.7482 0 00 4207.7166 7468.6969 0 -4207.7166 7468.6969

K5 = 0 7468.6969 17675.9161 0 -7468.6969 8837.9580-53027.7482 0 0 53027.7482 0 0

0 -4207.7166 -7468.6969 0 4207.7166 -7468.69690 7468.6969 8837.9580 0 -7468.6969 17675.9161


1.570779631.6694E-05

1

1.66940949E-05 0.999999999861 0 0 0 0-0.999999999861 1.66940949E-05 0 0 0 0

T = 0 0 1 0 0 00 0 0 1.66940949E-05 0.999999999861 00 0 0 -0.999999999861 1.66940949E-05 00 0 0 0 0 1

1.66940949E-05 -0.999999999861 0 0 0 00.999999999861 1.66940949E-05 0 0 0 0

0 0 1 0 0 0

= 0 0 0 1.66940949E-05 -0.999999999861 00 0 0 0.999999999861 1.66940949E-05 00 0 0 0 0 1


0.8853 -4207.7166 -7468.6969 -0.8853 4207.7166 -7468.696953027.7482 0.0702 0.1247 -53027.7482 -0.0702 0.1247

0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580-0.8853 4207.7166 7468.6969 0.8853 -4207.7166 7468.6969

-53027.7482 -0.0702 -0.1247 53027.7482 0.0702 -0.12470.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161

16 17 18 7 8 94207.7166 0.8150 -7468.6969 -4207.7166 -0.8150 -7468.6969 16

0.8150 53027.7481 0.1247 -0.8150 -53027.7481 0.1247 17-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580 18

K = -4207.7166 -0.8150 7468.6969 4207.7166 0.8150 7468.6969 7-0.8150 -53027.7481 -0.1247 0.8150 53027.7481 -0.1247 8

-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161 9

TT

𝜽 = x = y =

BARRA 6



72403.2715 0 0 -72403.2715 0 00 669.4089 1740.4633 0 -669.4089 1740.4633

K6 = 0 1740.4633 6033.6060 0 -1740.4633 3016.8030-72403.2715 0 0 72403.2715 0 0

0 -669.4089 -1740.4633 0 669.4089 -1740.46330 1740.4633 3016.8030 0 -1740.4633 6033.6060


010

1 0 0 0 0 00 1 0 0 0 0

T = 0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 0

= 0 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

TT

𝜽 = x = y =


72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.00000.0000 669.4089 1740.4633 0.0000 -669.4089 1740.46330.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030

-72403.2715 0.0000 0.0000 72403.2715 0.0000 0.00000.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.46330.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060

10 11 12 13 14 1572403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 10

0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 110.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 12

K = -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 130.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 140.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 15

BARRA 7



72403.2715 0 0 -72403.2715 0 00 669.4089 1740.4633 0 -669.4089 1740.4633

K7 = 0 1740.4633 6033.6060 0 -1740.4633 3016.8030-72403.2715 0 0 72403.2715 0 0

0 -669.4089 -1740.4633 0 669.4089 -1740.46330 1740.4633 3016.8030 0 -1740.4633 6033.6060


010

1 0 0 0 0 00 1 0 0 0 0

T = 0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 0

= 0 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1


72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.00000.0000 669.4089 1740.4633 0.0000 -669.4089 1740.46330.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030

-72403.2715 0.0000 0.0000 72403.2715 0.0000 0.00000.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.46330.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060

13 14 15 16 17 1872403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 13

0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 140.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 15

K = -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 160.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 170.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 18

TT

𝜽 = x = y =

BARRA 8



53027.7482 0 0 -53027.7482 0 00 4207.7166 7468.6969 0 -4207.7166 7468.6969

K8 = 0 7468.6969 17675.9161 0 -7468.6969 8837.9580-53027.7482 0 0 53027.7482 0 0

0 -4207.7166 -7468.6969 0 4207.7166 -7468.69690 7468.6969 8837.9580 0 -7468.6969 17675.9161


1.570779631.6694E-05

1

1.66940949E-05 0.999999999861 0 0 0 0-0.999999999861 1.66940949E-05 0 0 0 0

T = 0 0 1 0 0 00 0 0 1.66940949E-05 0.999999999861 00 0 0 -0.999999999861 1.66940949E-05 00 0 0 0 0 1

1.66940949E-05 -0.999999999861 0 0 0 00.999999999861 1.66940949E-05 0 0 0 0

0 0 1 0 0 0

= 0 0 0 1.66940949E-05 -0.999999999861 00 0 0 0.999999999861 1.66940949E-05 00 0 0 0 0 1

TT

𝜽 = x = y =


0.8853 -4207.7166 -7468.6969 -0.8853 4207.7166 -7468.696953027.7482 0.0702 0.1247 -53027.7482 -0.0702 0.1247

0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580-0.8853 4207.7166 7468.6969 0.8853 -4207.7166 7468.6969

-53027.7482 -0.0702 -0.1247 53027.7482 0.0702 -0.12470.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161

19 20 21 10 11 124207.7166 0.8150 -7468.6969 -4207.7166 -0.8150 -7468.6969 19

0.8150 53027.7481 0.1247 -0.8150 -53027.7481 0.1247 20-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580 21

K = -4207.7166 -0.8150 7468.6969 4207.7166 0.8150 7468.6969 10-0.8150 -53027.7481 -0.1247 0.8150 53027.7481 -0.1247 11

-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161 12

BARRA 9



53027.7482 0 0 -53027.7482 0 00 4207.7166 7468.6969 0 -4207.7166 7468.6969

K9 = 0 7468.6969 17675.9161 0 -7468.6969 8837.9580-53027.7482 0 0 53027.7482 0 0

0 -4207.7166 -7468.6969 0 4207.7166 -7468.69690 7468.6969 8837.9580 0 -7468.6969 17675.9161


1.570779631.6694E-05

1

1.66940949E-05 0.999999999861 0 0 0 0-0.999999999861 1.66940949E-05 0 0 0 0

T = 0 0 1 0 0 00 0 0 1.66940949E-05 0.999999999861 00 0 0 -0.999999999861 1.66940949E-05 00 0 0 0 0 1

1.66940949E-05 -0.999999999861 0 0 0 00.999999999861 1.66940949E-05 0 0 0 0

0 0 1 0 0 0

= 0 0 0 1.66940949E-05 -0.999999999861 00 0 0 0.999999999861 1.66940949E-05 00 0 0 0 0 1


0.8853 -4207.7166 -7468.6969 -0.8853 4207.7166 -7468.696953027.7482 0.0702 0.1247 -53027.7482 -0.0702 0.1247

0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580-0.8853 4207.7166 7468.6969 0.8853 -4207.7166 7468.6969

-53027.7482 -0.0702 -0.1247 53027.7482 0.0702 -0.12470.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161

22 23 24 13 14 154207.7166 0.8150 -7468.6969 -4207.7166 -0.8150 -7468.6969 22

0.8150 53027.7481 0.1247 -0.8150 -53027.7481 0.1247 23-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580 24

K = -4207.7166 -0.8150 7468.6969 4207.7166 0.8150 7468.6969 13-0.8150 -53027.7481 -0.1247 0.8150 53027.7481 -0.1247 14

-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161 15

BARRA 10

TT

𝜽 = x = y =



53027.7482 0 0 -53027.7482 0 00 4207.7166 7468.6969 0 -4207.7166 7468.6969

K10 = 0 7468.6969 17675.9161 0 -7468.6969 8837.9580-53027.7482 0 0 53027.7482 0 0

0 -4207.7166 -7468.6969 0 4207.7166 -7468.69690 7468.6969 8837.9580 0 -7468.6969 17675.9161


1.570779631.6694E-05

1

1.66940949E-05 0.999999999861 0 0 0 0-0.999999999861 1.66940949E-05 0 0 0 0

T = 0 0 1 0 0 00 0 0 1.66940949E-05 0.999999999861 00 0 0 -0.999999999861 1.66940949E-05 00 0 0 0 0 1

1.66940949E-05 -0.999999999861 0 0 0 00.999999999861 1.66940949E-05 0 0 0 0

0 0 1 0 0 0

= 0 0 0 1.66940949E-05 -0.999999999861 00 0 0 0.999999999861 1.66940949E-05 00 0 0 0 0 1

TT

𝜽 = x = y =


0.8853 -4207.7166 -7468.6969 -0.8853 4207.7166 -7468.696953027.7482 0.0702 0.1247 -53027.7482 -0.0702 0.1247

0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580-0.8853 4207.7166 7468.6969 0.8853 -4207.7166 7468.6969

-53027.7482 -0.0702 -0.1247 53027.7482 0.0702 -0.12470.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161

25 26 27 16 17 184207.7166 0.8150 -7468.6969 -4207.7166 -0.8150 -7468.6969 25

0.8150 53027.7481 0.1247 -0.8150 -53027.7481 0.1247 26-7468.6969 0.1247 17675.9161 7468.6969 -0.1247 8837.9580 27

K = -4207.7166 -0.8150 7468.6969 4207.7166 0.8150 7468.6969 16-0.8150 -53027.7481 -0.1247 0.8150 53027.7481 -0.1247 17

-7468.6969 0.1247 8837.9580 7468.6969 -0.1247 17675.9161 18

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 26 271 76610.98811751 0.815006239958 7468.696922989 -72403.27152699 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 0.815006239958 53697.15709234 1740.338574725 0 -669.4089453309 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03 7468.696922989 1740.338574725 23709.52201412 0 -1740.46325786 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 -72403.27152699 0 0 149014.2596445 0.815006239958 7468.69692 -72403.27153 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 0 0 0 0 0 05 0 -669.4089453309 -1740.46325786 0.815006239958 54366.56603767 -0.12468314 0 -669.408945 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 0 0 0 0 0 06 0 1740.46325786 3016.802980291 7468.696922989 -0.124683135197 29743.128 0 -1740.46326 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 0 0 0 0 0 07 0 0 0 -72403.27152699 0 0 76610.988118 0.81500624 7468.69692 0 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 0 0 08 0 0 0 0 -669.4089453309 -1740.46326 0.81500624 53697.1571 -1740.58794 0 0 0 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 0 0 09 0 0 0 0 1740.46325786 3016.80298 7468.696923 -1740.58794 23709.522 0 0 0 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 0 0 0

10 -4207.716590524 -0.815006239958 -7468.696922989 0 0 0 0 0 0 80818.7047 1.63001248 0 -72403.2715 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 011 -0.815006239958 -53027.748147 0.124683135197 0 0 0 0 0 0 1.63001248 106724.905 1740.46326 0 -669.408945 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 012 7468.696922989 -0.124683135197 8837.958026768 0 0 0 0 0 0 0 1740.46326 41385.4381 0 -1740.46326 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0

K = 13 0 0 0 -4207.716590524 -0.815006239958 -7468.69692 0 0 0 -72403.2715 0 0 80818.7047 72404.9015 0 0 -72403.2715 0 0 0 0 -4207.71659 -0.81500624 7468.6969229889 0 0 014 0 0 0 -0.815006239958 -53027.748147 0.12468314 0 0 0 0 -669.408945 -1740.46326 1.63001248 106724.905 -1071.05431 1740.46326 0 -669.408945 0 0 0 -0.81500624 -53027.74815 -0.12468313519734 0 0 015 0 0 0 7468.696922989 -0.124683135197 8837.95803 0 0 0 0 1740.46326 3016.80298 0 -1740.46326 43125.9013 6033.60596 0 -1740.46326 0 0 0 -7468.69692 0.124683135 8837.9580267684 0 0 016 0 0 0 0 0 0 -4207.716591 -0.81500624 -7468.69692 0 0 0 0 -72403.2715 0 8415.43318 72404.9015 0 0 0 0 0 0 0 -4207.7165905239 -0.81500624 7468.696922988917 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 -669.408945 -1738.83325 106055.496 669.408945 0 0 0 0 0 0 -0.81500623995806 -53027.74815 -0.1246831351973418 0 0 0 0 0 0 7468.696923 -0.12468314 8837.95803 0 0 0 0 0 1740.46326 3016.80298 0 33611.3688 0 0 0 0 0 0 -7468.6969229889 0.124683135 8837.958026768419 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 4207.71659 0.81500624 -7468.69692 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.12468314 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -7468.69692 0.12468314 17675.9161 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 4207.71659 0.81500624 -7468.6969229889 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.81500624 53027.74815 0.124683135197341 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -7468.69692 0.124683135 17675.9160535368 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 4207.7165905239 0.81500624 -7468.696922988926 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.815006239958063 53027.74815 0.12468313519734127 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -7468.6969229889 0.124683135 17675.9160535368

CALCULO DE DESPLAZAMIENTOS Q=KD

Q1 0 76610.98811751 0.815006239958 7468.696922989 -72403.27152699 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 D1Q2 -11.44 0.815006239958 53697.15709234 1740.338574725 0 -669.4089453309 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 D2Q3 -9.91 7468.696922989 1740.338574725 23709.52201412 0 -1740.46325786 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 D3Q4 0 -72403.27152699 0 0 149014.2596445 0.815006239958 7468.69692 -72403.27153 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 D4Q5 -19.25 0 -669.4089453309 -1740.46325786 0.815006239958 54366.56603767 -0.12468314 0 -669.408945 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 D5Q6 5.29 0 1740.46325786 3016.802980291 7468.696922989 -0.124683135197 29743.128 0 -1740.46326 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 D6Q7 0 0 0 0 -72403.27152699 0 0 76610.988118 0.81500624 7468.69692 0 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 D7Q8 -7.81 0 0 0 0 -669.4089453309 -1740.46326 0.81500624 53697.1571 -1740.58794 0 0 0 0 0 0 -0.81500624 -53027.7481 -0.12468314 D8Q9 4.62 = 0 0 0 0 1740.46325786 3016.80298 7468.696923 -1740.58794 23709.522 0 0 0 0 0 0 -7468.69692 0.12468314 8837.95803 X D9

Q10 0 -4207.716590524 -0.815006239958 -7468.696922989 0 0 0 0 0 0 80818.7047 1.63001248 0 -72403.2715 0 0 0 0 0 D10Q11 15.89 -0.815006239958 -53027.748147 0.124683135197 0 0 0 0 0 0 1.63001248 106724.905 1740.46326 0 -669.408945 1740.46326 0 0 0 D11Q12 -13.77 7468.696922989 -0.124683135197 8837.958026768 0 0 0 0 0 0 0 1740.46326 41385.4381 0 -1740.46326 3016.80298 0 0 0 D12Q13 0 0 0 0 -4207.716590524 -0.815006239958 -7468.69692 0 0 0 -72403.2715 0 0 80818.7047 72404.9015 0 0 -72403.2715 0 D13Q14 -23.7 0 0 0 -0.815006239958 -53027.748147 0.12468314 0 0 0 0 -669.408945 -1740.46326 1.63001248 106724.905 -1071.05431 1740.46326 0 -669.408945 D14Q15 9.15 0 0 0 7468.696922989 -0.124683135197 8837.95803 0 0 0 0 1740.46326 3016.80298 0 -1740.46326 43125.9013 6033.60596 0 -1740.46326 D15Q16 0 0 0 0 0 0 0 -4207.716591 -0.81500624 -7468.69692 0 0 0 0 -72403.2715 0 8415.43318 72404.9015 0 D16Q17 -7.81 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 -669.408945 -1738.83325 106055.496 669.408945 D17Q18 4.62 0 0 0 0 0 0 7468.696923 -0.12468314 8837.95803 0 0 0 0 0 1740.46326 3016.80298 0 33611.3688 D18

0.000829923 2.28715428236E-05 -9.5118980139E-05 0.000823055 0.000117742369 -8.2716909574E-05 0.000824649 -0.00014065442048 -6.950706174E-05 0.00033411559 1.58451518619E-05 -0.00011689921253 0.00033453087422 0.00012305052091 -0.00011047195285 0.00043499499407 -0.00013891355879 -0.000165470294641.590115E-05 3.74461103422E-05 -4.7818640925E-06 1.586567E-05 4.80441558683E-06 -4.0680908285E-06 1.585652E-05 -4.5352158423E-06 -1.7620908616E-06 3.997426414E-06 1.87098480509E-05 -2.2704657489E-06 4.03122079352E-06 4.60956739834E-06 -2.3438956164E-06 7.24499855531E-06 -4.4616167053E-06 -3.0008293103E-06-8.51829E-05 -5.8760561641E-06 6.4015998469E-05 -8.30488E-05 -2.3036919626E-05 8.70235251512E-06 -8.29635E-05 2.89171626111E-05 1.33070505563E-05 -8.469037853E-06 -3.2740078423E-06 -1.0833847682E-07 -1.1106511193E-05 -2.5574919804E-05 1.19675193494E-05 -3.2186816546E-05 2.88497851161E-05 1.44719508489E-050.000819281 2.28204662685E-05 -9.2416934944E-05 0.000826113 0.00011982078332 -8.398029055E-05 0.000827676 -0.00014268168338 -7.0366267501E-05 0.0003327663305 1.58142600164E-05 -0.00011544403256 0.00033336454388 0.00012509082864 -0.00011080821024 0.00043528725393 -0.00014092293877 -0.00016585379944-1.0214E-05 3.5175924653E-07 3.68567305762E-06 -1.01396E-05 2.77828230004E-05 1.82894544214E-06 -1.01509E-05 9.58202407593E-06 -2.4399546356E-06 -2.596640449E-06 1.86346945531E-07 1.32740896916E-06 -2.6850521861E-06 9.29964047221E-06 1.53726033693E-06 -9.3955745322E-06 9.37230329163E-06 2.97537630368E-06

-3.22704E-05 -3.6670660974E-06 2.98206686321E-06 -3.35659E-05 -1.5035935748E-05 4.54905774587E-05 -3.28969E-05 1.87046707437E-05 3.0909885293E-06 4.03319135E-06 -1.9331680762E-06 4.91217035847E-06 6.06974771807E-06 -1.5602517878E-05 -4.1174332547E-06 -5.9173022922E-06 1.75356367159E-05 5.6240605647E-060.000812312 2.27417096866E-05 -9.1343562252E-05 0.000819115 0.00012269616923 -8.3209677323E-05 0.000834397 -0.00014547819621 -7.2950418875E-05 0.0003301005628 1.57586627259E-05 -0.00011436817941 0.00033068322344 0.00012795499061 -0.00010977361463 0.00043467169184 -0.00014373140838 -0.00016650121818-5.72759E-06 -8.2909244294E-08 1.10084667535E-06 -5.76666E-06 5.12284999287E-06 2.24331735549E-06 -5.74649E-06 3.26764532164E-05 4.20559839705E-06 -1.417114867E-06 -3.8935206545E-08 9.48844813176E-07 -1.3625241559E-06 4.94256493318E-06 8.12161922613E-07 2.12910577012E-06 1.39544358883E-05 3.37637496679E-08-0.00013962 -2.1038780489E-06 1.85075931633E-05 -0.000140248 1.82223104131E-05 4.57026970632E-06 -0.000142846 -1.6111453871E-05 6.38192931953E-05 -5.937886144E-05 -1.6043402029E-06 2.06016513215E-05 -6.0075623322E-05 2.03982394543E-05 2.15104670146E-05 -4.4351079724E-05 -1.8791243005E-05 1.68548191133E-050.000409295 7.49373096193E-06 -2.3707789782E-05 0.0004097 1.73724500247E-05 -2.3208925442E-05 0.000411558 -2.4886236652E-05 -1.5366050287E-05 0.0002465884304 5.8318430073E-06 -6.4029832111E-05 0.00024009731536 1.83072082097E-05 -5.8258077624E-05 0.00025724573168 -2.4150983185E-05 -8.9582005734E-05

1.238275E-05 1.8743364654E-05 -2.6910164319E-06 1.237328E-05 3.2663525934E-06 -2.3647916058E-06 1.238892E-05 -3.1522830639E-06 -1.2162056639E-06 3.936567971E-06 1.87729433305E-05 -2.1591300416E-06 3.95229303183E-06 3.20054780219E-06 -2.1361008225E-06 6.20738196936E-06 -3.1156721719E-06 -2.4179433971E-06-0.000121069 -3.2846886547E-06 2.41013603668E-06 -0.000120183 -1.3361053568E-05 1.25759515992E-05 -0.000120418 1.66517461238E-05 8.86564847129E-06 -5.392207724E-05 -2.6667587334E-06 4.40007675832E-05 -5.3402178076E-05 -1.3656337225E-05 1.41890144437E-05 -6.5120492018E-05 1.6325940914E-05 2.45642944796E-050.000417423 7.64168750406E-06 -2.7539028123E-05 0.000418054 1.49254245789E-05 -2.1997096514E-05 0.000420027 -2.2587576551E-05 -1.4485328019E-05 0.0002428944064 5.92677657071E-06 -6.4667269322E-05 0.00024970829168 1.59221523649E-05 -5.9843857311E-05 0.00026518593095 -2.1861084489E-05 -9.1870678418E-05-1.23804E-05 1.30401380404E-08 2.33048405881E-06 -1.23937E-05 1.08568319531E-05 1.76145393046E-06 -1.24936E-05 7.98879317739E-06 -8.7539719389E-07 -4.364191261E-06 1.03218674041E-08 2.05650552258E-06 -4.3923526275E-06 1.09245724284E-05 1.90774268204E-06 -1.0147517572E-05 7.92346440815E-06 3.16493342581E-06-0.00015852 -5.1527321166E-06 1.77799917088E-05 -0.000159915 -3.6335861715E-05 9.14753379883E-06 -0.000160957 4.14965210856E-05 1.16693808884E-05 -6.742798873E-05 -3.8767646459E-06 2.00172547551E-05 -6.7886880799E-05 -3.7914151378E-05 4.61191505795E-05 -9.8715146834E-05 4.17947472006E-05 3.34981491672E-050.000175888 8.74472814924E-06 -1.2306648858E-05 0.000178421 0.00013021442752 -2.7595077058E-05 0.000182174 -0.00013896787504 -5.3676133617E-06 7.120214788E-05 5.90337082863E-06 -2.2111244479E-05 7.05257667572E-05 0.00013537544474 -2.136746304E-05 0.00017569561489 -0.00014128387793 -3.466610989E-05-1.87593E-08 1.01247942283E-07 3.61593340691E-07 3.97086E-09 4.73215384941E-06 6.04553023781E-07 8.804145E-08 1.40246537535E-05 2.09219080699E-06 4.185779804E-07 7.44913428357E-08 1.05142127881E-07 4.31020188635E-07 4.73009976247E-06 2.30686455867E-07 3.92879581795E-06 1.40533858918E-05 -7.4338212108E-07-0.000151368 -5.0182408036E-06 1.56146422671E-05 -0.000152869 -4.1861369126E-05 1.92912182777E-05 -0.000155865 4.6887245801E-05 -6.9334391004E-07 -6.063663381E-05 -3.4089515988E-06 2.09444260744E-05 -6.0498423513E-05 -4.3983572252E-05 1.82661437062E-05 -9.5583338596E-05 4.73960966479E-05 6.3694623436E-05

D1 -0.0030 m.D2 -0.0002 m.D3 0.0003 rad.D4 -0.0031 m.D5 -0.0009 m.D6 0.0005 rad.D7 -0.0032 m.D8 = -0.0006 m.D9 -0.0004 rad.

D10 -0.0004 m.D11 0.0000 m.D12 0.0000 rad.D13 -0.0003 m.D14 -0.0006 m.D15 0.0012 rad.D16 -0.0036 m.D17 -0.0004 m.D18 0.0012 rad.

NOTA: los desplazamientos del 19 al 27 son cero

REACCIONES

-0.0030-0.00020.0003-0.0031

Q19 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 -0.0009Q20 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.0005Q21 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -0.0032Q22 0 0 0 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 -0.0006Q23 = 0 0 0 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 X -0.0004Q24 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 -0.0004Q25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0.0000Q26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0.0000Q27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 -0.0003

-0.00060.0012-0.0036-0.00040.0012

Q19 1.3981Q20 -0.0874Q21 -2.6564Q22 -7.4798Q23 = 32.1473Q24 8.0982Q25 6.0817Q26 22.0601Q27 -16.2396

FUERZAS EN LAS BARRAS

BARRA 1

q1 =k1 TD

q1 72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 1 0 0 0 0 0 -0.0030q2 0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 0 1 0 0 0 0 -0.0002q3 = 0.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 x 0 0 1 0 0 0 x 0.0003q4 -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 0 0 0 1 0 0 -0.0031q5 0.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 0 0 0 0 1 0 -0.0009q6 0.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 0 0 0 0 0 1 0.0005

q1 8.620449554493 72403.271527 0 0 -72403.2715 0 0q2 1.846884112013 0 669.408945 1740.46326 0 -669.408945 1740.46326q3 = 4.39634370897 0 1740.46326 6033.60596 0 -1740.46326 3016.80298q4 -8.620449554493 -72403.27153 0 0 72403.2715 0 0q5 -1.846884112013 0 -669.408945 -1740.46326 0 669.408945 -1740.46326q6 5.207453673498 0 1740.46326 3016.80298 0 -1740.46326 6033.60596

Fuerzas Finalesq1 8.620449554492q2 13.28688411201q3 = 14.30634370897q4 -8.620449554492q5 9.593115887987q6 -4.702546326502

Corte en la sección (0<x<5.2)

N = -8.620V = 4.40x-13.29

V = -13.287V = 9.590

M= -2.2x^2 +13.29x-14.31M= -14.306 (x=0) xM= -4.690 (x=5.2)

M maximo = 5.761 (x=3.02)

8.62

-1.847

5.207

8.62

1.847

4.396

11.44Tn-m

9.91Tn-m

11.44 Tn-m

9.91Tn-m

4.70

8.62

9.59

8.6213.29

14.31

4.4 TN/m

Diagramas-14.306

9.590 -4.690

5.761-8.620 -13.287

NORMAL CORTANTE MOMENTO

BARRA 2

q2 =k2 TD

q4 72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 1 0 0 0 0 0 -0.0031q5 0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 0 1 0 0 0 0 -0.0009q6 = 0.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 x 0 0 1 0 0 0 x 0.0005q7 -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 0 0 0 1 0 0 -0.0032q8 0.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 0 0 0 0 1 0 -0.0006q9 0.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 0 0 0 0 0 1 -0.0004

q4 7.694856926075 72403.271527 0 0 -72403.2715 0 0q5 -0.077612866331 0 669.408945 1740.46326 0 -669.408945 1740.46326q6 = 1.261196867004 0 1740.46326 6033.60596 0 -1740.46326 3016.80298q7 -7.694856926075 -72403.27153 0 0 72403.2715 0 0q8 0.077612866331 0 -669.408945 -1740.46326 0 669.408945 -1740.46326q9 -1.664783771925 0 1740.46326 3016.80298 0 -1740.46326 6033.60596

Fuerzas Finalesq4 7.694856926075q5 7.732387133669q6 = 5.881196867004q7 -7.694856926075q8 7.887612866331q9 -6.284783771925

Corte en la sección (0<x<3.55)N = 7.695V = 4.4x-7.73

v = -7.730 (x=0)v = 7.890 (x=3.55)

M= 7.73x-2.2x^2-5.88M= -5.881 (x=0) xM= -1.538 (x=3.55)

M maximo = 0.910 (x=1.76)

Diagramas-5.881

7.695 7.890 -1.538

0.910-7.730


BARRA 3

q3 =k3 TD

q10 53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000 0 1 0 0 0 0 -0.0004q11 0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969 -1 0 0 0 0 0 0.0000q12 = 0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580 x 0 0 1 0 0 0 x 0.0000q1 -53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000 0 0 0 0 1 0 -0.0030q2 0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969 0 0 0 -1 0 0 -0.0002q3 0.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161 0 0 0 0 0 1 0.0003

q10 13.2870 0.8852502599 53027.7482 0 -0.88525026 -53027.7482 0q11 -8.620227740787 -4207.716576 0.07024402 7468.69692 4207.71658 -0.07024402 7468.69692q12 = -16.29546477082 -7468.696923 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803q1 -13.28702802076 -0.88525026 -53027.7482 0 0.88525026 53027.7482 0q2 8.620227740787 4207.7165763 -0.07024402 -7468.69692 -4207.71658 0.07024402 -7468.69692q3 -14.30634370897 -7468.696923 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161

Corte en la sección (0 < x < 2.8)N = 13.287 xV = 8.620M= 16.295-13.287x

M= 16.295 (x=0)M= -20.909 (x=2.8)

Diagramas13.287 8.620 -20.909

1.665

7.695

0.078

7.695

0.078

1.261

16.295

13.287

8.62

14.306

13.287

8.62

+ +

+

-

-

7.81Tn-m

4.62Tn-m

7.81 Tn-m

4.62Tn-m

6.28

7.695

7.89

7.6957.73

5.88

4.4 TN/m

+

16.295


BARRA 4

q4 =k4 TD

q13 53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000 0 1 0 0 0 0 -0.0003q14 0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969 -1 0 0 0 0 0 -0.0006q15 = 0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580 x 0 0 1 0 0 0 x 0.0012q4 -53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000 0 0 0 0 1 0 -0.0031q5 0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969 0 0 0 -1 0 0 -0.0009q6 0.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161 0 0 0 0 0 1 0.0005

q13 17.3255 0.8852502599 53027.7482 0 -0.88525026 -53027.7482 0q14 0.92588186188 -4207.716576 0.07024402 7468.69692 4207.71658 -0.07024402 7468.69692q15 = 4.465531150178 -7468.696923 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803q4 -17.32548756731 -0.88525026 -53027.7482 0 0.88525026 53027.7482 0q5 -0.92588186188 4207.7165763 -0.07024402 -7468.69692 -4207.71658 0.07024402 -7468.69692q6 -1.178650540502 -7468.696923 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161

Corte en la sección (0 < x < 2.8)N = -17.326 xV = -0.926M= 0.926x-4.466

M= -4.466M= -1.873

Diagramas-17.326 -0.926 -1.873

-

-4.466


BARRA 5

q5 =k5 TD

q16 53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 -0.0036q17 0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969 -1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0004q18 = 0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580 x 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 x 0.0012q7 -53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 -0.0032q8 0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 -0.0006q9 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

q16 7.8875 0.8852502599 53027.7482 0 -0.88525026 -53027.7482 0q17 7.69498860156 -4207.716576 0.07024402 7468.69692 4207.71658 -0.07024402 7468.69692q18 21.03242576361 -7468.696923 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803q7 = -7.88748440656 -0.88525026 -53027.7482 0 0.88525026 53027.7482 0q8 -7.69498860156 4207.7165763 -0.07024402 -7468.69692 -4207.71658 0.07024402 -7468.69692q9 6.284783771925 -7468.696923 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161

Corte en la sección (0 < x < 2.8)N = -7.888 xV = -7.695M= 7.695x-21.032

M= -21.032M= 0.514

17.325

0.926

4.466

0.926

1.179

17.326

7.888

7.695

21.032

7.695

6.285

7.888

+ +

+

- -

Diagramas-7.888 -7.695 0.514

-21.032


BARRA 6

q6 =k6 TD

q10 72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0004q11 0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000q12 = 0.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 x 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 x 0.0000q13 -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 -0.0003q14 0.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 -0.0006q15 0.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0012

q10 -7.2223 72403.271527 0 0 -72403.2715 0 0q11 2.515698880313 0 669.408945 1740.46326 0 -669.408945 1740.46326q12 4.832462838688 0 1740.46326 6033.60596 0 -1740.46326 3016.80298q13 = 7.222322844878 -72403.27153 0 0 72403.2715 0 0q14 -2.515698880313 0 -669.408945 -1740.46326 0 669.408945 -1740.46326q15 8.249171338937 0 1740.46326 3016.80298 0 -1740.46326 6033.60596

Fuerzas Finalesq10 -7.2223q11 18.4057q12 = 18.6025q13 7.2223q14 13.3743q15 -5.5208

Corte en la sección (0 < x < 5.2)N = 7.222V = 6.11x-18.41

V = -18.410 (x=0)V = 13.362 (x=5.2)

M= 18.41x-3.06x^2-18.6 xM= -18.600 (x=0)M= -5.610 (x=5.2)

M maximo = 9.090 (x=3.01)

8.249

7.2222.516

7.222

2.516

4.832

- -

+

15.89Tn-m

13.77Tn-m

15.89 Tn-m

13.77Tn-m

7.222

5.52

7.222

13.3718.41

18.60

6.11TN/m

Diagramas-18.600

7.222 13.362 -5.610

9.090-18.410


BARRA 7

q7 =k7 TD

q13 72403.2715 0.0000 0.0000 -72403.2715 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0003q14 0.0000 669.4089 1740.4633 0.0000 -669.4089 1740.4633 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 -0.0006q15 = 0.0000 1740.4633 6033.6060 0.0000 -1740.4633 3016.8030 x 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 x 0.0012q16 -72403.2715 0.0000 0.0000 72403.2715 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 -0.0036q17 0.0000 -669.4089 -1740.4633 0.0000 669.4089 -1740.4633 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 -0.0004q18 0.0000 1740.4633 3016.8030 0.0000 -1740.4633 6033.6060 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0012

q13 241.0898 72403.271527 0 0 -72403.2715 0 0q14 4.057265577031 0 669.408945 1740.46326 0 -669.408945 1740.46326q15 10.45816523952 0 1740.46326 6033.60596 0 -1740.46326 3016.80298q16 = -241.089832058 -72403.27153 0 0 72403.2715 0 0q17 -4.057265577031 0 -669.408945 -1740.46326 0 669.408945 -1740.46326q18 10.63961576104 x 0 1740.46326 3016.80298 0 -1740.46326 6033.60596

Fuerzas Finalesq13 241.0898q14 11.8673q15 = 15.0782q16 -241.0898q17 3.7527q18 6.0196

Corte en la sección (0 < x < 3.55)

N = -241.090V = 4.4x-11.87

V = -11.867 (x=0)V = 3.750 (x=3.55)

M= 11.87x-2.2x^2-15.08 xM= -15.080 (x=0)M= -0.667 (x=3.55)

M maximo = 0.931 (x=2.7)

241.0898

10.639

241.0898

-4.0574.057

10.458

+

7.81Tn-m

4.62Tn-m

7.81 Tn-m

4.62Tn-m

241.0898

6.02

241.0898

3.7511.87

15.08

4.4TN/m

Diagramas-15.080

3.750 -0.667

0.931-241.090 -11.867


BARRA 8

q8 =k8 TD

q19 53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0q20 0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969 -1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0q21 = 0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580 x 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 x 0q10 -53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 -0.0004q11 0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 0.0000q12 0.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000

q19 -0.0874 0.8852502599 53027.7482 0 -0.88525026 -53027.7482 0q20 -1.398128168767 -4207.716576 0.07024402 7468.69692 4207.71658 -0.07024402 7468.69692q21 -2.65635693126 -7468.696923 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803q10 = 0.087393667202 -0.88525026 -53027.7482 0 0.88525026 53027.7482 0q11 1.398128168767 4207.7165763 -0.07024402 -7468.69692 -4207.71658 0.07024402 -7468.69692q12 -2.306998067864 -7468.696923 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161

Corte en la sección (0 < x < 2.8)N = 0.087 xV = 1.398M= 2.656 -1.398x

M= 2.656M= -1.258

0.087

0.087

1.398

2.656

1.398

2.307

Diagramas0.087 1.398 -1.258

2.656


BARRA 9

q9=k9 TD

q22 53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0q23 0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969 -1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0q24 = 0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580 x 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 x 0q13 -53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 -0.0003q14 0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 -0.0006q15 0.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0012

q22 32.1472 0.8852502599 53027.7482 0 -0.88525026 -53027.7482 0q23 7.480382594792 -4207.716576 0.07024402 7468.69692 4207.71658 -0.07024402 7468.69692q24 8.098243561017 -7468.696923 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803q13 = -32.14716634337 -0.88525026 -53027.7482 0 0.88525026 53027.7482 0q14 -7.480382594792 4207.7165763 -0.07024402 -7468.69692 -4207.71658 0.07024402 -7468.69692q15 18.45711465049 -7468.696923 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161

XCorte en la sección (0 < x < 2.8)

N = -32.147V = -7.480M= 7.48x-8.098

M= -8.098M= 12.846

7.480

32.147

32.147

7.480

8.098

18.457

+ +

Diagramas

-32.147 -7.480 12.846

-8.098


BARRA 10

q10 =k10 TD

q25 53027.7482 0.0000 0.0000 -53027.7482 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0q26 0.0000 4207.7166 7468.6969 0.0000 -4207.7166 7468.6969 -1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0q27 = 0.0000 7468.6969 17675.9161 0.0000 -7468.6969 8837.9580 x 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 x 0q16 -53027.7482 0.0000 0.0000 53027.7482 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 -0.0036q17 0.0000 -4207.7166 -7468.6969 0.0000 4207.7166 -7468.6969 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 -0.0004q18 0.0000 7468.6969 8837.9580 0.0000 -7468.6969 17675.9161 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0012

q25 22.0602 0.8852502599 53027.7482 0 -0.88525026 -53027.7482 0q26 -6.081350941608 -4207.716576 0.07024402 7468.69692 4207.71658 -0.07024402 7468.69692q27 -16.23962014549 -7468.696923 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803q16 = -22.06022731629 -0.88525026 -53027.7482 0 0.88525026 53027.7482 0q17 6.081350941608 4207.7165763 -0.07024402 -7468.69692 -4207.71658 0.07024402 -7468.69692q18 -5.34917569722 -7468.696923 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161

XCorte en la sección (0 < x < 2.8)

N = -22.060V = 6.081M= 16.239 -6.081x

M= 16.239M= -0.788

6.081

22.060

22.060

6.081

16.239

5.349

- -

+

Diagramas-22.060 6.081 -0.788

16.239


- +

+

-

MATRIZ DE RIGIDEZ DE TODA LA ESTRUCTURA1 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 76610.9881 0.81500624 7468.69692 -72403.2715 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 0.81500624 53697.1571 1740.33857 0 -669.408945 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03 7468.69692 1740.33857 23709.522 0 -1740.46326 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 -72403.2715 0 0 149014.26 0.81500624 7468.69692 -72403.2715 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 0 0 0 0 0 05 0 -669.408945 -1740.46326 0.81500624 54366.566 -0.12468314 0 -669.408945 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 0 0 0 0 0 06 0 1740.46326 3016.80298 7468.69692 -0.12468314 29743.128 0 -1740.46326 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 0 0 0 0 0 07 0 0 0 -72403.2715 0 0 76610.9881 0.81500624 7468.69692 0 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 0 0 0 08 0 0 0 0 -669.408945 -1740.46326 0.81500624 53697.1571 -1740.58794 0 0 0 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 0 0 0 09 0 0 0 0 1740.46326 3016.80298 7468.69692 -1740.58794 23709.522 0 0 0 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 0 0 0 0

10 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 80818.7047 1.63001248 0 -72403.2715 0 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 0 0 0 011 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 1.63001248 106724.905 1740.46326 0 -669.408945 1740.46326 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 0 0 0 012 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 0 1740.46326 41385.4381 0 -1740.46326 3016.80298 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 0 0 0 013 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 -72403.2715 0 0 80818.7047 72404.9015 0 0 -72403.2715 0 0 0 0 -4207.71659 -0.81500624 7468.69692 0 0 014 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 -669.408945 -1740.46326 1.63001248 106724.905 -1071.05431 1740.46326 0 -669.408945 0 0 0 -0.81500624 -53027.7481 -0.12468314 0 0 015 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 1740.46326 3016.80298 0 -1740.46326 43125.9013 6033.60596 0 -1740.46326 0 0 0 -7468.69692 0.12468314 8837.95803 0 0 016 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 -72403.2715 0 8415.43318 72404.9015 0 0 0 0 0 0 0 -4207.71659 -0.81500624 7468.6969217 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 -669.408945 -1738.83325 106055.496 669.408945 0 0 0 0 0 0 -0.81500624 -53027.7481 -0.1246831418 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 1740.46326 3016.80298 0 33611.3688 0 0 0 0 0 0 -7468.69692 0.12468314 8837.9580319 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 4207.71659 0.81500624 -7468.69692 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.12468314 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -7468.69692 0.12468314 17675.9161 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 4207.71659 0.81500624 -7468.69692 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.12468314 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -7468.69692 0.12468314 17675.9161 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4207.71659 -0.81500624 -7468.69692 0 0 0 0 0 0 4207.71659 0.81500624 -7468.6969226 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.81500624 -53027.7481 0.12468314 0 0 0 0 0 0 0.81500624 53027.7481 0.1246831427 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7468.69692 -0.12468314 8837.95803 0 0 0 0 0 0 -7468.69692 0.12468314 17675.9161

1 2 3 4 5 6 10 11 12 13 14 1572403.2715 0 0 -72403.2715 0 0 1 72403.2715 0 0 -72403.2715 0 0 10

0 669.408945 1740.46326 0 -669.408945 1740.46326 2 0 669.408945 1740.46326 0 -669.408945 1740.46326 11

K1 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 3 K5 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 12-72403.2715 0 0 72403.2715 0 0 4 -72403.2715 0 0 72403.2715 0 0 13

0 -669.408945 -1740.46326 0 669.408945 -1740.46326 5 0 -669.408945 -1740.46326 0 669.408945 -1740.46326 140 1740.46326 3016.80298 0 -1740.46326 6033.60596 6 0 1740.46326 3016.80298 0 -1740.46326 6033.60596 15

4 5 6 7 8 9 13 14 15 16 17 1872403.2715 0 0 -72403.2715 0 0 4 72403.2715 0 0 -72403.2715 0 0 13

0 669.408945 1740.46326 0 -669.408945 1740.46326 5 0 669.408945 1740.46326 0 -669.408945 1740.46326 14K2 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 6 K6 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 15

-72403.2715 0 0 72403.2715 0 0 7 -72403.2715 0 0 72403.2715 0 0 160 -669.408945 -1740.46326 0 669.408945 -1740.46326 8 0 -669.408945 -1740.46326 0 669.408945 -1740.46326 170 1740.46326 3016.80298 0 -1740.46326 6033.60596 9 0 1740.46326 3016.80298 0 -1740.46326 6033.60596 18

10 11 12 1 2 3 19 20 21 10 11 124207.71659 0.81500624 -7468.69692 -4207.71659 -0.81500624 -7468.69692 10 4207.71659 0.81500624 -7468.69692 -4207.71659 -0.81500624 -7468.69692 190.81500624 53027.7481 0.12468314 -0.81500624 -53027.7481 0.12468314 11 0.81500624 53027.7481 0.12468314 -0.81500624 -53027.7481 0.12468314 20

K3 -7468.69692 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803 12 K7 -7468.69692 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803 21-4207.71659 -0.81500624 7468.69692 4207.71659 0.81500624 7468.69692 1 -4207.71659 -0.81500624 7468.69692 4207.71659 0.81500624 7468.69692 10-0.81500624 -53027.7481 -0.12468314 0.81500624 53027.7481 -0.12468314 2 -0.81500624 -53027.7481 -0.12468314 0.81500624 53027.7481 -0.12468314 11-7468.69692 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161 3 -7468.69692 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161 12

13 14 15 4 5 6 22 23 24 13 14 154207.71659 0.81500624 -7468.69692 -4207.71659 -0.81500624 -7468.69692 13 4207.71659 0.81500624 -7468.69692 -4207.71659 -0.81500624 -7468.69692 220.81500624 53027.7481 0.12468314 -0.81500624 -53027.7481 0.12468314 14 0.81500624 53027.7481 0.12468314 -0.81500624 -53027.7481 0.12468314 23

K4 -7468.69692 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803 15 K8 -7468.69692 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803 24-4207.71659 -0.81500624 7468.69692 4207.71659 0.81500624 7468.69692 4 -4207.71659 -0.81500624 7468.69692 4207.71659 0.81500624 7468.69692 13-0.81500624 -53027.7481 -0.12468314 0.81500624 53027.7481 -0.12468314 5 -0.81500624 -53027.7481 -0.12468314 0.81500624 53027.7481 -0.12468314 14-7468.69692 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161 6 -7468.69692 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161 15

16 17 18 7 8 9 25 26 27 16 17 184207.71659 0.81500624 -7468.69692 -4207.71659 -0.81500624 -7468.69692 16 4207.71659 0.81500624 -7468.69692 -4207.71659 -0.81500624 -7468.69692 250.81500624 53027.7481 0.12468314 -0.81500624 -53027.7481 0.12468314 17 0.81500624 53027.7481 0.12468314 -0.81500624 -53027.7481 0.12468314 26

K5 -7468.69692 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803 18 K9 -7468.69692 0.12468314 17675.9161 7468.69692 -0.12468314 8837.95803 27-4207.71659 -0.81500624 7468.69692 4207.71659 0.81500624 7468.69692 7 -4207.71659 -0.81500624 7468.69692 4207.71659 0.81500624 7468.69692 16-0.81500624 -53027.7481 -0.12468314 0.81500624 53027.7481 -0.12468314 8 -0.81500624 -53027.7481 -0.12468314 0.81500624 53027.7481 -0.12468314 17-7468.69692 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161 9 -7468.69692 0.12468314 8837.95803 7468.69692 -0.12468314 17675.9161 18

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 26 271 72403.2715 0 0 -72403.2715 0 0 12 0 669.408945 1740.46326 0 -669.408945 1740.46326 23 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 34 -72403.2715 0 0 72403.2715 0 0 45 0 -669.408945 -1740.46326 0 669.408945 -1740.46326 56 0 1740.46326 3016.80298 0 -1740.46326 6033.60596 67 4207.71659 0.81500624 7468.69692 78 0.81500624 53027.7481 -0.12468314 89 7468.69692 -0.12468314 17675.9161 9

10 4207.71659 0.81500624 7468.69692 -4207.71659 -0.81500624 7468.69692 1011 0.81500624 53027.7481 -0.12468314 -0.81500624 -53027.7481 -0.12468314 1112 7468.69692 -0.12468314 17675.9161 -7468.69692 0.12468314 8837.95803 1213 4207.71659 0.81500624 7468.69692 -4207.71659 -0.81500624 7468.69692 1314 0.81500624 53027.7481 -0.12468314 -0.81500624 -53027.7481 -0.12468314 1415 7468.69692 -0.12468314 17675.9161 -7468.69692 0.12468314 8837.95803 1516 4207.71659 0.81500624 7468.69692 -4207.71659 -0.81500624 7468.69692 1617 0.81500624 53027.7481 -0.12468314 -0.81500624 -53027.7481 -0.12468314 1718 7468.69692 -0.12468314 17675.9161 -7468.69692 0.12468314 8837.95803 1819 -4207.71659 -0.81500624 -7468.69692 4207.71659 0.81500624 -7468.69692 1920 -0.81500624 -53027.7481 0.12468314 0.81500624 53027.7481 0.12468314 2021 7468.69692 -0.12468314 8837.95803 -7468.69692 0.12468314 17675.9161 2122 -4207.71659 -0.81500624 -7468.69692 4207.71659 0.81500624 -7468.69692 2223 -0.81500624 -53027.7481 0.12468314 0.81500624 53027.7481 0.12468314 2324 7468.69692 -0.12468314 8837.95803 -7468.69692 0.12468314 17675.9161 2425 -4207.71659 -0.81500624 -7468.69692 4207.71659 0.81500624 -7468.69692 2526 -0.81500624 -53027.7481 0.12468314 0.81500624 53027.7481 0.12468314 2627 7468.69692 -0.12468314 8837.95803 -7468.69692 0.12468314 17675.9161 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

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 26 271 4207.71659 0.81500624 7468.69692 -4207.71659 -0.81500624 7468.69692 12 0.81500624 53027.7481 -0.12468314 -0.81500624 -53027.7481 -0.12468314 23 7468.69692 -0.12468314 17675.9161 -7468.69692 0.12468314 8837.95803 34 72403.2715 0 0 -72403.2715 0 0 -4207.71659 -0.81500624 7468.69692 45 0 669.408945 1740.46326 0 -669.408945 1740.46326 -0.81500624 -53027.7481 -0.12468314 56 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 -7468.69692 0.12468314 8837.95803 67 -72403.2715 0 0 72403.2715 0 0 -4207.71659 -0.81500624 7468.69692 78 0 -669.408945 -1740.46326 0 669.408945 -1740.46326 -0.81500624 -53027.7481 -0.12468314 89 0 1740.46326 3016.80298 0 -1740.46326 6033.60596 -7468.69692 0.12468314 8837.95803 9

10 -4207.71659 -0.81500624 -7468.69692 4207.71659 0.81500624 -7468.69692 1011 -0.81500624 -53027.7481 0.12468314 0.81500624 53027.7481 0.12468314 1112 7468.69692 -0.12468314 8837.95803 -7468.69692 0.12468314 17675.9161 1213 -4207.71659 -0.81500624 -7468.69692 4207.71659 0.81500624 -7468.69692 1314 -0.81500624 -53027.7481 0.12468314 0.81500624 53027.7481 0.12468314 1415 7468.69692 -0.12468314 8837.95803 -7468.69692 0.12468314 17675.9161 1516 -4207.71659 -0.81500624 -7468.69692 4207.71659 0.81500624 -7468.69692 1617 -0.81500624 -53027.7481 0.12468314 0.81500624 53027.7481 0.12468314 1718 7468.69692 -0.12468314 8837.95803 -7468.69692 0.12468314 17675.9161 1819 1920 2021 2122 2223 2324 2425 2526 2627 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

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 26 271 12 23 34 4207.71659 0.81500624 7468.69692 45 0.81500624 53027.7481 -0.12468314 56 7468.69692 -0.12468314 17675.9161 67 78 89 9

10 72403.2715 0 0 -72403.2715 0 0 1011 0 669.408945 1740.46326 0 -669.408945 1740.46326 1112 0 1740.46326 6033.60596 0 -1740.46326 3016.80298 1213 -72403.2715 0 0 72403.2715 0 0 1314 0 -669.408945 -1740.46326 0 669.408945 -1740.46326 1415 0 1740.46326 3016.80298 0 -1740.46326 6033.60596 1516 1617 1718 1819 1920 2021 2122 22

23 2324 2425 2526 2627 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

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 26 271 12 23 34 45 56 67 78 89 9

10 1011 1112 1213 72403.2715 0 0 -72403.2715 0 1314 0 669.408945 1740.46326 0 -669.408945 1415 0 1740.46326 6033.60596 0 -1740.46326 1516 -72403.2715 0 0 72403.2715 0 1617 0 -669.408945 -1740.46326 0 669.408945 1718 0 1740.46326 3016.80298 0 -1740.46326 1819 1920 2021 2122 2223 2324 2425 2526 2627 27

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