Trabajo Final de Estructuras II(1)

1469
3.275 m 3.725 m 2.075 m 5.000 m L1x= 2.075 m L1y L2x= 5.000 m L2y L3x= 2.050 m Lmá L4x= 3.875 m Lmáx(x) 5.000 m TIPOLOGÍA 1. LOSA ALIGERADA EN 1-D: 250.0 kg/m2 13 cm 200.0 kg/m2 14.9 cm 280.0 kg/m2 17 cm 230.0 kg/m2 H L-A =

description

ANALISIS MATRICIAL

Transcript of Trabajo Final de Estructuras II(1)

Page 1: Trabajo Final de Estructuras II(1)

PREDIMENSIONAMIENTO

3.275 m

3.725 m

2.075 m 5.000 m

L1x= 2.075 m L1y=L2x= 5.000 m L2y=L3x= 2.050 m Lmáx(y)L4x= 3.875 m

Lmáx(x) 5.000 m

TIPOLOGÍA

1. LOSA ALIGERADA EN 1-D:

250.0 kg/m213 cm

200.0 kg/m2

14.9 cm

280.0 kg/m217 cm

230.0 kg/m2

HL-A=

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3. LOSA MACIZA EN 1-D:

15.5 cm 17.5 cm δLM= 420.0 kg/m2

DIMENSIONES DE VIGAS

hv = 0.42 m 0.45 m

VP 0.14 m

bv 0.18 m0.23 m

DIMENSIONES DE COLUMNAS

1.638 m A1 A2

1.638 m A6 A7

1.863 m

1.863 m A12 A13

HL-M=

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1.863 m A12 A13

1.038 m 1.038 m 2.500 m 2.500 m

A1 1.699 m2A2 5.793 m2

A3 5.772 m2

A4 4.851 m2

A5 3.173 m2

1.638 m

1.125 m

1.863 m

1.038 m 2.500 m

PESOS

1. PESO DE LOSA ALIGERADA

2.803 Tn

4. PESO DE TABIQUERIA REPARTIDA

1.514 Tn

7. PESO DE COLUMNAS

0.450 Tn

0.420 Tn

δ C.A=

δ TAB.R=

δ COL.1=

δ COL.T=

VS

VP

A11

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N3 2.803 Tn 0 0.937 Tn2 2.803 Tn 0.932 Tn 0.937 Tn1 2.803 Tn 0.932 Tn 0.937 Tn

28.812 Tn

a) Se asume:

F'c= 210 kg/cm2ϕ= 3.5 %C= 1.3f'y= 4200 kg/cm2

PREDIMENSIONAMIENTO DE LA PLACA DE CONCRETO

1.638 m

1.638 m

1.863 m

1.863 m

δ C.A δ CONT δ ENL

PSERV=

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1.863 m

2.075 m 5.000 m

82.775 m2 VP = 0.25 m

#C = 15 col VS = 0.25 m

Ac = 1.313 m2 COL = 0.25 m

he3 = 1.4 m he2 = 2.8 m

1. PESO DE LOSA ALIGERADA

18.260 Tn

4. PESO DE TABIQUERIA REPARTIDA

10.590 Tn

7. PESO DE COLUMNAS

4.410 Tn

8.820 Tn

9.135 Tn

N3 18.260 Tn 0 6.622 Tn2 18.260 Tn 6.517 Tn 6.622 Tn1 18.260 Tn 6.517 Tn 6.622 Tn

DENSIDAD = 0.876 Tn/m2

V= 37.305 Tn

ATT =

δ C.A=

δ TAB.R=

δ COL.3=

δ COL.2=

δ COL.1=

δ C.A δ CONT δ ENL

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Ac= 13125 cm2

K8.60 m 501.045 Tn.m 0.4171 15.561 Tn5.80 m 460.005 Tn.m 0.3830 14.286 Tn3.00 m 240.116 Tn.m 0.1999 7.457 Tn

1201.167 Tn.m 1

CÁLCULO DE CENTRO DE GRAVEDAD Y CENTRO DE MASA

0.35 m 0.35 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

3.275 m

hn δ Sis*hn Fs

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3.275 m

3.725 m

2.075 m 5.000 m

A1 57.200 m2 X1 6.500 mA2 0.588 m2 X2 0.125 mA3 12.338 m2 X3 4.575 mA4 9.400 m2 X4 11.000 mA5 3.250 m2 X5 6.500 m

82.775 m2

3.275 m

3.725 m

2.075 m 5.000 m

32

1

2

3

A B

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0.00137 m4 0.00137 m4

Eje X Iy X*IyA 0.175 m 0.00137 m4 0.000239 m5B 2.075 m 0.00137 m4 0.002837 m5C 7.075 m 0.00137 m4 0.009673 m5D 9.125 m 0.00137 m4 0.012476 m5E 12.825 m 0.00137 m4 0.017534 m5

0.00684 m4 0.042759 m5

CÁLCULO DE FUERZAS SÍSMICAS

Eje Iy KA 0.001367 m4 0.200 B 0.001367 m4 0.200 C 0.001367 m4 0.200 D 0.001367 m4 0.200 E 0.001367 m4 0.200

0.006836 m4

Eje Ix K1 0.004466 m4 0.333 2 0.004466 m4 0.333 3 0.004466 m4 0.333

0.013398 m4

IyA IyB

A B

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CÁLCULO DE CENTRO DE GRAVEDAD Y CENTRO DE MASA CON PLACAS

0.35 m 1.50 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

3.275 m

3.725 m

2.075 m 5.000 m

A1 57.2000 m2 X1 6.500 m

32

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A2 0.5875 m2 X2 0.125 mA3 12.3375 m2 X3 4.575 mA4 9.4000 m2 X4 11.000 mA5 3.2500 m2 X5 6.500 m

82.775 m2

3.275 m

3.725 m

2.075 m 5.000 m

0.00137 m4 0.00286 m4

Eje X Iy X*IyA 0.1750 m 0.00137 m4 0.000239 m5B 2.0750 m 0.00286 m4 0.005944 m5C 7.0750 m 0.25439 m4 1.799814 m5D 9.1250 m 0.00137 m4 0.012476 m5E 12.8250 m 0.00286 m4 0.036738 m5

0.26285 m4 1.855211 m5

IyA IyB

1

2

3

A B

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82.775 m2

1.325 m2 VP = 0.25 m

#C = 12 col VS = 0.25 m

Ac = 1.050 m2 COL = 0.25 m

he3 = 1.4 m he2 = 2.8 m

1. PESO DE LOSA ALIGERADA

18.260 Tn

4. PESO DE TABIQUERIA REPARTIDA

10.452 Tn

7. PESO DE COLUMNAS

3.528 Tn

7.056 Tn

7.308 Tn

N3 18.260 Tn 0 6.622 Tn2 18.260 Tn 6.432 Tn 6.622 Tn1 18.260 Tn 6.432 Tn 6.622 Tn

ATT =

Ap=

δ C.A=

δ TAB.R=

δ COL.3=

δ COL.2=

δ COL.1=

δ C.A δ CONT δ ENL

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DENSIDAD = 0.922 Tn/m2

V= 39.260 Tn

Ac= 10500 cm2

K8.60 m 518.649 Tn.m 0.4117 16.165 Tn5.80 m 486.575 Tn.m 0.3863 15.165 Tn3.00 m 254.455 Tn.m 0.2020 7.931 Tn

1259.679 Tn.m 1

CÁLCULO DE FUERZAS SÍSMICAS

Eje Iy KA 0.001367 m4 0.005 B 0.002865 m4 0.011 C 0.254391 m4 0.968 D 0.001367 m4 0.005 E 0.002865 m4 0.011

0.262854 m4

Eje Ix K1 0.075987 m4 0.492 2 0.004466 m4 0.029 3 0.073885 m4 0.479

0.154339 m4

hn δ Sis*hn Fs

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PREDIMENSIONAMIENTO

5.000 m 2.050 m 3.875 m

L1y= 3.725 mL2y= 3.275 m

Lmáx(y) 3.725 m

2. LOSA ALIGERADA EN 2-D:

14.9 m 17 cmHL-A=

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4. LOSA MACIZA EN 2-D:

12.42 cm

420.0 kg/m2 9.31 cm

9.69 cm

hv =

VS0.25 m bv

A3 A4 A5

A8 A9 A10

A13A13 A14 A15

HL-M=

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A13A13A13

A14 A15

2.500 m 1.025 m 1.025 m 1.938 m 1.938 m

A6 3.050 m2 A11A7 11.708 m2 A12

A8 11.674 m2 A13

A9 9.705 m2 A14

A10 6.781 m2 A15ATmáx

tc0.25 m

0.25 m bc

Ac= 0.0625 m2ATT= 11.7083 m2

Avx= 0.8219 m2Avg= 1.6344 m2

Avy= 0.8125 m2

2. PESO DE CONTRAPISO 3. PESO DE ENLUCIDO

0.932 Tn

5. PESO DE COBERTURA 6. PESO DE VIGAS

1.171 Tn

8. PESO DE CARGA VIVA O SOBRECARGA

S/ct=1= 2.329 Tn

S/ct=2= 2.329 Tn

δ CONT=

δ COB=

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S/ct=3= 1.165 Tn

0.937 Tn 0 1.171 Tn 1.473 Tn 0.420 Tn0.937 Tn 1.514 Tn 0 1.473 Tn 0.420 Tn0.937 Tn 1.514 Tn 0 1.473 Tn 0.450 Tn

42.084 Tn

Ac1= 304.89 cm2 bc=

251.32 cm2

Ac2= 197.74 cm2 tc=

PREDIMENSIONAMIENTO DE LA PLACA DE CONCRETO

δ ENL δ TAB.R δ COB δ Vg δ COL

PUlt=

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5.000 m 2.050 m 3.875 m

0.25 m 0.45 m

Avx =0.25 m 0.30 m Avp =

Avy =0.25 m 0.35 m

2.8 m he1 = 2.9 m

2. PESO DE CONTRAPISO 3. PESO DE ENLUCIDO

6.517 Tn

5. PESO DE COBERTURA 6. PESO DE VIGAS

8.278 Tn

8. PESO DE TABIQUERÍA PERIMÉTRICA 9. PESO DE CARGA VIVA O SOBRECARGA

3.918 Tn

9.692 Tn

10.104 Tn

6.622 Tn 0 8.278 Tn 14.738 Tn 4.410 Tn6.622 Tn 10.590 Tn 0 14.738 Tn 8.820 Tn6.622 Tn 10.590 Tn 0 14.738 Tn 9.135 Tn

Vc= 7.680 Kg/cm2 An= 4857.117 cm2

δ CONT=

δ COB=

δ TAB.P 3 =

δ TAB.P 2 =

δ TAB.P 1 =

δ ENL δ TAB.R δ COB δ Vg δ COL

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AM= -0.83 mASUMO: tm= 0.250 m

Lm= -3.307 m

15.561 Tn

15.561 Tn 15.561 Tn14.286 Tn 29.847 Tn 14.286 Tn7.457 Tn 37.305 Tn

7.457 Tn

CÁLCULO DE CENTRO DE GRAVEDAD Y CENTRO DE MASA

0.35 m 0.35 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

Fs Qs

1

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5.000 m 2.050 m 3.875 m

6.500 m Y1 4.800 m0.125 m Y2 1.425 m X

4.575 m Y3 1.425 m Cg

11.000 m Y4 1.425 m Y

6.500 m Y5 0.125 m

5.000 m 2.050 m 3.875 m

1

43

5

C D

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0.00137 m4 0.00137 m4

X*Iy Xr Eje Y0.000239 m5

6.255 m

1 0.1250.002837 m5 2 3.725 m0.009673 m5 3 6.8750.012476 m50.017534 m5

0.042759 m5

0.131 m

0.44 m

0.424 m

CÁLCULO DE FUERZAS SÍSMICAS

F1 F2 F31.491 Tn 2.857 Tn 3.112 Tn1.491 Tn 2.857 Tn 3.112 Tn1.491 Tn 2.857 Tn 3.112 Tn1.491 Tn 2.857 Tn 3.112 Tn1.491 Tn 2.857 Tn 3.112 Tn

F1 F2 F32.486 Tn 4.762 Tn 5.187 Tn2.486 Tn 4.762 Tn 5.187 Tn2.486 Tn 4.762 Tn 5.187 Tn

IyC IyD

C D

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CÁLCULO DE CENTRO DE GRAVEDAD Y CENTRO DE MASA CON PLACAS

0.35 m 0.35 m

0.25 m 0.25 m

0.35 m 0.35 m

0.25 m 0.25 m

0.25 m 0.35 m

2.30 m 0.25 m

5.000 m 2.050 m 3.875 m

6.500 m Y1 4.800 m

1

43

5

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0.125 m Y2 1.425 m X

4.575 m Y3 1.425 m Cg

11.000 m Y4 1.425 m Y

6.500 m Y5 0.125 m

5.000 m 2.050 m 3.875 m

0.25439 m4 0.00137 m4

X*Iy Xr Eje Y0.000239 m5

7.058 m

1 0.1250.005944 m5 2 3.7251.799814 m5 3 6.8750.012476 m50.036738 m5

1.855211 m5

IyC IyD

C D

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0.246 m

0.45 m

-0.379 m

0.25 m 0.45 m

Avx =0.25 m 0.30 m Avp =

Avy =0.25 m 0.35 m

2.8 m he1 = 2.9 m

2. PESO DE CONTRAPISO 3. PESO DE ENLUCIDO

6.432 Tn

5. PESO DE COBERTURA 6. PESO DE VIGAS

8.278 Tn

8. PESO DE TABIQUERÍA PERIMÉTRICA 9. PESO DE CARGA VIVA O SOBRECARGA

3.385 Tn

8.372 Tn

8.728 Tn

6.622 Tn 0 8.278 Tn 13.775 Tn 3.528 Tn6.622 Tn 10.452 Tn 0 13.775 Tn 7.056 Tn6.622 Tn 10.452 Tn 0 13.775 Tn 7.308 Tn

δ CONT=

δ COB=

δ TAB.P 3 =

δ TAB.P 2 =

δ TAB.P 1 =

δ ENL δ TAB.R δ COB δ Vg δ COL

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Vc= 7.680 Kg/cm2 An= 5111.739 cm2

AM= -0.54 mASUMO: tm= 0.250 m

Lm= -2.155 m

16.165 Tn

16.165 Tn 16.165 Tn15.165 Tn 31.330 Tn 15.165 Tn7.931 Tn 39.260 Tn

7.931 Tn

CÁLCULO DE FUERZAS SÍSMICAS

F1 F2 F30.041 Tn 0.079 Tn 0.084 Tn0.086 Tn 0.165 Tn 0.176 Tn7.675 Tn 14.677 Tn 15.644 Tn0.041 Tn 0.079 Tn 0.084 Tn0.086 Tn 0.165 Tn 0.176 Tn

F1 F2 F33.905 Tn 7.466 Tn 7.959 Tn0.229 Tn 0.439 Tn 0.468 Tn3.797 Tn 7.260 Tn 7.738 Tn

Fs Qs

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PREDIMENSIONAMIENTO

Longitud Mínima en la Dirección de la Losa:

1-DHL-A Arcilla

13 cm 250.0 kg/m217 cm 280.0 kg/m220 cm 300.0 kg/m225 cm 350.0 kg/m2

1.125 m

30 cm 420.0 kg/m2

# Pisos 3hi 3.00 mht 2.80 m

δCA 2400 kg/m3

s/c1 200 kg/m2s/c2 200 kg/m2

3.875 m s/c3 200 kg/m2s/c(azotea) 100 kg/m2

δ Tab. Repartida 130 kg/m2δ Lad. Pandereta 1350 kg/m2

δ Cobertura 100 kg/m2δ Enlucido 80 kg/m2

δ Contrapiso 80 kg/m2

2. LOSA ALIGERADA EN 2-D:

300.0 kg/m2

13 cm

250.0 kg/m2

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4. LOSA MACIZA EN 2-D:

12.50 cm

10.00 cm 10.73 cm 12.50 cm

9.69 cm δLM= 300.0 kg/m2

0.27 m 0.30 m

0.09 m0.12 m 0.25 m

0.15 m

A5

A5 A6

A10

A12

1.125 m

0.738 m

A15

A16 A17

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A15A15

1.938 m

0.663 m25.117 m2

5.114 m2 8.225 m2

4.066 m2 91.0 m2

3.609 m211.708 m2

1.6344 m2

3. PESO DE ENLUCIDO

0.937 Tn

6. PESO DE VIGAS

1.473 Tn

Avacios=

ATotal=

δ ENL=

δ Vg=

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δ M δ V0.420 Tn 6.803 Tn 1.165 Tn0.420 Tn 8.078 Tn 2.329 Tn0.450 Tn 8.108 Tn 2.329 Tn

22.990 Tn 5.823 Tn

25 cm

10 cm 35 cm

2.80 m

2.80 m

1.125 m

3.00 m

0.738 m

δ COL

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3.00 m

3.875 m

8.438 m216.250 m2

7.813 m2

em= 0.13 m

3. PESO DE ENLUCIDO

6.622 Tn

6. PESO DE VIGAS

14.738 Tn

9. PESO DE CARGA VIVA O SOBRECARGA

S/ct=1= 16.293 Tn

S/ct=2= 16.293 Tn

S/ct=3= 8.146 Tn

δ M δ V δ Sis4.410 Tn 3.918 Tn 56.225 Tn 8.146 Tn 58.261 Tn8.820 Tn 9.692 Tn 75.238 Tn 16.293 Tn 79.311 Tn9.135 Tn 10.104 Tn 75.966 Tn 16.293 Tn 80.039 Tn

217.611 Tn

δ ENL=

δ Vg=

δ COL δ TAB.P

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0.250 m-3.307 m

0.35 m

0.25 m

0.35 m

0.25 m

0.35 m

0.25 m

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1.125 m

3.875 m

6.679 m

3.706 m

0.00447 m4

1.125 m

0.00447 m4

0.00447 m4

3.875 m

Ix3

Ix2

Ix1

4

E

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0.00137 m4

Y Ix Y*Ix Yr0.125 0.00447 m4 0.000558 m5

3.575 m3.725 m 0.00447 m4 0.016636 m56.875 0.00447 m4 0.030705 m5

0.01340 m4 0.047899 m5

IyE

E

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0.35 m

0.25 m

0.35 m

0.25 m

1.50 m

0.25 m

1.125 m

3.875 m

4

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6.679 m

3.706 m

0.07389 m4

1.125 m

0.00447 m4

0.07599 m4

3.875 m

0.00286 m4

Y Ix Y*Ix Yr0.125 0.07599 m4 0.009498 m5

3.461 m3.725 0.00447 m4 0.016636 m56.875 0.07389 m4 0.507962 m5

0.15434 m4 0.534097 m5

Ix3

Ix2

Ix1

IyE

E

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7.888 m215.188 m2

7.300 m2

em= 0.13 m

3. PESO DE ENLUCIDO

6.622 Tn

6. PESO DE VIGAS

13.775 Tn

9. PESO DE CARGA VIVA O SOBRECARGA

S/ct=1= 16.080 Tn

S/ct=2= 16.080 Tn

S/ct=3= 8.040 Tn

δ M δ V3.528 Tn 3.385 Tn 4.452 Tn 58.298 Tn 8.040 Tn7.056 Tn 8.372 Tn 8.904 Tn 79.872 Tn 16.080 Tn7.308 Tn 8.728 Tn 9.222 Tn 80.798 Tn 16.080 Tn

δ ENL=

δ Vg=

δ COL δ TAB.P δ Placas

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0.250 m-2.155 m

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Longitud Mínima en la Dirección de la Losa:

1-D 2-DTecnopor Arcilla Tecnopor

200.0 kg/m2 300.0 kg/m2 250.0 kg/m2230.0 kg/m2 330.0 kg/m2 280.0 kg/m2250.0 kg/m2 350.0 kg/m2 300.0 kg/m2300.0 kg/m2 400.0 kg/m2 350.0 kg/m2370.0 kg/m2 470.0 kg/m2 420.0 kg/m2

Z 0.4U 1S 1.2Tp 0.6

R 7

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1.40 m

1.40 m

1.40 m

1.40 m

1.50 m

1.50 m

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1.50 m

δ Sis58.261 Tn79.311 Tn80.039 Tn

217.611 Tn

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δ V δ Sis8.040 Tn 60.308 Tn16.080 Tn 83.892 Tn16.080 Tn 84.818 Tn

229.019 Tn

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ANÁLISIS MÉTODO MUTTO - PÓRTICO 2-2

DATOS:

210 kg/cm2

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

Ic= 89322.9167 cm4 kc= 319.0104 cm3 K = 2.8680 a= 0.5892 D= 187.9451 cm3 Kl= 6253.1255 kg/cm

Ic= 89322.9167 cm4 kc= 319.0104 cm3

f'c (kg/cm2) =

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K = 2.8680 a= 0.5892 D= 187.9451 cm3 Kl= 6253.1255 kg/cm

Ic= 89322.9167 cm4 kc= 297.7431 cm3 K = 3.0728 a= 0.7043 D= 209.7023 cm3 Kl= 6077.7499 kg/cm

207.50 cm

0.468 Tn

0.439 Tn

0.229 Tn

N hn Fs

3 280 cm 0.468 Tn

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2 280 cm 0.439 Tn

1 300 cm 0.229 Tn

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ANÁLISIS MÉTODO MUTTO - PÓRTICO 2-2

E= 217370.65 kg/cm2

R= 8

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

Ic= 89322.9167 cm4 kc= 319.0104 cm3 K = 4.0582 a= 0.6699 D= 213.6946 cm3 Kl= 7109.8360 kg/cm

Ic= 89322.9167 cm4 kc= 319.0104 cm3

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K = 4.0582 a= 0.6699 D= 213.6946 cm3 Kl= 7109.8360 kg/cm

Ic= 89322.9167 cm4 kc= 297.7431 cm3 K = 4.3480 a= 0.7637 D= 227.3883 cm3 Kl= 6590.3383 kg/cm

207.50 cm 500.00 cm

Qs Kl ∆re

0.468 Tn 32.420 Tn/cm 0.0144 cm

Page 55: Trabajo Final de Estructuras II(1)

0.907 Tn 32.420 Tn/cm 0.0280 cm

1.136 Tn 31.062 Tn/cm 0.0366 cm

Page 56: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO 2-2

VIGAS

25 cm 25 cm

35 cm

25 cm 25 cm

35 cm

25 cm 25 cm

35 cm

Ic= 89322.9167 cm4 Ic= kc= 319.0104 cm3 kc= K = 4.0931 K = a= 0.6718 a= D= 214.2991 cm3 D= Kl= 7129.9491 kg/cm Kl=

Ic= 89322.9167 cm4 Ic= kc= 319.0104 cm3 kc=

Page 57: Trabajo Final de Estructuras II(1)

K = 4.0931 K = a= 0.6718 a= D= 214.2991 cm3 D= Kl= 7129.9491 kg/cm Kl=

Ic= 89322.9167 cm4 Ic= kc= 297.7431 cm3 kc= K = 4.3855 K = a= 0.7651 a= D= 227.8012 cm3 D= Kl= 6602.3047 kg/cm Kl=

500.00 cm 205.00 cm

∆3e

∆2e

∆1e

∆tr ∆rr

0.0790 cm 0.0866 cm 0.4738 cm

∆te

Page 58: Trabajo Final de Estructuras II(1)

0.0645 cm 0.1678 cm 0.3872 cm

0.0366 cm 0.2194 cm 0.2194 cm

Page 59: Trabajo Final de Estructuras II(1)

VIGAS

25 cm

45 cm

Iv

45 cm

Iv189843.75 189843.75

Kv Kv914.90964 379.688

25 cm

45 cm

Iv

45 cm

Iv189843.75 189843.75

Kv Kv914.90964 379.688

25 cm

45 cm

Iv

45 cm

Iv189843.75 189843.75

Kv Kv914.90964 379.688

89322.9167 cm4 Ic= 89322.9167 cm4319.0104 cm3 kc= 319.0104 cm3

4.4387 K = 1.53570.6894 a= 0.4343

219.9186 cm3 D= 138.5618 cm37316.9160 kg/cm Kl= 4610.0908 kg/cm

89322.9167 cm4 Ic= 89322.9167 cm4319.0104 cm3 kc= 319.0104 cm3

Page 60: Trabajo Final de Estructuras II(1)

4.4387 K = 1.53570.6894 a= 0.4343

219.9186 cm3 D= 138.5618 cm37316.9160 kg/cm Kl= 4610.0908 kg/cm

89322.9167 cm4 Ic= 89322.9167 cm4297.7431 cm3 kc= 297.7431 cm3

4.7557 K = 1.64540.7780 a= 0.5885

231.6341 cm3 D= 175.2300 cm36713.3934 kg/cm Kl= 5078.6465 kg/cm

205.00 cm 387.50 cm

0.08 cm

0.06 cm

0.04 cm

D

0.00169

Page 61: Trabajo Final de Estructuras II(1)

0.00138

0.00073

Page 62: Trabajo Final de Estructuras II(1)

25 cm 25 cm

45 cm

lv189843.75

Kv926.067

25 cm 25 cm

45 cm

lv189843.75

Kv926.067

25 cm 25 cm

45 cm

lv189843.75

Kv926.067

280.00 cm

32.420 Tn/cm

Page 63: Trabajo Final de Estructuras II(1)

280.00 cm

32.420 Tn/cm

300.00 cm

31.062 Tn/cm

Page 64: Trabajo Final de Estructuras II(1)
Page 65: Trabajo Final de Estructuras II(1)

45 cm

lv189843.75

Kv489.919

45 cm

lv189843.75

Kv489.919

45 cm

lv189843.75

Kv489.919

Page 66: Trabajo Final de Estructuras II(1)
Page 67: Trabajo Final de Estructuras II(1)
Page 68: Trabajo Final de Estructuras II(1)
Page 69: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO A-A

DATOS:

210 kg/cm2

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

f'c (kg/cm2) =

Page 70: Trabajo Final de Estructuras II(1)

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 1.1306 a= 0.5209 D= 79.1245 cm3 Kl= 2293.2458 kg/cm

327.50 cm

0.084 Tn

0.079 Tn

0.041 Tn

N hn Fs Qs

3 280 cm 0.084 Tn 0.084 Tn

Page 71: Trabajo Final de Estructuras II(1)

2 280 cm 0.079 Tn 0.163 Tn

1 300 cm 0.041 Tn 0.204 Tn

Page 72: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO A-A

E= 217370.65 Kg/cm2

R= 8

35 cm 25 cm

30 cm25 cm

35 cm 25 cm

30 cm25 cm

35 cm 25 cm

30 cm25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 73: Trabajo Final de Estructuras II(1)

K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 2.1247 a= 0.6363 D= 96.6658 cm3 Kl= 2801.6408 kg/cm

327.50 cm 372.50 cm

Qs Kl ∆re

0.084 Tn 6.282 Tn/cm 0.0134 cm 0.0673 cm

∆te

Page 74: Trabajo Final de Estructuras II(1)

0.163 Tn 6.282 Tn/cm 0.0259 cm 0.0539 cm

0.204 Tn 7.292 Tn/cm 0.0280 cm 0.0280 cm

Page 75: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO A-A

VIGAS

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 0.9278

280.00 cm a= 0.3169 D= 51.5771 cm3 Kl= 1716.0231 kg/cm 6.282 Tn/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 76: Trabajo Final de Estructuras II(1)

K = 0.9278280.00 cm

a= 0.3169 D= 51.5771 cm3 Kl= 1716.0231 kg/cm 6.282 Tn/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 0.9941

300.00 cm a= 0.4990 D= 75.8041 cm3 Kl= 2197.0104 kg/cm 7.292 Tn/cm

372.50 cm

∆3e

∆2e

∆1e

∆tr ∆rr D

0.0673 cm 0.0803 cm 0.404 cm 0.00144

∆te

Page 77: Trabajo Final de Estructuras II(1)

0.0539 cm 0.1556 cm 0.324 cm 0.00116

0.0280 cm 0.1680 cm 0.168 cm 0.00056

Page 78: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO A-A

6.282 Tn/cm

Page 79: Trabajo Final de Estructuras II(1)

6.282 Tn/cm

7.292 Tn/cm

0.07 cm

0.05 cm

0.03 cm

D

0.00144

Page 80: Trabajo Final de Estructuras II(1)

0.00116

0.00056

Page 81: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO B-B

DATOS:

210 kg/cm2

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

f'c (kg/cm2) =

Page 82: Trabajo Final de Estructuras II(1)

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 1.1306 a= 0.5209 D= 79.1245 cm3 Kl= 2293.2458 kg/cm

327.50 cm

0.176 Tn

0.165 Tn

0.086 Tn

N hn Fs Qs

3 280 cm 0.176 Tn 0.176 Tn

Page 83: Trabajo Final de Estructuras II(1)

2 280 cm 0.165 Tn 0.341 Tn

1 300 cm 0.086 Tn 0.428 Tn

Page 84: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO B-B

E= 217370.65 Kg/cm2

R= 8

35 cm 25 cm

30 cm25 cm

35 cm 25 cm

30 cm25 cm

35 cm 25 cm

30 cm25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 85: Trabajo Final de Estructuras II(1)

K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 2.1247 a= 0.6363 D= 96.6658 cm3 Kl= 2801.6408 kg/cm

327.50 cm 372.50 cm

Qs Kl ∆re

0.176 Tn 6.282 Tn/cm 0.0280 cm 0.1411 cm

∆te

Page 86: Trabajo Final de Estructuras II(1)

0.341 Tn 6.282 Tn/cm 0.0543 cm 0.1130 cm

0.428 Tn 7.292 Tn/cm 0.0587 cm 0.0587 cm

Page 87: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO B-B

VIGAS

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 0.9278

280.00 cm a= 0.3169 D= 51.5771 cm3 Kl= 1716.0231 kg/cm 6.282 Tn/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 88: Trabajo Final de Estructuras II(1)

K = 0.9278280.00 cm

a= 0.3169 D= 51.5771 cm3 Kl= 1716.0231 kg/cm 6.282 Tn/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 0.9941

300.00 cm a= 0.4990 D= 75.8041 cm3 Kl= 2197.0104 kg/cm 7.292 Tn/cm

372.50 cm

∆3e

∆2e

∆1e

∆tr ∆rr D

0.1411 cm 0.1682 cm 0.8464 cm 0.00302

∆te

Page 89: Trabajo Final de Estructuras II(1)

0.1130 cm 0.3261 cm 0.6781 cm 0.00242

0.0587 cm 0.3521 cm 0.3521 cm 0.00117

Page 90: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO B-B

6.282 Tn/cm

Page 91: Trabajo Final de Estructuras II(1)

6.282 Tn/cm

7.292 Tn/cm

0.14 cm

0.11 cm

0.06 cm

D

0.00302

Page 92: Trabajo Final de Estructuras II(1)

0.00242

0.00117

Page 93: Trabajo Final de Estructuras II(1)
Page 94: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO D-D

DATOS:

210 kg/cm2

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

f'c (kg/cm2) =

Page 95: Trabajo Final de Estructuras II(1)

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 1.1306 a= 0.5209 D= 79.1245 cm3 Kl= 2293.2458 kg/cm

327.50 cm

0.084 Tn

0.079 Tn

0.041 Tn

N hn Fs Qs

3 280 cm 0.084 Tn 0.084 Tn

Page 96: Trabajo Final de Estructuras II(1)

2 280 cm 0.079 Tn 0.163 Tn

1 300 cm 0.041 Tn 0.204 Tn

Page 97: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO D-D

E= 217370.65 Kg/cm2

R= 8

35 cm 25 cm

30 cm25 cm

35 cm 25 cm

30 cm25 cm

35 cm 25 cm

30 cm25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 98: Trabajo Final de Estructuras II(1)

K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 2.1247 a= 0.6363 D= 96.6658 cm3 Kl= 2801.6408 kg/cm

327.50 cm 372.50 cm

Qs Kl ∆re

0.084 Tn 6.282 Tn/cm 0.0134 cm 0.0673 cm

∆te

Page 99: Trabajo Final de Estructuras II(1)

0.163 Tn 6.282 Tn/cm 0.0259 cm 0.0539 cm

0.204 Tn 7.292 Tn/cm 0.0280 cm 0.0280 cm

Page 100: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO D-D

VIGAS

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 0.9278

280.00 cm a= 0.3169 D= 51.5771 cm3 Kl= 1716.0231 kg/cm 6.282 Tn/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 101: Trabajo Final de Estructuras II(1)

K = 0.9278280.00 cm

a= 0.3169 D= 51.5771 cm3 Kl= 1716.0231 kg/cm 6.282 Tn/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 0.9941

300.00 cm a= 0.4990 D= 75.8041 cm3 Kl= 2197.0104 kg/cm 7.292 Tn/cm

372.50 cm

∆3e

∆2e

∆1e

∆tr ∆rr D

0.0673 cm 0.0803 cm 0.4040 cm 0.00144

∆te

Page 102: Trabajo Final de Estructuras II(1)

0.0539 cm 0.1556 cm 0.3237 cm 0.00116

0.0280 cm 0.1680 cm 0.1680 cm 0.00056

Page 103: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO D-D

6.282 Tn/cm

Page 104: Trabajo Final de Estructuras II(1)

6.282 Tn/cm

7.292 Tn/cm

0.07 cm

0.05 cm

0.03 cm

D

0.00144

Page 105: Trabajo Final de Estructuras II(1)

0.00116

0.00056

Page 106: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO E-E

DATOS:

210 kg/cm2

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

35 cm 35 cm

25 cm 25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

f'c (kg/cm2) =

Page 107: Trabajo Final de Estructuras II(1)

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 1.1306 a= 0.5209 D= 79.1245 cm3 Kl= 2293.2458 kg/cm

327.50 cm

0.176 Tn

0.165 Tn

0.086 Tn

N hn Fs Qs

3 280 cm 0.176 Tn 0.176 Tn

Page 108: Trabajo Final de Estructuras II(1)

2 280 cm 0.165 Tn 0.341 Tn

1 300 cm 0.086 Tn 0.428 Tn

Page 109: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO E-E

E= 217370.65 Kg/cm2

R= 8

150 cm 25 cm

30 cm25 cm

150 cm 25 cm

30 cm25 cm

150 cm 25 cm

30 cm25 cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 162.7604 cm3

Page 110: Trabajo Final de Estructuras II(1)

K = 1.9831 a= 0.4979 D= 81.0339 cm3 Kl= 2696.0817 kg/cm

Ic= 45572.9167 cm4 kc= 151.9097 cm3 K = 2.1247 a= 0.6363 D= 96.6658 cm3 Kl= 2801.6408 kg/cm

327.50 cm 372.50 cm

Qs Kl ∆re

0.176 Tn 6.833 Tn/cm 0.0258 cm 0.1137 cm

∆te

Page 111: Trabajo Final de Estructuras II(1)

0.341 Tn 6.833 Tn/cm 0.0500 cm 0.0879 cm

0.428 Tn 11.283 Tn/cm 0.0379 cm 0.0379 cm

Page 112: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO E-E

VIGAS

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

30 cm

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 195312.5000 cm4 kc= 697.5446 cm3 K = 0.2165

280.00 cm a= 0.0977 D= 68.1290 cm3 Kl= 2266.7201 kg/cm 6.833 Tn/cm

Ic= 195312.5000 cm4 kc= 697.5446 cm3

Page 113: Trabajo Final de Estructuras II(1)

K = 0.2165280.00 cm

a= 0.0977 D= 68.1290 cm3 Kl= 2266.7201 kg/cm 6.833 Tn/cm

Ic= 195312.5000 cm4 kc= 651.0417 cm3 K = 0.2319

300.00 cm a= 0.3279 D= 213.5031 cm3 Kl= 6187.9089 kg/cm 11.283 Tn/cm

372.50 cm

∆3e

∆2e

∆1e

∆tr ∆rr D

0.1137 cm 0.1547 cm 0.6820 cm 0.00244

∆te

Page 114: Trabajo Final de Estructuras II(1)

0.0879 cm 0.2998 cm 0.5273 cm 0.00188

0.0379 cm 0.2275 cm 0.2275 cm 0.00076

Page 115: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MUTTO - PÓRTICO E-E

6.833 Tn/cm

Page 116: Trabajo Final de Estructuras II(1)

6.833 Tn/cm

11.283 Tn/cm

0.11 cm

0.09 cm

0.04 cm

D

0.00244

Page 117: Trabajo Final de Estructuras II(1)

0.00188

0.00076

Page 118: Trabajo Final de Estructuras II(1)

METRADO DE CARGAS

1.638 m

A1

1.638 m

1.863 m

1.863 m

1.038 m 1.038 m

# Pisos 3hi 3.00 mht 2.80 m

δCA 2400 kg/m3s/c1 200 kg/m2s/c2 200 kg/m2s/c3 200 kg/m2

s/c(azotea) 100 kg/m2δ Tab. Repartida 130 kg/m2δ Lad. Pandereta 1350 kg/m2

δ Cobertura 100 kg/m2δ Enlucido 80 kg/m2

δ Contrapiso 80 kg/m2

1

2

3

A B

Page 119: Trabajo Final de Estructuras II(1)

PÓRTICO A-A, B-B, D-D, E-E

0.180 = CM0.000 = CV

2.80 m

0.391 = CM0.000 = CV

2.80 m

0.391 = CM0.000 = CV

3.00 m

3.275 m

Page 120: Trabajo Final de Estructuras II(1)

METRADO DE CARGAS

A2 A3

A12A13

2.500 m 2.500 m 1.025 m

0.35 m

C 0.25 m P2

1.50 m

P1 0.25 m P3

B C

Page 121: Trabajo Final de Estructuras II(1)

0.180 = CM 0.180 = CM0.000 = CV 0.000 = CV

0.391 = CM 0.391 = CM0.000 = CV 0.000 = CV

0.391 = CM 0.391 = CM0.000 = CV 0.000 = CV

3.275 m 3.725 m

Page 122: Trabajo Final de Estructuras II(1)

METRADO DE CARGAS

A3 A4

A14

1.025 m 1.938 m 1.938 m

0.25 m 0.25 m

0.45 m2.30 m VP

1.50 m 0.25 m

0.30 m0.25 m VS

D E

Page 123: Trabajo Final de Estructuras II(1)

COMBOS W1 W2

COMBO 1 0.54684 0.54684

COMBO 2 Y 3 0.48825 0.48825

COMBO 4 Y 5 0.35154 0.35154

Page 124: Trabajo Final de Estructuras II(1)

A5

1.125 m

0.738 m

A16

E

Page 125: Trabajo Final de Estructuras II(1)

W2 W3

0.54684 0.252

0.48825 0.225

0.35154 0.162

Page 126: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 1

f'c= 210

E= 2173706.51

0.0000

0.0000

0.0000

3.275

A

1

4

714

12

10

7

4

1

Page 127: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

0.54684

3.275

R= 0.895M= 0.489

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 128: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

0.54684

3.275

R= 0.895M= 0.489

ELEMENTO N° 14

0.252

3.275

R= 0.413M= 0.225

0.225238125

0

-0.41265

0.488766731

Page 129: Trabajo Final de Estructuras II(1)

0-0.8954505

0.488766731

0-0.8954505

Page 130: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.77 0.00

0.00 440.28

0.00 660.41

-63399.77 0.00

0.00 -440.28

0.00 660.41

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 131: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.77 0.00

0.00 440.28

0.00 660.41

-63399.77 0.00

0.00 -440.28

0.00 660.41

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.77 0.00

0.00 440.28

0.00 660.41

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 132: Trabajo Final de Estructuras II(1)

-63399.77 0.00

0.00 -440.28

0.00 660.41

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.3 0.0

0.0 541.5

0.0 758.1

-67928.3 0.0

0.0 -541.5

0.0 758.1

COORDENADAS GLOBALES

541.50.0

-758.1

-541.5

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 133: Trabajo Final de Estructuras II(1)

0.0-758.1

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 134: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.33 0.00

0.00 541.52

0.00 758.13

-67928.33 0.00

0.00 -541.52

0.00 758.13

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 135: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.33 0.00

0.00 541.52

0.00 758.13

-67928.33 0.00

0.00 -541.52

0.00 758.13

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 136: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 137: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.5 0.0

0.0 417.7

0.0 684.0

-49779.5 0.0

0.0 -417.7

0.0 684.0

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 138: Trabajo Final de Estructuras II(1)

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 139: Trabajo Final de Estructuras II(1)

0.0

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 140: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 141: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 142: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 143: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 144: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 145: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 146: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 147: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 148: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 149: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.00000

Page 150: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.00

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.00

T =

1 00 10 0

Page 151: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.000

T =

1 00 10 00 00 00 0

Page 152: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.00-0.06-0.13

+0.000.06

Page 153: Trabajo Final de Estructuras II(1)

F' =

-0.08

ELEMENTO 12

F' =

0.00-0.04-0.10

+0.000.04-0.05

ELEMENTO 14

F' =

0.00-0.02-0.06

+0.000.02-0.02

N hn ∆re

3 2.80 cm -0.0001 cm

2 2.80 cm 0.0000 cm

1 3.00 cm 0.0000 cm

Page 154: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 1

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 155: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 0.0000Uz2 0.0000Uz3 0.0000

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

0.54684

3.275

R= 0.895 R=M= 0.489 M=

Page 156: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.54684

3.275

R= 0.895 R=M= 0.489 M=

ELEMENTO N° 15

0.252

3.275

R= 0.413 R=M= 0.225 M=

-0.06615 0.29139

-0.882

-0.1435455 0.63231

Page 157: Trabajo Final de Estructuras II(1)

-1.91394

-0.1435455 0.63231

-1.91394

-0.9-0.5-1.9-0.1-1.00.6-0.9-0.5-1.9

F= -0.1-1.00.6-0.4-0.2-0.9-0.1-0.50.30.00.00.0

Page 158: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0.00 -63399.77 0.00

660.41 0.00 -440.28

1320.83 0.00 -660.41

0.00 63399.77 0.00

-660.41 0.00 440.28

660.41 0.00 -660.41

440.28 0.00 660.410.00 63399.77 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 159: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0.00 -63399.77 0.00

660.41 0.00 -440.28

1320.83 0.00 -660.41

0.00 63399.77 0.00

-660.41 0.00 440.28

660.41 0.00 -660.41

440.28 0.00 660.410.00 63399.77 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0.00 -63399.77 0.00

660.41 0.00 -440.28

1320.83 0.00 -660.41

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 160: Trabajo Final de Estructuras II(1)

0.00 63399.77 0.00

-660.41 0.00 440.28

660.41 0.00 -660.41

440.28 0.00 660.410.00 63399.77 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0.0 -67928.3 0.0

758.1 0.0 -541.5

1415.2 0.0 -758.1

0.0 67928.3 0.0

-758.1 0.0 541.5

707.6 0.0 -758.1

0.0 -758.167928.3 0.0

0.0 1415.2

0.0 758.1

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 161: Trabajo Final de Estructuras II(1)

-67928.3 0.00.0 707.6

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 162: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0.00 -67928.33 0.00

758.13 0.00 -541.52

1415.17 0.00 -758.13

0.00 67928.33 0.00

-758.13 0.00 541.52

707.59 0.00 -758.13

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 163: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0.00 -67928.33 0.00

758.13 0.00 -541.52

1415.17 0.00 -758.13

0.00 67928.33 0.00

-758.13 0.00 541.52

707.59 0.00 -758.13

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 164: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 165: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0.0 -49779.5 0.0

684.0 0.0 -417.7

1493.4 0.0 -684.0

0.0 49779.5 0.0

-684.0 0.0 417.7

746.7 0.0 -684.0

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 166: Trabajo Final de Estructuras II(1)

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 167: Trabajo Final de Estructuras II(1)

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 168: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 169: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 170: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 171: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 172: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 173: Trabajo Final de Estructuras II(1)

U1y -0.000033Ɵ1x -0.000098U2y -0.000078Ɵ2x -0.000025U3y -0.000038Ɵ3x 0.000149U4y -0.000051Ɵ4x -0.000087U5y -0.000121Ɵ5x -0.000021U6y = -0.000059Ɵ6x 0.000129U7y -0.000057Ɵ7x -0.000067U8y -0.000135Ɵ8x -0.000016U9y -0.000065Ɵ9x 0.000095Uz1 -0.000013Uz2 -0.000035Uz3 -0.000050

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 174: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 175: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 176: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 177: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 178: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 179: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 180: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.00000.90 0.83050.49

=0.3550

0.00 0.00000.90 0.9604

Page 181: Trabajo Final de Estructuras II(1)

0.49 0.4097

0.00 0.00000.90 0.85060.49

=0.3909

0.00 0.00000.90 0.94030.49 0.4399

0.00 0.00000.41 0.38870.23

=0.1673

0.00 0.00000.41 0.43660.23 0.2048

∆tr ∆rr

0.0000 cm -0.0003 cm -0.0001 cm

0.0000 cm -0.0002 cm -0.0001 cm

0.0000 cm -0.0001 cm -0.0001 cm

∆te

Page 182: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 1

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 183: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

0.54684

3.725

1.018 R= 1.0180.632 M= 0.632

Page 184: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.54684

3.725

1.018 R= 1.0180.632 M= 0.632

ELEMENTO N° 15

0.252

3.725

0.469 R= 0.4690.291 M= 0.291

-0.46935

Page 185: Trabajo Final de Estructuras II(1)

-1.0184895

-1.0184895

Page 186: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0.00

660.41

660.41

0.00

-660.41

1320.83

63399.773

440.276

660.414

1320.829

Page 187: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0.00

660.41

660.41

0.00

-660.41

1320.83

63399.773

440.276

660.414

1320.829

660.414

0.00

660.41

660.41

Page 188: Trabajo Final de Estructuras II(1)

0.00

-660.41

1320.83

0.0

758.1

707.6

0.0

-758.1

1415.2

-541.5 0.0 -758.10.0 -67928.3 0.0

758.1 0.0 707.6

541.5 0.0 758.1

Page 189: Trabajo Final de Estructuras II(1)

0.0 67928.3 0.0758.1 0.0 1415.2

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 190: Trabajo Final de Estructuras II(1)

0.00

758.13

707.59

0.00

-758.13

1415.17

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 191: Trabajo Final de Estructuras II(1)

0.00

758.13

707.59

0.00

-758.13

1415.17

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 192: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 193: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0.0

684.0

746.7

0.0

-684.0

1493.4

Page 194: Trabajo Final de Estructuras II(1)

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.7

Page 195: Trabajo Final de Estructuras II(1)

0.0 -528.7 1313.0

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 196: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

Page 197: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 198: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 199: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 200: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 201: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z 0.0000u1y 0.0000u1x -0.0001

F' =

F'ay 2.07

Page 202: Trabajo Final de Estructuras II(1)

F' =

F'az -0.07F'ax -0.07F'1y -2.07F'1z 0.07F'1x -0.14

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z 0.0000u2y -0.0001u2x 0.0000

F' =

F'by 4.96F'bz -0.02F'bx -0.03F'2y -4.96F'2z 0.02F'2x -0.04

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z 0.0000u3y 0.0000u3x 0.0001

F' =

F'cy 2.39F'cz 0.09F'cx 0.09F'3y -2.39

Page 203: Trabajo Final de Estructuras II(1)

F' =F'3z -0.09F'3x 0.19

u =

u1z 0.0000

u' =

u1y 0.0000u1x -0.0001u4z 0.0000u4y -0.0001u4x -0.0001

F' =

F'1y 1.24F'1z -0.15F'1x -0.22F'4y -1.24F'4z 0.15F'4x -0.21

u =

u2z 0.0000

u' =

u2y -0.0001u2x 0.0000u5z 0.0000u5y -0.0001u5x 0.0000

F' =

F'2y 2.93F'2z -0.05F'2x -0.07F'5y -2.93F'5z 0.05F'5x -0.06

Page 204: Trabajo Final de Estructuras II(1)

u =

u3z 0.0000

u' =

u3y 0.0000u3x 0.0001u6z 0.0000u6y -0.0001u6x 0.0001

F' =

F'3y 1.43F'3z 0.20F'3x 0.29F'6y -1.43F'6z -0.20F'6x 0.27

u =

u4z 0.0000

u' =

u4y -0.0001u4x -0.0001u7z -0.0001u7y -0.0001u7x -0.0001

F' =

F'4y 0.39F'4z -0.12F'4x -0.18F'7y -0.39F'7z 0.12F'7x -0.17

Page 205: Trabajo Final de Estructuras II(1)

u =

u5z 0.0000

u' =

u5y -0.0001u5x 0.0000u8z -0.0001u8y -0.0001u8x 0.0000

F' =

F'5y 0.93F'5z -0.04F'5x -0.05F'8y -0.93F'8z 0.04F'8x -0.05

u =

u6z 0.0000

u' =

u6y -0.0001u6x 0.0001u9z -0.0001u9y -0.0001u9x 0.0001

F' =

F'6y 0.45F'6z 0.16F'6x 0.24F'9y -0.45F'9z -0.16F'9x 0.21

Page 206: Trabajo Final de Estructuras II(1)

u =

u1z 0.0000

u' =

u1y 0.0000u1x -0.0001u2z 0.0000u2y -0.0001u2x 0.0000

F' =

F'1y 0.00F'1z -0.06F'1x -0.13F'2y 0.00F'2z 0.06F'2x -0.08

u =

u2z 0.0000

u' =

u2y -0.0001u2x 0.0000u3z 0.0000u3y 0.0000u3x 0.0001

F' =

F'2y 0.00F'2z 0.05F'2x 0.04F'3y 0.00F'3z -0.05F'3x 0.16

u =

u4z 0.0000

u' =

u4y -0.0001u4x -0.0001

Page 207: Trabajo Final de Estructuras II(1)

u = u5z 0.0000 u' =u5y -0.0001u5x 0.0000

F' =

F'4y 0.00F'4z -0.04F'4x -0.10F'5y 0.00F'5z 0.04F'5x -0.05

u =

u5z 0.0000

u' =

u5y -0.0001u5x 0.0000u6z 0.0000u6y -0.0001u6x 0.0001

F' =

F'5y 0.00F'5z 0.04F'5x 0.02F'6y 0.00F'6z -0.04F'6x 0.12

u =

u7z -0.0001

u' =

u7y -0.0001u7x -0.0001u8z -0.0001u8y -0.0001u8x 0.0000

Page 208: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z -0.02F'7x -0.06F'8y 0.00F'8z 0.02F'8x -0.02

u =

u8z -0.0001

u' =

u8y -0.0001u8x 0.0000u9z -0.0001u9y -0.0001u9x 0.0001

F' =

F'8y 0.00F'8z 0.02F'8x 0.00F'9y 0.00F'9z -0.02F'9x 0.08

ELEMENTO 11

F' =

0.00 0.000.05 1.020.04

+0.63

0.00 0.00-0.05 1.02

Page 209: Trabajo Final de Estructuras II(1)

F' =

0.16 0.63

ELEMENTO 13

F' =

0.00 0.000.04 1.020.02

+0.63

0.00 0.00-0.04 1.020.12 0.63

ELEMENTO 15

F' =

0.00 0.000.02 0.470.00

+0.29

0.00 0.00-0.02 0.470.08 0.29

∆rr D

-0.0001 cm -0.00003

-0.0001 cm -0.00005

-0.0001 cm -0.00003

Page 210: Trabajo Final de Estructuras II(1)
Page 211: Trabajo Final de Estructuras II(1)
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Page 214: Trabajo Final de Estructuras II(1)
Page 215: Trabajo Final de Estructuras II(1)
Page 216: Trabajo Final de Estructuras II(1)
Page 217: Trabajo Final de Estructuras II(1)
Page 218: Trabajo Final de Estructuras II(1)
Page 219: Trabajo Final de Estructuras II(1)
Page 220: Trabajo Final de Estructuras II(1)
Page 221: Trabajo Final de Estructuras II(1)
Page 222: Trabajo Final de Estructuras II(1)
Page 223: Trabajo Final de Estructuras II(1)
Page 224: Trabajo Final de Estructuras II(1)
Page 225: Trabajo Final de Estructuras II(1)
Page 226: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 227: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

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0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

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u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y 0.0000u'1z 0.0000u'1x -0.0001

Page 230: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0001u'2z 0.0000u'2x 0.0000

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y 0.0000u'3z 0.0000u'3x 0.0001

Page 231: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z 0.0000u'1x -0.0001u'4y -0.0001u'4z 0.0000u'4x -0.0001

u'2y -0.0001u'2z 0.0000u'2x 0.0000u'5y -0.0001u'5z 0.0000u'5x 0.0000

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u'3y 0.0000u'3z 0.0000u'3x 0.0001u'6y -0.0001u'6z 0.0000u'6x 0.0001

u'4y -0.0001u'4z 0.0000u'4x -0.0001u'7y -0.0001u'7z 0.0001u'7x -0.0001

Page 233: Trabajo Final de Estructuras II(1)

u'5y -0.0001u'5z 0.0000u'5x 0.0000u'8y -0.0001u'8z 0.0001u'8x 0.0000

u'6y -0.0001u'6z 0.0000u'6x 0.0001u'9y -0.0001u'9z 0.0001u'9x 0.0001

Page 234: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z 0.0000u'1x -0.0001u'2y 0.0000u'2z -0.0001u'2x 0.0000

u'2y 0.0000u'2z -0.0001u'2x 0.0000u'3y 0.0000u'3z 0.0000u'3x 0.0001

u'4y 0.0000u'4z -0.0001u'4x -0.0001

Page 235: Trabajo Final de Estructuras II(1)

u'5y 0.0000u'5z -0.0001u'5x 0.0000

u'5y 0.0000u'5z -0.0001u'5x 0.0000u'6y 0.0000u'6z -0.0001u'6x 0.0001

u'7y -0.0001u'7z -0.0001u'7x -0.0001u'8y -0.0001u'8z -0.0001u'8x 0.0000

Page 236: Trabajo Final de Estructuras II(1)

u'8y -0.0001u'8z -0.0001u'8x 0.0000u'9y -0.0001u'9z -0.0001u'9x 0.0001

0.00001.0727

=0.67620.00000.9642

Page 237: Trabajo Final de Estructuras II(1)

0.7905

0.00001.0576

=0.65580.00000.97930.7546

0.00000.4912

=0.29550.00000.44750.3686

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7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

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0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

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8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 283: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

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ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 2

f'c= 210

E= 2173706.51

0.0841

0.0789

0.0412

3.275

A

1

4

714

12

10

7

4

1

Page 295: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

0.48825

3.275

R= 0.800M= 0.436

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 296: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

0.48825

3.275

R= 0.800M= 0.436

ELEMENTO N° 14

0.225

3.275

R= 0.368M= 0.201

0.201105469

0.0840777207

-0.3684375

0.436398867

Page 297: Trabajo Final de Estructuras II(1)

0.0788782281-0.799509375

0.436398867

0.0412495515-0.799509375

Page 298: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.77 0.00

0.00 440.28

0.00 660.41

-63399.77 0.00

0.00 -440.28

0.00 660.41

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 299: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.77 0.00

0.00 440.28

0.00 660.41

-63399.77 0.00

0.00 -440.28

0.00 660.41

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.77 0.00

0.00 440.28

0.00 660.41

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 300: Trabajo Final de Estructuras II(1)

-63399.77 0.00

0.00 -440.28

0.00 660.41

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.33 0.00

0.00 541.52

0.00 758.13

-67928.33 0.00

0.00 -541.52

0.00 758.13

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 301: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 302: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 303: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 304: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 305: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 306: Trabajo Final de Estructuras II(1)

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 307: Trabajo Final de Estructuras II(1)

0.0

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 308: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 309: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 310: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 311: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 312: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 313: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 314: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 315: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 316: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 317: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.000

Page 318: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.000

T =

1 00 10 0

Page 319: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.000

T =

1 00 10 00 00 00 0

Page 320: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.00-0.13-0.25

+0.000.13

Page 321: Trabajo Final de Estructuras II(1)

F' =

-0.18

ELEMENTO 12

F' =

0.00-0.09-0.18

+0.000.09-0.13

ELEMENTO 14

F' =

0.00-0.04-0.09

+0.000.04-0.05

N hn ∆re

3 2.80 cm 0.0006 cm

2 2.80 cm 0.0005 cm

1 3.00 cm 0.0002 cm

Page 322: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 2

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 323: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 0.0412Uz2 0.0789Uz3 0.0841

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

0.48825

3.275

R= 0.800 R=M= 0.436 M=

Page 324: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.48825

3.275

R= 0.800 R=M= 0.436 M=

ELEMENTO N° 15

0.225

3.275

R= 0.368 R=M= 0.201 M=

-0.0590625 0.260167969

-0.7875

-0.128165625 0.564564492

Page 325: Trabajo Final de Estructuras II(1)

-1.708875

-0.128165625 0.564564492

-1.708875

-0.8-0.4-1.7-0.1-0.90.6-0.8-0.4-1.7

F= -0.1-0.90.6-0.4-0.2-0.8-0.1-0.40.30.00.10.1

Page 326: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0.00 -63399.77 0.00

660.41 0.00 -440.28

1320.83 0.00 -660.41

0.00 63399.77 0.00

-660.41 0.00 440.28

660.41 0.00 -660.41

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 327: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0.00 -63399.77 0.00

660.41 0.00 -440.28

1320.83 0.00 -660.41

0.00 63399.77 0.00

-660.41 0.00 440.28

660.41 0.00 -660.41

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0.00 -63399.77 0.00

660.41 0.00 -440.28

1320.83 0.00 -660.41

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 328: Trabajo Final de Estructuras II(1)

0.00 63399.77 0.00

-660.41 0.00 440.28

660.41 0.00 -660.41

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0.00 -67928.33 0.00

758.13 0.00 -541.52

1415.17 0.00 -758.13

0.00 67928.33 0.00

-758.13 0.00 541.52

707.59 0.00 -758.13

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 329: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 330: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 331: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 332: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 333: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 334: Trabajo Final de Estructuras II(1)

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 335: Trabajo Final de Estructuras II(1)

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 336: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 337: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 338: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 339: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 340: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 341: Trabajo Final de Estructuras II(1)

U1y -0.000027Ɵ1x -0.000155U2y -0.000070Ɵ2x -0.000064U3y -0.000036Ɵ3x 0.000063U4y -0.000042Ɵ4x -0.000125U5y -0.000109Ɵ5x -0.000053U6y = -0.000055Ɵ6x 0.000066U7y -0.000047Ɵ7x -0.000082U8y -0.000121Ɵ8x -0.000027U9y -0.000061Ɵ9x 0.000061Uz1 0.000232Uz2 0.000458Uz3 0.000584

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 342: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 343: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 344: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 345: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 346: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 347: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 348: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.00000.80 0.66840.44

=0.1877

0.00 0.00000.80 0.9306

Page 349: Trabajo Final de Estructuras II(1)

0.44 0.2558

0.00 0.00000.80 0.70560.44

=0.2556

0.00 0.00000.80 0.89340.44 0.3097

0.00 0.00000.37 0.32460.20

=0.1089

0.00 0.00000.37 0.41230.20 0.1497

∆tr ∆rr

0.0001 cm 0.0035 cm 0.0008 cm

0.0002 cm 0.0027 cm 0.0014 cm

0.0002 cm 0.0014 cm 0.0014 cm

∆te

Page 350: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 2

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 351: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

0.48825

3.725

0.909 R= 0.9090.565 M= 0.565

Page 352: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.48825

3.725

0.909 R= 0.9090.565 M= 0.565

ELEMENTO N° 15

0.225

3.725

0.419 R= 0.4190.260 M= 0.260

-0.4190625

Page 353: Trabajo Final de Estructuras II(1)

-0.909365625

-0.909365625

Page 354: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0.00

660.41

660.41

0.00

-660.41

1320.83

63399.773

440.276

660.414

1320.829

Page 355: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0.00

660.41

660.41

0.00

-660.41

1320.83

63399.773

440.276

660.414

1320.829

660.414

0.00

660.41

660.41

Page 356: Trabajo Final de Estructuras II(1)

0.00

-660.41

1320.83

0.00

758.13

707.59

0.00

-758.13

1415.17

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 357: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 358: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 359: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 360: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 361: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 362: Trabajo Final de Estructuras II(1)

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.7

Page 363: Trabajo Final de Estructuras II(1)

0.0 -528.7 1313.0

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 364: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

Page 365: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 366: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 367: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 368: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 369: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z 0.0002u1y 0.0000u1x -0.0002

F' =

F'ay 1.70

Page 370: Trabajo Final de Estructuras II(1)

F' =

F'az 0.00F'ax 0.05F'1y -1.70F'1z 0.00F'1x -0.05

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z 0.0002u2y -0.0001u2x -0.0001

F' =

F'by 4.46F'bz 0.06F'bx 0.11F'2y -4.46F'2z -0.06F'2x 0.07

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z 0.0002u3y 0.0000u3x 0.0001

F' =

F'cy 2.26F'cz 0.14F'cx 0.19F'3y -2.26

Page 371: Trabajo Final de Estructuras II(1)

F' =F'3z -0.14F'3x 0.24

u =

u1z 0.0002

u' =

u1y 0.0000u1x -0.0002u4z 0.0005u4y 0.0000u4x -0.0001

F' =

F'1y 1.03F'1z -0.09F'1x -0.14F'4y -1.03F'4z 0.09F'4x -0.12

u =

u2z 0.0002

u' =

u2y -0.0001u2x -0.0001u5z 0.0005u5y -0.0001u5x -0.0001

F' =

F'2y 2.63F'2z 0.03F'2x 0.04F'5y -2.63F'5z -0.03F'5x 0.05

Page 372: Trabajo Final de Estructuras II(1)

u =

u3z 0.0002

u' =

u3y 0.0000u3x 0.0001u6z 0.0005u6y -0.0001u6x 0.0001

F' =

F'3y 1.34F'3z 0.22F'3x 0.31F'6y -1.34F'6z -0.22F'6x 0.31

u =

u4z 0.0005

u' =

u4y 0.0000u4x -0.0001u7z 0.0006u7y 0.0000u7x -0.0001

F' =

F'4y 0.32F'4z -0.09F'4x -0.14F'7y -0.32F'7z 0.09F'7x -0.11

Page 373: Trabajo Final de Estructuras II(1)

u =

u5z 0.0005

u' =

u5y -0.0001u5x -0.0001u8z 0.0006u8y -0.0001u8x 0.0000

F' =

F'5y 0.83F'5z 0.01F'5x 0.00F'8y -0.83F'8z -0.01F'8x 0.02

u =

u6z 0.0005

u' =

u6y -0.0001u6x 0.0001u9z 0.0006u9y -0.0001u9x 0.0001

F' =

F'6y 0.42F'6z 0.17F'6x 0.23F'9y -0.42F'9z -0.17F'9x 0.23

Page 374: Trabajo Final de Estructuras II(1)

u =

u1z 0.0002

u' =

u1y 0.0000u1x -0.0002u2z 0.0002u2y -0.0001u2x -0.0001

F' =

F'1y 0.00F'1z -0.13F'1x -0.25F'2y 0.00F'2z 0.13F'2x -0.18

u =

u2z 0.0002

u' =

u2y -0.0001u2x -0.0001u3z 0.0002u3y 0.0000u3x 0.0001

F' =

F'2y 0.00F'2z -0.01F'2x -0.06F'3y 0.00F'3z 0.01F'3x 0.02

u =

u4z 0.0005

u' =

u4y 0.0000u4x -0.0001

Page 375: Trabajo Final de Estructuras II(1)

u = u5z 0.0005 u' =u5y -0.0001u5x -0.0001

F' =

F'4y 0.00F'4z -0.09F'4x -0.18F'5y 0.00F'5z 0.09F'5x -0.13

u =

u5z 0.0005

u' =

u5y -0.0001u5x -0.0001u6z 0.0005u6y -0.0001u6x 0.0001

F' =

F'5y 0.00F'5z -0.01F'5x -0.05F'6y 0.00F'6z 0.01F'6x 0.02

u =

u7z 0.0006

u' =

u7y 0.0000u7x -0.0001u8z 0.0006u8y -0.0001u8x 0.0000

Page 376: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z -0.04F'7x -0.09F'8y 0.00F'8z 0.04F'8x -0.05

u =

u8z 0.0006

u' =

u8y -0.0001u8x 0.0000u9z 0.0006u9y -0.0001u9x 0.0001

F' =

F'8y 0.00F'8z 0.00F'8x -0.03F'9y 0.00F'9z 0.00F'9x 0.03

ELEMENTO 11

F' =

0.00 0.00-0.01 0.91-0.06

+0.56

0.00 0.000.01 0.91

Page 377: Trabajo Final de Estructuras II(1)

F' =

0.02 0.56

ELEMENTO 13

F' =

0.00 0.00-0.01 0.91-0.05

+0.56

0.00 0.000.01 0.910.02 0.56

ELEMENTO 15

F' =

0.00 0.000.00 0.42-0.03

+0.26

0.00 0.000.00 0.420.03 0.26

∆rr D

0.0008 cm 0.00027

0.0014 cm 0.00048

0.0014 cm 0.00046

Page 378: Trabajo Final de Estructuras II(1)
Page 379: Trabajo Final de Estructuras II(1)
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Page 381: Trabajo Final de Estructuras II(1)
Page 382: Trabajo Final de Estructuras II(1)
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Page 384: Trabajo Final de Estructuras II(1)
Page 385: Trabajo Final de Estructuras II(1)
Page 386: Trabajo Final de Estructuras II(1)
Page 387: Trabajo Final de Estructuras II(1)
Page 388: Trabajo Final de Estructuras II(1)
Page 389: Trabajo Final de Estructuras II(1)
Page 390: Trabajo Final de Estructuras II(1)
Page 391: Trabajo Final de Estructuras II(1)
Page 392: Trabajo Final de Estructuras II(1)
Page 393: Trabajo Final de Estructuras II(1)
Page 394: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 395: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 396: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 397: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y 0.0000u'1z -0.0002u'1x -0.0002

Page 398: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0001u'2z -0.0002u'2x -0.0001

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y 0.0000u'3z -0.0002u'3x 0.0001

Page 399: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z -0.0002u'1x -0.0002u'4y 0.0000u'4z -0.0005u'4x -0.0001

u'2y -0.0001u'2z -0.0002u'2x -0.0001u'5y -0.0001u'5z -0.0005u'5x -0.0001

Page 400: Trabajo Final de Estructuras II(1)

u'3y 0.0000u'3z -0.0002u'3x 0.0001u'6y -0.0001u'6z -0.0005u'6x 0.0001

u'4y 0.0000u'4z -0.0005u'4x -0.0001u'7y 0.0000u'7z -0.0006u'7x -0.0001

Page 401: Trabajo Final de Estructuras II(1)

u'5y -0.0001u'5z -0.0005u'5x -0.0001u'8y -0.0001u'8z -0.0006u'8x 0.0000

u'6y -0.0001u'6z -0.0005u'6x 0.0001u'9y -0.0001u'9z -0.0006u'9x 0.0001

Page 402: Trabajo Final de Estructuras II(1)

u'1y 0.0002u'1z 0.0000u'1x -0.0002u'2y 0.0002u'2z -0.0001u'2x -0.0001

u'2y 0.0002u'2z -0.0001u'2x -0.0001u'3y 0.0002u'3z 0.0000u'3x 0.0001

u'4y 0.0005u'4z 0.0000u'4x -0.0001

Page 403: Trabajo Final de Estructuras II(1)

u'5y 0.0005u'5z -0.0001u'5x -0.0001

u'5y 0.0005u'5z -0.0001u'5x -0.0001u'6y 0.0005u'6z -0.0001u'6x 0.0001

u'7y 0.0006u'7z 0.0000u'7x -0.0001u'8y 0.0006u'8z -0.0001u'8x 0.0000

Page 404: Trabajo Final de Estructuras II(1)

u'8y 0.0006u'8z -0.0001u'8x 0.0000u'9y 0.0006u'9z -0.0001u'9x 0.0001

0.00000.8991

=0.50390.00000.9197

Page 405: Trabajo Final de Estructuras II(1)

0.5868

0.00000.9010

=0.51010.00000.91770.5880

0.00000.4199

=0.23270.00000.41820.2909

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7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

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0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

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8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 451: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

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ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 3

f'c= 210

E= 2173706.51

-0.0841

-0.0789

-0.0412

3.275

A

1

4

714

12

10

7

4

1

Page 463: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

0.48825

3.275

R= 0.800M= 0.436

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 464: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

0.48825

3.275

R= 0.800M= 0.436

ELEMENTO N° 14

0.225

3.275

R= 0.368M= 0.201

0.201105469

-0.0840777207

-0.3684375

0.436398867

Page 465: Trabajo Final de Estructuras II(1)

-0.0788782281-0.799509375

0.436398867

-0.0412495515-0.799509375

Page 466: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 467: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 468: Trabajo Final de Estructuras II(1)

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 469: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 470: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 471: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 472: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 473: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 474: Trabajo Final de Estructuras II(1)

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 475: Trabajo Final de Estructuras II(1)

0.0

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 476: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 477: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 478: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 479: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 480: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 481: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 482: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 483: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 484: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 485: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.000000

Page 486: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.0000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.0000

T =

1 00 10 0

Page 487: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.0000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.0000

T =

1 00 10 00 00 00 0

Page 488: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.0000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.000.020.01

+0.00-0.02

Page 489: Trabajo Final de Estructuras II(1)

F' =

0.04

ELEMENTO 12

F' =

0.000.010.01

+0.00-0.010.04

ELEMENTO 14

F' =

0.000.00-0.01

+0.000.000.01

N hn ∆re

3 2.80 cm -0.0007 cm

2 2.80 cm -0.0005 cm

1 3.00 cm -0.0003 cm

Page 490: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 3

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 491: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 -0.0412Uz2 -0.0789Uz3 -0.0841

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

0.48825

3.275

R= 0.800 R=M= 0.436 M=

Page 492: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.48825

3.275

R= 0.800 R=M= 0.436 M=

ELEMENTO N° 15

0.225

3.275

R= 0.368 R=M= 0.201 M=

-0.0590625 0.260167969

-0.7875

-0.128165625 0.564564492

Page 493: Trabajo Final de Estructuras II(1)

-1.708875

-0.128165625 0.564564492

-1.708875

-0.8-0.4-1.7-0.1-0.90.6-0.8-0.4-1.7

F= -0.1-0.90.6-0.4-0.2-0.8-0.1-0.40.30.0-0.1-0.1

Page 494: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 495: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 496: Trabajo Final de Estructuras II(1)

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 497: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 498: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 499: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 500: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 501: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 502: Trabajo Final de Estructuras II(1)

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 503: Trabajo Final de Estructuras II(1)

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 504: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 505: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 506: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 507: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 508: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 509: Trabajo Final de Estructuras II(1)

U1y -0.000032Ɵ1x -0.000020U2y -0.000069Ɵ2x 0.000019U3y -0.000032Ɵ3x 0.000204U4y -0.000049Ɵ4x -0.000030U5y -0.000108Ɵ5x 0.000014U6y = -0.000050Ɵ6x 0.000165U7y -0.000054Ɵ7x -0.000037U8y -0.000120Ɵ8x -0.000002U9y -0.000055Ɵ9x 0.000108Uz1 -0.000256Uz2 -0.000520Uz3 -0.000674

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 510: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 511: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 512: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 513: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 514: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 515: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 516: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.00000.80 0.81460.44

=0.4463

0.00 0.00000.80 0.7844

Page 517: Trabajo Final de Estructuras II(1)

0.44 0.4758

0.00 0.00000.80 0.81340.44

=0.4425

0.00 0.00000.80 0.78560.44 0.4757

0.00 0.00000.37 0.36960.20

=0.1899

0.00 0.00000.37 0.36730.20 0.2160

∆tr ∆rr

-0.0002 cm -0.0040 cm -0.0009 cm

-0.0003 cm -0.0031 cm -0.0016 cm

-0.0003 cm -0.0015 cm -0.0015 cm

∆te

Page 518: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 3

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 519: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

0.48825

3.725

0.909 R= 0.9090.565 M= 0.565

Page 520: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.48825

3.725

0.909 R= 0.9090.565 M= 0.565

ELEMENTO N° 15

0.225

3.725

0.419 R= 0.4190.260 M= 0.260

-0.4190625

Page 521: Trabajo Final de Estructuras II(1)

-0.909365625

-0.909365625

Page 522: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

Page 523: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

Page 524: Trabajo Final de Estructuras II(1)

0

-660.414

1320.829

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 525: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 526: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 527: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 528: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 529: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 530: Trabajo Final de Estructuras II(1)

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.7

Page 531: Trabajo Final de Estructuras II(1)

0.0 -528.7 1313.0

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 532: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

Page 533: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 534: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 535: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 536: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 537: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z -0.0003u1y 0.0000u1x 0.0000

F' =

F'ay 2.00

Page 538: Trabajo Final de Estructuras II(1)

F' =

F'az -0.13F'ax -0.18F'1y -2.00F'1z 0.13F'1x -0.20

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z -0.0003u2y -0.0001u2x 0.0000

F' =

F'by 4.40F'bz -0.10F'bx -0.16F'2y -4.40F'2z 0.10F'2x -0.14

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

F' =

F'cy 2.01F'cz 0.02F'cx -0.03F'3y -2.01

Page 539: Trabajo Final de Estructuras II(1)

F' =F'3z -0.02F'3x 0.10

u =

u1z -0.0003

u' =

u1y 0.0000u1x 0.0000u4z -0.0005u4y 0.0000u4x 0.0000

F' =

F'1y 1.18F'1z -0.18F'1x -0.25F'4y -1.18F'4z 0.18F'4x -0.26

u =

u2z -0.0003

u' =

u2y -0.0001u2x 0.0000u5z -0.0005u5y -0.0001u5x 0.0000

F' =

F'2y 2.60F'2z -0.12F'2x -0.16F'5y -2.60F'5z 0.12F'5x -0.17

Page 540: Trabajo Final de Estructuras II(1)

u =

u3z -0.0003

u' =

u3y 0.0000u3x 0.0002u6z -0.0005u6y 0.0000u6x 0.0002

F' =

F'3y 1.21F'3z 0.14F'3x 0.20F'6y -1.21F'6z -0.14F'6x 0.18

u =

u4z -0.0005

u' =

u4y 0.0000u4x 0.0000u7z -0.0007u7y -0.0001u7x 0.0000

F' =

F'4y 0.37F'4z -0.13F'4x -0.19F'7y -0.37F'7z 0.13F'7x -0.19

Page 541: Trabajo Final de Estructuras II(1)

u =

u5z -0.0005

u' =

u5y -0.0001u5x 0.0000u8z -0.0007u8y -0.0001u8x 0.0000

F' =

F'5y 0.82F'5z -0.07F'5x -0.10F'8y -0.82F'8z 0.07F'8x -0.11

u =

u6z -0.0005

u' =

u6y 0.0000u6x 0.0002u9z -0.0007u9y -0.0001u9x 0.0001

F' =

F'6y 0.38F'6z 0.12F'6x 0.19F'9y -0.38F'9z -0.12F'9x 0.15

Page 542: Trabajo Final de Estructuras II(1)

u =

u1z -0.0003

u' =

u1y 0.0000u1x 0.0000u2z -0.0003u2y -0.0001u2x 0.0000

F' =

F'1y 0.00F'1z 0.02F'1x 0.01F'2y 0.00F'2z -0.02F'2x 0.04

u =

u2z -0.0003

u' =

u2y -0.0001u2x 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

F' =

F'2y 0.00F'2z 0.11F'2x 0.14F'3y 0.00F'3z -0.11F'3x 0.26

u =

u4z -0.0005

u' =

u4y 0.0000u4x 0.0000

Page 543: Trabajo Final de Estructuras II(1)

u = u5z -0.0005 u' =u5y -0.0001u5x 0.0000

F' =

F'4y 0.00F'4z 0.01F'4x 0.01F'5y 0.00F'5z -0.01F'5x 0.04

u =

u5z -0.0005

u' =

u5y -0.0001u5x 0.0000u6z -0.0005u6y 0.0000u6x 0.0002

F' =

F'5y 0.00F'5z 0.08F'5x 0.10F'6y 0.00F'6z -0.08F'6x 0.19

u =

u7z -0.0007

u' =

u7y -0.0001u7x 0.0000u8z -0.0007u8y -0.0001u8x 0.0000

Page 544: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z 0.00F'7x -0.01F'8y 0.00F'8z 0.00F'8x 0.01

u =

u8z -0.0007

u' =

u8y -0.0001u8x 0.0000u9z -0.0007u9y -0.0001u9x 0.0001

F' =

F'8y 0.00F'8z 0.04F'8x 0.03F'9y 0.00F'9z -0.04F'9x 0.11

ELEMENTO 11

F' =

0.00 0.000.11 0.910.14

+0.56

0.00 0.00-0.11 0.91

Page 545: Trabajo Final de Estructuras II(1)

F' =

0.26 0.56

ELEMENTO 13

F' =

0.00 0.000.08 0.910.10

+0.56

0.00 0.00-0.08 0.910.19 0.56

ELEMENTO 15

F' =

0.00 0.000.04 0.420.03

+0.26

0.00 0.00-0.04 0.420.11 0.26

∆rr D

-0.0009 cm -0.00033

-0.0016 cm -0.00057

-0.0015 cm -0.00051

Page 546: Trabajo Final de Estructuras II(1)
Page 547: Trabajo Final de Estructuras II(1)
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Page 549: Trabajo Final de Estructuras II(1)
Page 550: Trabajo Final de Estructuras II(1)
Page 551: Trabajo Final de Estructuras II(1)
Page 552: Trabajo Final de Estructuras II(1)
Page 553: Trabajo Final de Estructuras II(1)
Page 554: Trabajo Final de Estructuras II(1)
Page 555: Trabajo Final de Estructuras II(1)
Page 556: Trabajo Final de Estructuras II(1)
Page 557: Trabajo Final de Estructuras II(1)
Page 558: Trabajo Final de Estructuras II(1)
Page 559: Trabajo Final de Estructuras II(1)
Page 560: Trabajo Final de Estructuras II(1)
Page 561: Trabajo Final de Estructuras II(1)
Page 562: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 563: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 564: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 565: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y 0.0000u'1z 0.0003u'1x 0.0000

Page 566: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0001u'2z 0.0003u'2x 0.0000

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y 0.0000u'3z 0.0003u'3x 0.0002

Page 567: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z 0.0003u'1x 0.0000u'4y 0.0000u'4z 0.0005u'4x 0.0000

u'2y -0.0001u'2z 0.0003u'2x 0.0000u'5y -0.0001u'5z 0.0005u'5x 0.0000

Page 568: Trabajo Final de Estructuras II(1)

u'3y 0.0000u'3z 0.0003u'3x 0.0002u'6y 0.0000u'6z 0.0005u'6x 0.0002

u'4y 0.0000u'4z 0.0005u'4x 0.0000u'7y -0.0001u'7z 0.0007u'7x 0.0000

Page 569: Trabajo Final de Estructuras II(1)

u'5y -0.0001u'5z 0.0005u'5x 0.0000u'8y -0.0001u'8z 0.0007u'8x 0.0000

u'6y 0.0000u'6z 0.0005u'6x 0.0002u'9y -0.0001u'9z 0.0007u'9x 0.0001

Page 570: Trabajo Final de Estructuras II(1)

u'1y -0.0003u'1z 0.0000u'1x 0.0000u'2y -0.0003u'2z -0.0001u'2x 0.0000

u'2y -0.0003u'2z -0.0001u'2x 0.0000u'3y -0.0003u'3z 0.0000u'3x 0.0002

u'4y -0.0005u'4z 0.0000u'4x 0.0000

Page 571: Trabajo Final de Estructuras II(1)

u'5y -0.0005u'5z -0.0001u'5x 0.0000

u'5y -0.0005u'5z -0.0001u'5x 0.0000u'6y -0.0005u'6z 0.0000u'6x 0.0002

u'7y -0.0007u'7z -0.0001u'7x 0.0000u'8y -0.0007u'8z -0.0001u'8x 0.0000

Page 572: Trabajo Final de Estructuras II(1)

u'8y -0.0007u'8z -0.0001u'8x 0.0000u'9y -0.0007u'9z -0.0001u'9x 0.0001

0.00001.0166

=0.70360.00000.8022

Page 573: Trabajo Final de Estructuras II(1)

0.8248

0.00000.9876

=0.66100.00000.83110.7596

0.00000.4572

=0.29500.00000.38100.3673

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7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

Page 591: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

Page 592: Trabajo Final de Estructuras II(1)

8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 619: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

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ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 4

f'c= 210

E= 2173706.51

0.0841

0.0789

0.0412

3.275

A

1

4

714

12

10

7

4

1

Page 631: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

0.35154

3.275

R= 0.576M= 0.314

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 632: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

0.35154

3.275

R= 0.576M= 0.314

ELEMENTO N° 14

0.162

3.275

R= 0.265M= 0.145

0.144795938

0.0840777207

-0.265275

0.314207184

Page 633: Trabajo Final de Estructuras II(1)

0.0788782281-0.57564675

0.314207184

0.0412495515-0.57564675

Page 634: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 635: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 636: Trabajo Final de Estructuras II(1)

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 637: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 638: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 639: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 640: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 641: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 642: Trabajo Final de Estructuras II(1)

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 643: Trabajo Final de Estructuras II(1)

0.0

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 644: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 645: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 646: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.90.00.0

-43765.90.00.0

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 647: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 648: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 649: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 650: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 651: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 652: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 653: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.00

Page 654: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.00

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.00

T =

1 00 10 0

Page 655: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.00

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.00

T =

1 00 10 00 00 00 0

Page 656: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.00

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.00-0.11-0.22

+0.000.11

Page 657: Trabajo Final de Estructuras II(1)

F' =

-0.16

ELEMENTO 12

F' =

0.00-0.08-0.16

+0.000.08-0.11

ELEMENTO 14

F' =

0.00-0.04-0.08

+0.000.04-0.05

N hn ∆re

3 2.80 cm 0.0006 cm

2 2.80 cm 0.0005 cm

1 3.00 cm 0.0002 cm

Page 658: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 4

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 659: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 0.0412Uz2 0.0789Uz3 0.0841

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

0.35154

3.275

R= 0.576 R=M= 0.314 M=

Page 660: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.35154

3.275

R= 0.576 R=M= 0.314 M=

ELEMENTO N° 15

0.162

3.275

R= 0.265 R=M= 0.145 M=

-0.042525 0.187320938

-0.567

-0.09227925 0.406486434

Page 661: Trabajo Final de Estructuras II(1)

-1.23039

-0.09227925 0.406486434

-1.23039

-0.6-0.3-1.2-0.1-0.70.4-0.6-0.3-1.2

F= -0.1-0.70.4-0.3-0.1-0.60.0-0.30.20.00.10.1

Page 662: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 663: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 664: Trabajo Final de Estructuras II(1)

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 665: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 666: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 667: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 668: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 669: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 670: Trabajo Final de Estructuras II(1)

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 671: Trabajo Final de Estructuras II(1)

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 672: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 673: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.0 0.0417.7 684.0684.0 1493.4

0.0 0.0-417.7 -684.0684.0 746.7

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 674: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.0 0.0283.9 528.7528.7 1313.0

0.0 0.0-283.9 -528.7528.7 656.5

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 675: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 676: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 677: Trabajo Final de Estructuras II(1)

U1y -0.000019Ɵ1x -0.000130U2y -0.000051Ɵ2x -0.000057U3y -0.000026Ɵ3x 0.000025U4y -0.000029Ɵ4x -0.000104U5y -0.000079Ɵ5x -0.000047U6y = -0.000041Ɵ6x 0.000034U7y -0.000033Ɵ7x -0.000066U8y -0.000087Ɵ8x -0.000023U9y -0.000045Ɵ9x 0.000038Uz1 0.000236Uz2 0.000466Uz3 0.000597

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 678: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 679: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 680: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 681: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 682: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 683: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 684: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.00000.58 0.46080.31

=0.0989

0.00 0.00000.58 0.6905

Page 685: Trabajo Final de Estructuras II(1)

0.31 0.1533

0.00 0.00000.58 0.49300.31

=0.1578

0.00 0.00000.58 0.65830.31 0.1998

0.00 0.00000.27 0.22740.14

=0.0671

0.00 0.00000.27 0.30320.14 0.0985

∆tr ∆rr

0.0001 cm 0.0036 cm 0.0008 cm

0.0002 cm 0.0028 cm 0.0014 cm

0.0002 cm 0.0014 cm 0.0014 cm

∆te

Page 686: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 4

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 687: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

0.35154

3.725

0.655 R= 0.6550.406 M= 0.406

Page 688: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.35154

3.725

0.655 R= 0.6550.406 M= 0.406

ELEMENTO N° 15

0.162

3.725

0.302 R= 0.3020.187 M= 0.187

-0.301725

Page 689: Trabajo Final de Estructuras II(1)

-0.65474325

-0.65474325

Page 690: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

Page 691: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

Page 692: Trabajo Final de Estructuras II(1)

0

-660.414

1320.829

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 693: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 694: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 695: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 696: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 697: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 698: Trabajo Final de Estructuras II(1)

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.7

Page 699: Trabajo Final de Estructuras II(1)

0.0 -528.7 1313.0

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 700: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

Page 701: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.5 0.0 0.00.0 -417.7 684.00.0 -684.0 746.7

49779.5 0.0 0.00.0 417.7 -684.00.0 -684.0 1493.4

Page 702: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.9 0.0 0.00.0 -283.9 528.70.0 -528.7 656.5

43765.9 0.0 0.00.0 283.9 -528.70.0 -528.7 1313.0

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 703: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 704: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 705: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z 0.0002u1y 0.0000u1x -0.0001

F' =

F'ay 1.18

Page 706: Trabajo Final de Estructuras II(1)

F' =

F'az 0.02F'ax 0.07F'1y -1.18F'1z -0.02F'1x -0.02

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z 0.0002u2y -0.0001u2x -0.0001

F' =

F'by 3.22F'bz 0.07F'bx 0.12F'2y -3.22F'2z -0.07F'2x 0.08

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z 0.0002u3y 0.0000u3x 0.0000

F' =

F'cy 1.66F'cz 0.12F'cx 0.17F'3y -1.66

Page 707: Trabajo Final de Estructuras II(1)

F' =F'3z -0.12F'3x 0.19

u =

u1z 0.0002

u' =

u1y 0.0000u1x -0.0001u4z 0.0005u4y 0.0000u4x -0.0001

F' =

F'1y 0.72F'1z -0.05F'1x -0.08F'4y -0.72F'4z 0.05F'4x -0.06

u =

u2z 0.0002

u' =

u2y -0.0001u2x -0.0001u5z 0.0005u5y -0.0001u5x 0.0000

F' =

F'2y 1.90F'2z 0.05F'2x 0.06F'5y -1.90F'5z -0.05F'5x 0.07

Page 708: Trabajo Final de Estructuras II(1)

u =

u3z 0.0002

u' =

u3y 0.0000u3x 0.0000u6z 0.0005u6y 0.0000u6x 0.0000

F' =

F'3y 0.98F'3z 0.17F'3x 0.23F'6y -0.98F'6z -0.17F'6x 0.24

u =

u4z 0.0005

u' =

u4y 0.0000u4x -0.0001u7z 0.0006u7y 0.0000u7x -0.0001

F' =

F'4y 0.23F'4z -0.06F'4x -0.09F'7y -0.23F'7z 0.06F'7x -0.07

Page 709: Trabajo Final de Estructuras II(1)

u =

u5z 0.0005

u' =

u5y -0.0001u5x 0.0000u8z 0.0006u8y -0.0001u8x 0.0000

F' =

F'5y 0.60F'5z 0.02F'5x 0.02F'8y -0.60F'8z -0.02F'8x 0.03

u =

u6z 0.0005

u' =

u6y 0.0000u6x 0.0000u9z 0.0006u9y 0.0000u9x 0.0000

F' =

F'6y 0.31F'6z 0.12F'6x 0.17F'9y -0.31F'9z -0.12F'9x 0.18

Page 710: Trabajo Final de Estructuras II(1)

u =

u1z 0.0002

u' =

u1y 0.0000u1x -0.0001u2z 0.0002u2y -0.0001u2x -0.0001

F' =

F'1y 0.00F'1z -0.11F'1x -0.22F'2y 0.00F'2z 0.11F'2x -0.16

u =

u2z 0.0002

u' =

u2y -0.0001u2x -0.0001u3z 0.0002u3y 0.0000u3x 0.0000

F' =

F'2y 0.00F'2z -0.02F'2x -0.07F'3y 0.00F'3z 0.02F'3x -0.02

u =

u4z 0.0005

u' =

u4y 0.0000u4x -0.0001

Page 711: Trabajo Final de Estructuras II(1)

u = u5z 0.0005 u' =u5y -0.0001u5x 0.0000

F' =

F'4y 0.00F'4z -0.08F'4x -0.16F'5y 0.00F'5z 0.08F'5x -0.11

u =

u5z 0.0005

u' =

u5y -0.0001u5x 0.0000u6z 0.0005u6y 0.0000u6x 0.0000

F' =

F'5y 0.00F'5z -0.02F'5x -0.06F'6y 0.00F'6z 0.02F'6x -0.01

u =

u7z 0.0006

u' =

u7y 0.0000u7x -0.0001u8z 0.0006u8y -0.0001u8x 0.0000

Page 712: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z -0.04F'7x -0.08F'8y 0.00F'8z 0.04F'8x -0.05

u =

u8z 0.0006

u' =

u8y -0.0001u8x 0.0000u9z 0.0006u9y 0.0000u9x 0.0000

F' =

F'8y 0.00F'8z 0.00F'8x -0.03F'9y 0.00F'9z 0.00F'9x 0.01

ELEMENTO 11

F' =

0.00 0.00-0.02 0.65-0.07

+0.41

0.00 0.000.02 0.65

Page 713: Trabajo Final de Estructuras II(1)

F' =

-0.02 0.41

ELEMENTO 13

F' =

0.00 0.00-0.02 0.65-0.06

+0.41

0.00 0.000.02 0.65-0.01 0.41

ELEMENTO 15

F' =

0.00 0.000.00 0.30-0.03

+0.19

0.00 0.000.00 0.300.01 0.19

∆rr D

0.0008 cm 0.00028

0.0014 cm 0.00049

0.0014 cm 0.00047

Page 714: Trabajo Final de Estructuras II(1)
Page 715: Trabajo Final de Estructuras II(1)
Page 716: Trabajo Final de Estructuras II(1)
Page 717: Trabajo Final de Estructuras II(1)
Page 718: Trabajo Final de Estructuras II(1)
Page 719: Trabajo Final de Estructuras II(1)
Page 720: Trabajo Final de Estructuras II(1)
Page 721: Trabajo Final de Estructuras II(1)
Page 722: Trabajo Final de Estructuras II(1)
Page 723: Trabajo Final de Estructuras II(1)
Page 724: Trabajo Final de Estructuras II(1)
Page 725: Trabajo Final de Estructuras II(1)
Page 726: Trabajo Final de Estructuras II(1)
Page 727: Trabajo Final de Estructuras II(1)
Page 728: Trabajo Final de Estructuras II(1)
Page 729: Trabajo Final de Estructuras II(1)
Page 730: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 731: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 732: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 733: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y 0.0000u'1z -0.0002u'1x -0.0001

Page 734: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0001u'2z -0.0002u'2x -0.0001

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y 0.0000u'3z -0.0002u'3x 0.0000

Page 735: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z -0.0002u'1x -0.0001u'4y 0.0000u'4z -0.0005u'4x -0.0001

u'2y -0.0001u'2z -0.0002u'2x -0.0001u'5y -0.0001u'5z -0.0005u'5x 0.0000

Page 736: Trabajo Final de Estructuras II(1)

u'3y 0.0000u'3z -0.0002u'3x 0.0000u'6y 0.0000u'6z -0.0005u'6x 0.0000

u'4y 0.0000u'4z -0.0005u'4x -0.0001u'7y 0.0000u'7z -0.0006u'7x -0.0001

Page 737: Trabajo Final de Estructuras II(1)

u'5y -0.0001u'5z -0.0005u'5x 0.0000u'8y -0.0001u'8z -0.0006u'8x 0.0000

u'6y 0.0000u'6z -0.0005u'6x 0.0000u'9y 0.0000u'9z -0.0006u'9x 0.0000

Page 738: Trabajo Final de Estructuras II(1)

u'1y 0.0002u'1z 0.0000u'1x -0.0001u'2y 0.0002u'2z -0.0001u'2x -0.0001

u'2y 0.0002u'2z -0.0001u'2x -0.0001u'3y 0.0002u'3z 0.0000u'3x 0.0000

u'4y 0.0005u'4z 0.0000u'4x -0.0001

Page 739: Trabajo Final de Estructuras II(1)

u'5y 0.0005u'5z -0.0001u'5x 0.0000

u'5y 0.0005u'5z -0.0001u'5x 0.0000u'6y 0.0005u'6z 0.0000u'6x 0.0000

u'7y 0.0006u'7z 0.0000u'7x -0.0001u'8y 0.0006u'8z -0.0001u'8x 0.0000

Page 740: Trabajo Final de Estructuras II(1)

u'8y 0.0006u'8z -0.0001u'8x 0.0000u'9y 0.0006u'9z 0.0000u'9x 0.0000

0.00000.6309

=0.33490.00000.6786

Page 741: Trabajo Final de Estructuras II(1)

0.3892

0.00000.6366

=0.34610.00000.67290.3994

0.00000.2972

=0.15880.00000.30630.1988

Page 742: Trabajo Final de Estructuras II(1)
Page 743: Trabajo Final de Estructuras II(1)
Page 744: Trabajo Final de Estructuras II(1)
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Page 750: Trabajo Final de Estructuras II(1)
Page 751: Trabajo Final de Estructuras II(1)
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Page 757: Trabajo Final de Estructuras II(1)
Page 758: Trabajo Final de Estructuras II(1)

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

Page 759: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

Page 760: Trabajo Final de Estructuras II(1)

8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

Page 761: Trabajo Final de Estructuras II(1)
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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 787: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

Page 788: Trabajo Final de Estructuras II(1)
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Page 798: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 5

f'c= 210

E= 2173706.51

-0.0841

-0.0789

-0.0412

3.275

A

1

4

714

12

10

7

4

1

Page 799: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

0.35154

3.275

R= 0.576M= 0.314

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 800: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

0.35154

3.275

R= 0.576M= 0.314

ELEMENTO N° 14

0.162

3.275

R= 0.265M= 0.145

0.144795938

-0.0840777207

-0.265275

0.314207184

Page 801: Trabajo Final de Estructuras II(1)

-0.0788782281-0.57564675

0.314207184

-0.0412495515-0.57564675

Page 802: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 803: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 804: Trabajo Final de Estructuras II(1)

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 805: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 806: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 807: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 808: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 809: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 810: Trabajo Final de Estructuras II(1)

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 811: Trabajo Final de Estructuras II(1)

0.00

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 812: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 813: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 814: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 815: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 816: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 817: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 818: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 819: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 820: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 821: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.000000

Page 822: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.000000

T =

1 00 10 0

Page 823: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

Page 824: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.000.030.04

+0.00-0.03

Page 825: Trabajo Final de Estructuras II(1)

F' =

0.06

ELEMENTO 12

F' =

0.000.030.03

+0.00-0.030.05

ELEMENTO 14

F' =

0.000.010.00

+0.00-0.010.02

N hn ∆re

3 2.80 cm -0.0007 cm

2 2.80 cm -0.0005 cm

1 3.00 cm -0.0003 cm

Page 826: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 5

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 827: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 -0.0412Uz2 -0.0789Uz3 -0.0841

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

0.35154

3.275

R= 0.576 R=M= 0.314 M=

Page 828: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.35154

3.275

R= 0.576 R=M= 0.314 M=

ELEMENTO N° 15

0.162

3.275

R= 0.265 R=M= 0.145 M=

-0.042525 0.187320938

-0.567

-0.09227925 0.406486434

Page 829: Trabajo Final de Estructuras II(1)

-1.23039

-0.09227925 0.406486434

-1.23039

-0.6-0.3-1.2-0.1-0.70.4-0.6-0.3-1.2

F= -0.1-0.70.4-0.3-0.1-0.60.0-0.30.20.0-0.1-0.1

Page 830: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 831: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 832: Trabajo Final de Estructuras II(1)

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 833: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 834: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 835: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 836: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 837: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 838: Trabajo Final de Estructuras II(1)

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 839: Trabajo Final de Estructuras II(1)

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 840: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 841: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 842: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 843: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 844: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 845: Trabajo Final de Estructuras II(1)

U1y -0.000023Ɵ1x 0.000004U2y -0.000050Ɵ2x 0.000025U3y -0.000022Ɵ3x 0.000166U4y -0.000036Ɵ4x -0.000008U5y -0.000077Ɵ5x 0.000020U6y = -0.000035Ɵ6x 0.000132U7y -0.000040Ɵ7x -0.000020U8y -0.000086Ɵ8x 0.000002U9y -0.000039Ɵ9x 0.000085Uz1 -0.000253Uz2 -0.000512Uz3 -0.000662

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 846: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 847: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 848: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 849: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 850: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 851: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 852: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.00000.58 0.60700.31

=0.3575

0.00 0.00000.58 0.5443

Page 853: Trabajo Final de Estructuras II(1)

0.31 0.3734

0.00 0.00000.58 0.60070.31

=0.3448

0.00 0.00000.58 0.55060.31 0.3658

0.00 0.00000.27 0.27240.14

=0.1481

0.00 0.00000.27 0.25820.14 0.1648

∆tr ∆rr

-0.0002 cm -0.0040 cm -0.0009 cm

-0.0003 cm -0.0031 cm -0.0016 cm

-0.0003 cm -0.0015 cm -0.0015 cm

∆te

Page 854: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 5

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 855: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

0.35154

3.725

0.655 R= 0.6550.406 M= 0.406

Page 856: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

0.35154

3.725

0.655 R= 0.6550.406 M= 0.406

ELEMENTO N° 15

0.162

3.725

0.302 R= 0.3020.187 M= 0.187

-0.301725

Page 857: Trabajo Final de Estructuras II(1)

-0.65474325

-0.65474325

Page 858: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

Page 859: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

Page 860: Trabajo Final de Estructuras II(1)

0

-660.414

1320.829

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 861: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 862: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 863: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 864: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 865: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 866: Trabajo Final de Estructuras II(1)

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.72

Page 867: Trabajo Final de Estructuras II(1)

0.00 -528.72 1312.98

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 868: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

Page 869: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 870: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 871: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 872: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 873: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z -0.0003u1y 0.0000u1x 0.0000

F' =

F'ay 1.48

Page 874: Trabajo Final de Estructuras II(1)

F' =

F'az -0.11F'ax -0.16F'1y -1.48F'1z 0.11F'1x -0.16

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z -0.0003u2y 0.0000u2x 0.0000

F' =

F'by 3.16F'bz -0.09F'bx -0.15F'2y -3.16F'2z 0.09F'2x -0.13

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

F' =

F'cy 1.42F'cz 0.00F'cx -0.06F'3y -1.42

Page 875: Trabajo Final de Estructuras II(1)

F' =F'3z 0.00F'3x 0.05

u =

u1z -0.0003

u' =

u1y 0.0000u1x 0.0000u4z -0.0005u4y 0.0000u4x 0.0000

F' =

F'1y 0.87F'1z -0.14F'1x -0.20F'4y -0.87F'4z 0.14F'4x -0.21

u =

u2z -0.0003

u' =

u2y 0.0000u2x 0.0000u5z -0.0005u5y -0.0001u5x 0.0000

F' =

F'2y 1.87F'2z -0.11F'2x -0.15F'5y -1.87F'5z 0.11F'5x -0.15

Page 876: Trabajo Final de Estructuras II(1)

u =

u3z -0.0003

u' =

u3y 0.0000u3x 0.0002u6z -0.0005u6y 0.0000u6x 0.0001

F' =

F'3y 0.86F'3z 0.09F'3x 0.13F'6y -0.86F'6z -0.09F'6x 0.11

u =

u4z -0.0005

u' =

u4y 0.0000u4x 0.0000u7z -0.0007u7y 0.0000u7x 0.0000

F' =

F'4y 0.27F'4z -0.10F'4x -0.14F'7y -0.27F'7z 0.10F'7x -0.15

Page 877: Trabajo Final de Estructuras II(1)

u =

u5z -0.0005

u' =

u5y -0.0001u5x 0.0000u8z -0.0007u8y -0.0001u8x 0.0000

F' =

F'5y 0.59F'5z -0.06F'5x -0.08F'8y -0.59F'8z 0.06F'8x -0.10

u =

u6z -0.0005

u' =

u6y 0.0000u6x 0.0001u9z -0.0007u9y 0.0000u9x 0.0001

F' =

F'6y 0.27F'6z 0.08F'6x 0.13F'9y -0.27F'9z -0.08F'9x 0.10

Page 878: Trabajo Final de Estructuras II(1)

u =

u1z -0.0003

u' =

u1y 0.0000u1x 0.0000u2z -0.0003u2y 0.0000u2x 0.0000

F' =

F'1y 0.00F'1z 0.03F'1x 0.04F'2y 0.00F'2z -0.03F'2x 0.06

u =

u2z -0.0003

u' =

u2y 0.0000u2x 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

F' =

F'2y 0.00F'2z 0.09F'2x 0.13F'3y 0.00F'3z -0.09F'3x 0.22

u =

u4z -0.0005

u' =

u4y 0.0000u4x 0.0000

Page 879: Trabajo Final de Estructuras II(1)

u = u5z -0.0005 u' =u5y -0.0001u5x 0.0000

F' =

F'4y 0.00F'4z 0.03F'4x 0.03F'5y 0.00F'5z -0.03F'5x 0.05

u =

u5z -0.0005

u' =

u5y -0.0001u5x 0.0000u6z -0.0005u6y 0.0000u6x 0.0001

F' =

F'5y 0.00F'5z 0.07F'5x 0.09F'6y 0.00F'6z -0.07F'6x 0.16

u =

u7z -0.0007

u' =

u7y 0.0000u7x 0.0000u8z -0.0007u8y -0.0001u8x 0.0000

Page 880: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z 0.01F'7x 0.00F'8y 0.00F'8z -0.01F'8x 0.02

u =

u8z -0.0007

u' =

u8y -0.0001u8x 0.0000u9z -0.0007u9y 0.0000u9x 0.0001

F' =

F'8y 0.00F'8z 0.03F'8x 0.03F'9y 0.00F'9z -0.03F'9x 0.09

ELEMENTO 11

F' =

0.00 0.000.09 0.650.13

+0.41

0.00 0.00-0.09 0.65

Page 881: Trabajo Final de Estructuras II(1)

F' =

0.22 0.41

ELEMENTO 13

F' =

0.00 0.000.07 0.650.09

+0.41

0.00 0.00-0.07 0.650.16 0.41

ELEMENTO 15

F' =

0.00 0.000.03 0.300.03

+0.19

0.00 0.00-0.03 0.300.09 0.19

∆rr D

-0.0009 cm -0.00032

-0.0016 cm -0.00055

-0.0015 cm -0.00051

Page 882: Trabajo Final de Estructuras II(1)
Page 883: Trabajo Final de Estructuras II(1)
Page 884: Trabajo Final de Estructuras II(1)
Page 885: Trabajo Final de Estructuras II(1)
Page 886: Trabajo Final de Estructuras II(1)
Page 887: Trabajo Final de Estructuras II(1)
Page 888: Trabajo Final de Estructuras II(1)
Page 889: Trabajo Final de Estructuras II(1)
Page 890: Trabajo Final de Estructuras II(1)
Page 891: Trabajo Final de Estructuras II(1)
Page 892: Trabajo Final de Estructuras II(1)
Page 893: Trabajo Final de Estructuras II(1)
Page 894: Trabajo Final de Estructuras II(1)
Page 895: Trabajo Final de Estructuras II(1)
Page 896: Trabajo Final de Estructuras II(1)
Page 897: Trabajo Final de Estructuras II(1)
Page 898: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 899: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 900: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 901: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y 0.0000u'1z 0.0003u'1x 0.0000

Page 902: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y 0.0000u'2z 0.0003u'2x 0.0000

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y 0.0000u'3z 0.0003u'3x 0.0002

Page 903: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z 0.0003u'1x 0.0000u'4y 0.0000u'4z 0.0005u'4x 0.0000

u'2y 0.0000u'2z 0.0003u'2x 0.0000u'5y -0.0001u'5z 0.0005u'5x 0.0000

Page 904: Trabajo Final de Estructuras II(1)

u'3y 0.0000u'3z 0.0003u'3x 0.0002u'6y 0.0000u'6z 0.0005u'6x 0.0001

u'4y 0.0000u'4z 0.0005u'4x 0.0000u'7y 0.0000u'7z 0.0007u'7x 0.0000

Page 905: Trabajo Final de Estructuras II(1)

u'5y -0.0001u'5z 0.0005u'5x 0.0000u'8y -0.0001u'8z 0.0007u'8x 0.0000

u'6y 0.0000u'6z 0.0005u'6x 0.0001u'9y 0.0000u'9z 0.0007u'9x 0.0001

Page 906: Trabajo Final de Estructuras II(1)

u'1y -0.0003u'1z 0.0000u'1x 0.0000u'2y -0.0003u'2z 0.0000u'2x 0.0000

u'2y -0.0003u'2z 0.0000u'2x 0.0000u'3y -0.0003u'3z 0.0000u'3x 0.0002

u'4y -0.0005u'4z 0.0000u'4x 0.0000

Page 907: Trabajo Final de Estructuras II(1)

u'5y -0.0005u'5z -0.0001u'5x 0.0000

u'5y -0.0005u'5z -0.0001u'5x 0.0000u'6y -0.0005u'6z 0.0000u'6x 0.0001

u'7y -0.0007u'7z 0.0000u'7x 0.0000u'8y -0.0007u'8z -0.0001u'8x 0.0000

Page 908: Trabajo Final de Estructuras II(1)

u'8y -0.0007u'8z -0.0001u'8x 0.0000u'9y -0.0007u'9z 0.0000u'9x 0.0001

0.00000.7484

=0.53460.00000.5611

Page 909: Trabajo Final de Estructuras II(1)

0.6271

0.00000.7232

=0.49700.00000.58630.5709

0.00000.3344

=0.22120.00000.26910.2751

Page 910: Trabajo Final de Estructuras II(1)
Page 911: Trabajo Final de Estructuras II(1)
Page 912: Trabajo Final de Estructuras II(1)
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Page 926: Trabajo Final de Estructuras II(1)

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

Page 927: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

Page 928: Trabajo Final de Estructuras II(1)

8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

Page 929: Trabajo Final de Estructuras II(1)
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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 955: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

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ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

f'c= 210

E= 2173706.51

0.1762

0.1653

0.0864

3.275

A

1

4

714

12

10

7

4

1

Page 967: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

10

3.275

R= 16.375M= 8.938

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 968: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

11

3.275

R= 18.013M= 9.832

ELEMENTO N° 14

20

3.275

R= 32.750M= 17.876

17.87604167

0.1761628435

-32.75

9.831822917

Page 969: Trabajo Final de Estructuras II(1)

0.1652686683-18.0125

8.938020833

0.0864276316-16.375

Page 970: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 971: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 972: Trabajo Final de Estructuras II(1)

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 973: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 974: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 975: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 976: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 977: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 978: Trabajo Final de Estructuras II(1)

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 979: Trabajo Final de Estructuras II(1)

0.00

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 980: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 981: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 982: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 983: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 984: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 985: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 986: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 987: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 988: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 989: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.000000

Page 990: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.000000

T =

1 00 10 0

Page 991: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

Page 992: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.00-1.23-2.65

+0.001.23

Page 993: Trabajo Final de Estructuras II(1)

F' =

-1.36

ELEMENTO 12

F' =

0.00-0.70-1.03

+0.000.70-1.28

ELEMENTO 14

F' =

0.00-2.39-7.48

+0.002.39-0.36

N hn ∆re

3 2.80 cm 0.0007 cm

2 2.80 cm 0.0002 cm

1 3.00 cm 0.0003 cm

Page 994: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 995: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 0.0864Uz2 0.1653Uz3 0.1762

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

10

3.275

R= 16.375 R=M= 8.938 M=

Page 996: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

11

3.275

R= 18.013 R=M= 9.832 M=

ELEMENTO N° 15

20

3.275

R= 32.750 R=M= 17.876 M=

6.313020833 11.56302083

-51.375

-4.043802083 13.875625

Page 997: Trabajo Final de Estructuras II(1)

-40.3625

-2.625 11.56302083

-35

-16.4-8.9

-35.0-2.6

-18.611.6-18.0-9.8

-40.4F= -4.0

-22.413.9-32.8-17.9-51.46.3

-18.611.60.10.20.2

Page 998: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 999: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 1000: Trabajo Final de Estructuras II(1)

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 1001: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1002: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1003: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1004: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 1005: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 1006: Trabajo Final de Estructuras II(1)

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1007: Trabajo Final de Estructuras II(1)

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1008: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1009: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1010: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1011: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 1012: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 1013: Trabajo Final de Estructuras II(1)

U1y -0.000991Ɵ1x -0.002103U2y -0.002118Ɵ2x -0.000378U3y -0.000889Ɵ3x 0.002575U4y -0.001692Ɵ4x -0.000913U5y -0.003550Ɵ5x -0.001251U6y = -0.001457Ɵ6x 0.002719U7y -0.002139Ɵ7x -0.007195U8y -0.004374Ɵ8x 0.002331U9y -0.001698Ɵ9x 0.003335Uz1 0.000277Uz2 0.000184Uz3 0.000746

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 1014: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 1015: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1016: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1017: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1018: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 1019: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 1020: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.000016.38 15.14928.94

=6.2868

0.00 0.000016.38 17.6008

Page 1021: Trabajo Final de Estructuras II(1)

8.94 7.5749

0.00 0.000018.01 17.30889.83

=8.8057

0.00 0.000018.01 18.71629.83 8.5533

0.00 0.000032.75 30.356917.88

=10.4009

0.00 0.000032.75 35.143117.88 17.5138

∆tr ∆rr

0.0006 cm 0.0045 cm 0.0034 cm

-0.0001 cm 0.0011 cm -0.0006 cm

0.0003 cm 0.0017 cm 0.0017 cm

∆te

Page 1022: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 1023: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

10

3.725

18.625 R= 18.62511.563 M= 11.563

Page 1024: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

12

3.725

22.350 R= 22.35013.876 M= 13.876

ELEMENTO N° 15

10

3.725

18.625 R= 18.62511.563 M= 11.563

-18.625

Page 1025: Trabajo Final de Estructuras II(1)

-22.35

-18.625

Page 1026: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

Page 1027: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

Page 1028: Trabajo Final de Estructuras II(1)

0

-660.414

1320.829

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 1029: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1030: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1031: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1032: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 1033: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 1034: Trabajo Final de Estructuras II(1)

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.72

Page 1035: Trabajo Final de Estructuras II(1)

0.00 -528.72 1312.98

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 1036: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

Page 1037: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 1038: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 1039: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 1040: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 1041: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z 0.0003u1y -0.0010u1x -0.0021

F' =

F'ay 62.81

Page 1042: Trabajo Final de Estructuras II(1)

F' =

F'az -1.27F'ax -1.21F'1y -62.81F'1z 1.27F'1x -2.59

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z 0.0003u2y -0.0021u2x -0.0004

F' =

F'by 134.29F'bz -0.13F'bx -0.07F'2y -134.29F'2z 0.13F'2x -0.32

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z 0.0003u3y -0.0009u3x 0.0026

F' =

F'cy 56.37F'cz 1.82F'cx 1.88F'3y -56.37

Page 1043: Trabajo Final de Estructuras II(1)

F' =F'3z -1.82F'3x 3.58

u =

u1z 0.0003

u' =

u1y -0.0010u1x -0.0021u4z 0.0002u4y -0.0017u4x -0.0009

F' =

F'1y 47.67F'1z -2.34F'1x -3.69F'4y -47.67F'4z 2.34F'4x -2.85

u =

u2z 0.0003

u' =

u2y -0.0021u2x -0.0004u5z 0.0002u5y -0.0035u5x -0.0013

F' =

F'2y 97.25F'2z -1.28F'2x -1.49F'5y -97.25F'5z 1.28F'5x -2.11

Page 1044: Trabajo Final de Estructuras II(1)

u =

u3z 0.0003

u' =

u3y -0.0009u3x 0.0026u6z 0.0002u6y -0.0015u6x 0.0027

F' =

F'3y 38.56F'3z 3.96F'3x 5.50F'6y -38.56F'6z -3.96F'6x 5.60

u =

u4z 0.0002

u' =

u4y -0.0017u4x -0.0009u7z 0.0007u7y -0.0021u7x -0.0072

F' =

F'4y 30.36F'4z -5.84F'4x -5.96F'7y -30.36F'7z 5.84F'7x -10.40

Page 1045: Trabajo Final de Estructuras II(1)

u =

u5z 0.0002

u' =

u5y -0.0035u5x -0.0013u8z 0.0007u8y -0.0044u8x 0.0023

F' =

F'5y 56.00F'5z 1.12F'5x 0.31F'8y -56.00F'8z -1.12F'8x 2.84

u =

u6z 0.0002

u' =

u6y -0.0015u6x 0.0027u9z 0.0007u9y -0.0017u9x 0.0033

F' =

F'6y 16.39F'6z 4.89F'6x 6.63F'9y -16.39F'9z -4.89F'9x 7.07

Page 1046: Trabajo Final de Estructuras II(1)

u =

u1z 0.0003

u' =

u1y -0.0010u1x -0.0021u2z 0.0003u2y -0.0021u2x -0.0004

F' =

F'1y 0.00F'1z -1.23F'1x -2.65F'2y 0.00F'2z 1.23F'2x -1.36

u =

u2z 0.0003

u' =

u2y -0.0021u2x -0.0004u3z 0.0003u3y -0.0009u3x 0.0026

F' =

F'2y 0.00F'2z 0.81F'2x 0.54F'3y 0.00F'3z -0.81F'3x 2.48

u =

u4z 0.0002

u' =

u4y -0.0017u4x -0.0009

Page 1047: Trabajo Final de Estructuras II(1)

u = u5z 0.0002 u' =u5y -0.0035u5x -0.0013

F' =

F'4y 0.00F'4z -0.70F'4x -1.03F'5y 0.00F'5z 0.70F'5x -1.28

u =

u5z 0.0002

u' =

u5y -0.0035u5x -0.0013u6z 0.0002u6y -0.0015u6x 0.0027

F' =

F'5y 0.00F'5z 0.18F'5x -0.96F'6y 0.00F'6z -0.18F'6x 1.64

u =

u7z 0.0007

u' =

u7y -0.0021u7x -0.0072u8z 0.0007u8y -0.0044u8x 0.0023

Page 1048: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z -2.39F'7x -7.48F'8y 0.00F'8z 2.39F'8x -0.36

u =

u8z 0.0007

u' =

u8y -0.0044u8x 0.0023u9z 0.0007u9y -0.0017u9x 0.0033

F' =

F'8y 0.00F'8z 2.24F'8x 3.83F'9y 0.00F'9z -2.24F'9x 4.49

ELEMENTO 11

F' =

0.00 0.000.81 18.630.54

+11.56

0.00 0.00-0.81 18.63

Page 1049: Trabajo Final de Estructuras II(1)

F' =

2.48 11.56

ELEMENTO 13

F' =

0.00 0.000.18 22.35-0.96

+13.88

0.00 0.00-0.18 22.351.64 13.88

ELEMENTO 15

F' =

0.00 0.002.24 18.633.83

+11.56

0.00 0.00-2.24 18.634.49 11.56

∆rr D

0.0034 cm 0.00121

-0.0006 cm -0.00020

0.0017 cm 0.00055

Page 1050: Trabajo Final de Estructuras II(1)
Page 1051: Trabajo Final de Estructuras II(1)
Page 1052: Trabajo Final de Estructuras II(1)
Page 1053: Trabajo Final de Estructuras II(1)
Page 1054: Trabajo Final de Estructuras II(1)
Page 1055: Trabajo Final de Estructuras II(1)
Page 1056: Trabajo Final de Estructuras II(1)
Page 1057: Trabajo Final de Estructuras II(1)
Page 1058: Trabajo Final de Estructuras II(1)
Page 1059: Trabajo Final de Estructuras II(1)
Page 1060: Trabajo Final de Estructuras II(1)
Page 1061: Trabajo Final de Estructuras II(1)
Page 1062: Trabajo Final de Estructuras II(1)
Page 1063: Trabajo Final de Estructuras II(1)
Page 1064: Trabajo Final de Estructuras II(1)
Page 1065: Trabajo Final de Estructuras II(1)
Page 1066: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 1067: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 1068: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 1069: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y -0.0010u'1z -0.0003u'1x -0.0021

Page 1070: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0021u'2z -0.0003u'2x -0.0004

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y -0.0009u'3z -0.0003u'3x 0.0026

Page 1071: Trabajo Final de Estructuras II(1)

u'1y -0.0010u'1z -0.0003u'1x -0.0021u'4y -0.0017u'4z -0.0002u'4x -0.0009

u'2y -0.0021u'2z -0.0003u'2x -0.0004u'5y -0.0035u'5z -0.0002u'5x -0.0013

Page 1072: Trabajo Final de Estructuras II(1)

u'3y -0.0009u'3z -0.0003u'3x 0.0026u'6y -0.0015u'6z -0.0002u'6x 0.0027

u'4y -0.0017u'4z -0.0002u'4x -0.0009u'7y -0.0021u'7z -0.0007u'7x -0.0072

Page 1073: Trabajo Final de Estructuras II(1)

u'5y -0.0035u'5z -0.0002u'5x -0.0013u'8y -0.0044u'8z -0.0007u'8x 0.0023

u'6y -0.0015u'6z -0.0002u'6x 0.0027u'9y -0.0017u'9z -0.0007u'9x 0.0033

Page 1074: Trabajo Final de Estructuras II(1)

u'1y 0.0003u'1z -0.0010u'1x -0.0021u'2y 0.0003u'2z -0.0021u'2x -0.0004

u'2y 0.0003u'2z -0.0021u'2x -0.0004u'3y 0.0003u'3z -0.0009u'3x 0.0026

u'4y 0.0002u'4z -0.0017u'4x -0.0009

Page 1075: Trabajo Final de Estructuras II(1)

u'5y 0.0002u'5z -0.0035u'5x -0.0013

u'5y 0.0002u'5z -0.0035u'5x -0.0013u'6y 0.0002u'6z -0.0015u'6x 0.0027

u'7y 0.0007u'7z -0.0021u'7x -0.0072u'8y 0.0007u'8z -0.0044u'8x 0.0023

Page 1076: Trabajo Final de Estructuras II(1)

u'8y 0.0007u'8z -0.0044u'8x 0.0023u'9y 0.0007u'9z -0.0017u'9x 0.0033

0.000019.4376

=12.10740.000017.8124

Page 1077: Trabajo Final de Estructuras II(1)

14.0456

0.000022.5323

=12.91200.000022.167715.5181

0.000020.8608

=15.39780.000016.389216.0566

Page 1078: Trabajo Final de Estructuras II(1)
Page 1079: Trabajo Final de Estructuras II(1)
Page 1080: Trabajo Final de Estructuras II(1)
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7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

Page 1095: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

Page 1096: Trabajo Final de Estructuras II(1)

8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 1123: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

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ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

f'c= 210

E= 2173706.51

0.0841

0.0789

0.0412

3.275

A

1

4

714

12

10

7

4

1

Page 1135: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

10

3.275

R= 16.375M= 8.938

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 1136: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

11

3.275

R= 18.013M= 9.832

ELEMENTO N° 14

20

3.275

R= 32.750M= 17.876

17.87604167

0.0840777207

-32.75

9.831822917

Page 1137: Trabajo Final de Estructuras II(1)

0.0788782281-18.0125

8.938020833

0.0412495515-16.375

Page 1138: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 1139: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 1140: Trabajo Final de Estructuras II(1)

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 1141: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1142: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1143: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1144: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 1145: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1146: Trabajo Final de Estructuras II(1)

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1147: Trabajo Final de Estructuras II(1)

0.00

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1148: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1149: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1150: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1151: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 1152: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 1153: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 1154: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 1155: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 1156: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 1157: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.000000

Page 1158: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.000000

T =

1 00 10 0

Page 1159: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

Page 1160: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.00-1.15-2.51

+0.001.15

Page 1161: Trabajo Final de Estructuras II(1)

F' =

-1.24

ELEMENTO 12

F' =

0.00-0.64-0.92

+0.000.64-1.19

ELEMENTO 14

F' =

0.00-2.37-7.43

+0.002.37-0.33

N hn ∆re

3 2.80 cm 0.0001 cm

2 2.80 cm -0.0004 cm

1 3.00 cm 0.0000 cm

Page 1162: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 1163: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 0.0412Uz2 0.0789Uz3 0.0841

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

10

3.275

R= 16.375 R=M= 8.938 M=

Page 1164: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

11

3.275

R= 18.013 R=M= 9.832 M=

ELEMENTO N° 15

20

3.275

R= 32.750 R=M= 17.876 M=

6.313020833 11.56302083

-51.375

-4.043802083 13.875625

Page 1165: Trabajo Final de Estructuras II(1)

-40.3625

-2.625 11.56302083

-35

-16.4-8.9

-35.0-2.6

-18.611.6-18.0-9.8

-40.4F= -4.0

-22.413.9-32.8-17.9-51.46.3

-18.611.60.00.10.1

Page 1166: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 1167: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 1168: Trabajo Final de Estructuras II(1)

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 1169: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1170: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1171: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1172: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 1173: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 1174: Trabajo Final de Estructuras II(1)

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1175: Trabajo Final de Estructuras II(1)

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1176: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1177: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1178: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1179: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 1180: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 1181: Trabajo Final de Estructuras II(1)

U1y -0.000993Ɵ1x -0.002029U2y -0.002118Ɵ2x -0.000332U3y -0.000887Ɵ3x 0.002652U4y -0.001696Ɵ4x -0.000860U5y -0.003549Ɵ5x -0.001214U6y = -0.001454Ɵ6x 0.002773U7y -0.002144Ɵ7x -0.007170U8y -0.004374Ɵ8x 0.002345U9y -0.001695Ɵ9x 0.003360Uz1 0.000010Uz2 -0.000352Uz3 0.000057

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 1182: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 1183: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1184: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1185: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1186: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 1187: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 1188: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.000016.38 15.22938.94

=6.4284

0.00 0.000016.38 17.5207

Page 1189: Trabajo Final de Estructuras II(1)

8.94 7.6954

0.00 0.000018.01 17.36789.83

=8.9081

0.00 0.000018.01 18.65729.83 8.6442

0.00 0.000032.75 30.381617.88

=10.4453

0.00 0.000032.75 35.118417.88 17.5501

∆tr ∆rr

0.0004 cm 0.0003 cm 0.0025 cm

-0.0004 cm -0.0021 cm -0.0022 cm

0.0000 cm 0.0001 cm 0.0001 cm

∆te

Page 1190: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 1191: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

10

3.725

18.625 R= 18.62511.563 M= 11.563

Page 1192: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

12

3.725

22.350 R= 22.35013.876 M= 13.876

ELEMENTO N° 15

10

3.725

18.625 R= 18.62511.563 M= 11.563

-18.625

Page 1193: Trabajo Final de Estructuras II(1)

-22.35

-18.625

Page 1194: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

Page 1195: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

Page 1196: Trabajo Final de Estructuras II(1)

0

-660.414

1320.829

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 1197: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1198: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1199: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1200: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 1201: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 1202: Trabajo Final de Estructuras II(1)

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.72

Page 1203: Trabajo Final de Estructuras II(1)

0.00 -528.72 1312.98

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 1204: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

Page 1205: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 1206: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 1207: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 1208: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 1209: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z 0.0000u1y -0.0010u1x -0.0020

F' =

F'ay 62.98

Page 1210: Trabajo Final de Estructuras II(1)

F' =

F'az -1.34F'ax -1.33F'1y -62.98F'1z 1.34F'1x -2.67

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z 0.0000u2y -0.0021u2x -0.0003

F' =

F'by 134.26F'bz -0.22F'bx -0.21F'2y -134.26F'2z 0.22F'2x -0.43

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z 0.0000u3y -0.0009u3x 0.0027

F' =

F'cy 56.24F'cz 1.76F'cx 1.76F'3y -56.24

Page 1211: Trabajo Final de Estructuras II(1)

F' =F'3z -1.76F'3x 3.51

u =

u1z 0.0000

u' =

u1y -0.0010u1x -0.0020u4z -0.0004u4y -0.0017u4x -0.0009

F' =

F'1y 47.75F'1z -2.39F'1x -3.75F'4y -47.75F'4z 2.39F'4x -2.93

u =

u2z 0.0000

u' =

u2y -0.0021u2x -0.0003u5z -0.0004u5y -0.0035u5x -0.0012

F' =

F'2y 97.24F'2z -1.37F'2x -1.60F'5y -97.24F'5z 1.37F'5x -2.23

Page 1212: Trabajo Final de Estructuras II(1)

u =

u3z 0.0000

u' =

u3y -0.0009u3x 0.0027u6z -0.0004u6y -0.0015u6x 0.0028

F' =

F'3y 38.49F'3z 3.92F'3x 5.44F'6y -38.49F'6z -3.92F'6x 5.53

u =

u4z -0.0004

u' =

u4y -0.0017u4x -0.0009u7z 0.0001u7y -0.0021u7x -0.0072

F' =

F'4y 30.38F'4z -5.87F'4x -5.98F'7y -30.38F'7z 5.87F'7x -10.45

Page 1213: Trabajo Final de Estructuras II(1)

u =

u5z -0.0004

u' =

u5y -0.0035u5x -0.0012u8z 0.0001u8y -0.0044u8x 0.0023

F' =

F'5y 56.00F'5z 1.08F'5x 0.25F'8y -56.00F'8z -1.08F'8x 2.77

u =

u6z -0.0004

u' =

u6y -0.0015u6x 0.0028u9z 0.0001u9y -0.0017u9x 0.0034

F' =

F'6y 16.37F'6z 4.87F'6x 6.61F'9y -16.37F'9z -4.87F'9x 7.03

Page 1214: Trabajo Final de Estructuras II(1)

u =

u1z 0.0000

u' =

u1y -0.0010u1x -0.0020u2z 0.0000u2y -0.0021u2x -0.0003

F' =

F'1y 0.00F'1z -1.15F'1x -2.51F'2y 0.00F'2z 1.15F'2x -1.24

u =

u2z 0.0000

u' =

u2y -0.0021u2x -0.0003u3z 0.0000u3y -0.0009u3x 0.0027

F' =

F'2y 0.00F'2z 0.88F'2x 0.65F'3y 0.00F'3z -0.88F'3x 2.61

u =

u4z -0.0004

u' =

u4y -0.0017u4x -0.0009

Page 1215: Trabajo Final de Estructuras II(1)

u = u5z -0.0004 u' =u5y -0.0035u5x -0.0012

F' =

F'4y 0.00F'4z -0.64F'4x -0.92F'5y 0.00F'5z 0.64F'5x -1.19

u =

u5z -0.0004

u' =

u5y -0.0035u5x -0.0012u6z -0.0004u6y -0.0015u6x 0.0028

F' =

F'5y 0.00F'5z 0.23F'5x -0.88F'6y 0.00F'6z -0.23F'6x 1.74

u =

u7z 0.0001

u' =

u7y -0.0021u7x -0.0072u8z 0.0001u8y -0.0044u8x 0.0023

Page 1216: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z -2.37F'7x -7.43F'8y 0.00F'8z 2.37F'8x -0.33

u =

u8z 0.0001

u' =

u8y -0.0044u8x 0.0023u9z 0.0001u9y -0.0017u9x 0.0034

F' =

F'8y 0.00F'8z 2.26F'8x 3.87F'9y 0.00F'9z -2.26F'9x 4.54

ELEMENTO 11

F' =

0.00 0.000.88 18.630.65

+11.56

0.00 0.00-0.88 18.63

Page 1217: Trabajo Final de Estructuras II(1)

F' =

2.61 11.56

ELEMENTO 13

F' =

0.00 0.000.23 22.35-0.88

+13.88

0.00 0.00-0.23 22.351.74 13.88

ELEMENTO 15

F' =

0.00 0.002.26 18.633.87

+11.56

0.00 0.00-2.26 18.634.54 11.56

∆rr D

0.0025 cm 0.00088

-0.0022 cm -0.00077

0.0001 cm 0.00002

Page 1218: Trabajo Final de Estructuras II(1)
Page 1219: Trabajo Final de Estructuras II(1)
Page 1220: Trabajo Final de Estructuras II(1)
Page 1221: Trabajo Final de Estructuras II(1)
Page 1222: Trabajo Final de Estructuras II(1)
Page 1223: Trabajo Final de Estructuras II(1)
Page 1224: Trabajo Final de Estructuras II(1)
Page 1225: Trabajo Final de Estructuras II(1)
Page 1226: Trabajo Final de Estructuras II(1)
Page 1227: Trabajo Final de Estructuras II(1)
Page 1228: Trabajo Final de Estructuras II(1)
Page 1229: Trabajo Final de Estructuras II(1)
Page 1230: Trabajo Final de Estructuras II(1)
Page 1231: Trabajo Final de Estructuras II(1)
Page 1232: Trabajo Final de Estructuras II(1)
Page 1233: Trabajo Final de Estructuras II(1)
Page 1234: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 1235: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 1236: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 1237: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y -0.0010u'1z 0.0000u'1x -0.0020

Page 1238: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0021u'2z 0.0000u'2x -0.0003

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y -0.0009u'3z 0.0000u'3x 0.0027

Page 1239: Trabajo Final de Estructuras II(1)

u'1y -0.0010u'1z 0.0000u'1x -0.0020u'4y -0.0017u'4z 0.0004u'4x -0.0009

u'2y -0.0021u'2z 0.0000u'2x -0.0003u'5y -0.0035u'5z 0.0004u'5x -0.0012

Page 1240: Trabajo Final de Estructuras II(1)

u'3y -0.0009u'3z 0.0000u'3x 0.0027u'6y -0.0015u'6z 0.0004u'6x 0.0028

u'4y -0.0017u'4z 0.0004u'4x -0.0009u'7y -0.0021u'7z -0.0001u'7x -0.0072

Page 1241: Trabajo Final de Estructuras II(1)

u'5y -0.0035u'5z 0.0004u'5x -0.0012u'8y -0.0044u'8z -0.0001u'8x 0.0023

u'6y -0.0015u'6z 0.0004u'6x 0.0028u'9y -0.0017u'9z -0.0001u'9x 0.0034

Page 1242: Trabajo Final de Estructuras II(1)

u'1y 0.0000u'1z -0.0010u'1x -0.0020u'2y 0.0000u'2z -0.0021u'2x -0.0003

u'2y 0.0000u'2z -0.0021u'2x -0.0003u'3y 0.0000u'3z -0.0009u'3x 0.0027

u'4y -0.0004u'4z -0.0017u'4x -0.0009

Page 1243: Trabajo Final de Estructuras II(1)

u'5y -0.0004u'5z -0.0035u'5x -0.0012

u'5y -0.0004u'5z -0.0035u'5x -0.0012u'6y -0.0004u'6z -0.0015u'6x 0.0028

u'7y 0.0001u'7z -0.0021u'7x -0.0072u'8y 0.0001u'8z -0.0044u'8x 0.0023

Page 1244: Trabajo Final de Estructuras II(1)

u'8y 0.0001u'8z -0.0044u'8x 0.0023u'9y 0.0001u'9z -0.0017u'9x 0.0034

0.000019.5020

=12.21680.000017.7480

Page 1245: Trabajo Final de Estructuras II(1)

14.1760

0.000022.5797

=12.99470.000022.120315.6121

0.000020.8812

=15.43200.000016.368816.0984

Page 1246: Trabajo Final de Estructuras II(1)
Page 1247: Trabajo Final de Estructuras II(1)
Page 1248: Trabajo Final de Estructuras II(1)
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Page 1251: Trabajo Final de Estructuras II(1)
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Page 1255: Trabajo Final de Estructuras II(1)
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Page 1262: Trabajo Final de Estructuras II(1)

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

Page 1263: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

Page 1264: Trabajo Final de Estructuras II(1)

8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 1291: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

Page 1292: Trabajo Final de Estructuras II(1)
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ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

f'c= 210

E= 2173706.51

0.1762

0.1653

0.0864

3.275

A

1

4

714

12

10

7

4

1

Page 1303: Trabajo Final de Estructuras II(1)

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5z

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

10

3.275

R= 16.375M= 8.938

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 1304: Trabajo Final de Estructuras II(1)

ELEMENTO N° 12

11

3.275

R= 18.013M= 9.832

ELEMENTO N° 14

20

3.275

R= 32.750M= 17.876

17.87604167

0.1761628435

-32.75

9.831822917

Page 1305: Trabajo Final de Estructuras II(1)

0.1652686683-18.0125

8.938020833

0.0864276316-16.375

Page 1306: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

Page 1307: Trabajo Final de Estructuras II(1)

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 1

0

1

C = 1320.829D = -660.414E = -660.414

63399.773 0

0 440.276

0 660.414

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

[ 〖�^1 〗 _11 ]=

Page 1308: Trabajo Final de Estructuras II(1)

-63399.773 0

0 -440.276

0 660.414

COORDENADAS GLOBALES

ELEMENTO N° 4

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 1309: Trabajo Final de Estructuras II(1)

0.00-758.13

ELEMENTO N° 5

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1310: Trabajo Final de Estructuras II(1)

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 7

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1311: Trabajo Final de Estructuras II(1)

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 8

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1312: Trabajo Final de Estructuras II(1)

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 9

raz = 67928.328

raax = 541.520

rabx = rbax = 758.129

r11x = r22x = 1415.174

r12x = r21x = 707.587

67928.328 0

0 541.520

0 758.129

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

Page 1313: Trabajo Final de Estructuras II(1)

-67928.328 0

0 -541.520

0 758.129

COORDENADAS GLOBALES

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 10

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1314: Trabajo Final de Estructuras II(1)

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 11

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1315: Trabajo Final de Estructuras II(1)

0.00

ELEMENTO N° 12

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1316: Trabajo Final de Estructuras II(1)

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

ELEMENTO N° 14

raz = 49779.538

raax = 417.706

rabx = rbax = 683.994

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1317: Trabajo Final de Estructuras II(1)

r11x = r22x = 1493.386

r12x = r21x = 746.693

49779.538 0

0 417.706

0 683.994

-49779.538 0

0 -417.706

0 683.994

COORDENADAS GLOBALES

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 15

raz = 43765.903

raax = 283.874

rabx = rbax = 528.716

r11x = r22x = 1312.977

r12x = r21x = 656.489

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1318: Trabajo Final de Estructuras II(1)

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

COORDENADAS GLOBALES

43765.900.000.00

-43765.900.000.00

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

1 21z 1y 1x 2z

5.1E+04 8.0E-12 -9.8E+01 -5.0E+048.0E-12 1.3E+05 6.8E+02 0.0E+00

-9.8E+01 6.8E+02 4.2E+03 0.0E+00-5.0E+04 0.0E+00 0.0E+00 9.5E+040.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 -4.4E+040.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 7.6E+02 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+020.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

Page 1319: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21z 1y 1x 2z

8.0E-12 1.3E+05 6.8E+02 0.0E+00-9.8E+01 6.8E+02 4.2E+03 0.0E+000.0E+00 -4.2E+02 -6.8E+02 8.0E-120.0E+00 6.8E+02 7.5E+02 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+009.8E+02 8.0E-12 -9.8E+01 9.8E+02-5.4E+02 -4.1E-12 7.6E+02 -5.4E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.3E+05 6.8E+02 -4.2E+02 6.8E+026.8E+02 4.2E+03 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 1.3E+05 -1.6E+026.8E+02 7.5E+02 -1.6E+02 5.5E+030.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 5.3E+02 6.6E+02

Page 1320: Trabajo Final de Estructuras II(1)

-6.8E+04 -4.6E-14 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 -6.8E+04 -4.6E-140.0E+00 0.0E+00 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00

1 21y 1x 2y 2x

1.6E-05 -3.3E-06 2.0E-07 -2.4E-06-3.3E-06 3.0E-04 2.4E-06 -4.9E-062.0E-07 2.4E-06 1.5E-05 4.8E-07-2.4E-06 -4.9E-06 4.8E-07 2.1E-04-8.8E-08 8.6E-07 1.7E-07 1.9E-06-1.1E-06 6.0E-05 -1.6E-06 -7.3E-071.6E-05 -3.4E-06 3.2E-07 -2.5E-06-3.2E-06 -2.1E-05 1.8E-06 2.8E-053.2E-07 2.1E-06 1.5E-05 5.0E-07-2.5E-06 2.8E-05 4.9E-07 -1.6E-05-1.4E-07 1.2E-06 2.8E-07 2.0E-06-1.8E-06 2.1E-05 -8.3E-07 2.8E-051.6E-05 -3.4E-06 3.7E-07 -2.5E-06-4.0E-06 1.2E-05 3.2E-06 -3.1E-063.7E-07 2.2E-06 1.5E-05 5.0E-07-2.5E-06 -2.8E-06 4.9E-07 7.9E-06-1.7E-07 1.2E-06 3.3E-07 2.0E-06-9.7E-07 -1.6E-07 -2.4E-06 -3.5E-063.4E-06 -1.8E-04 -6.6E-07 -1.0E-041.0E-05 -3.6E-04 -2.0E-06 -2.2E-041.7E-05 -3.8E-04 -3.3E-06 -2.4E-04

U1zU1y

Page 1321: Trabajo Final de Estructuras II(1)

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.0

Ɵ1x

Ɵ2x

Ɵ3x

Ɵ4x

Ɵ5x

Ɵ6x

Ɵ7x

Ɵ8x

Ɵ9x

Page 1322: Trabajo Final de Estructuras II(1)

K' =

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 3

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

Page 1323: Trabajo Final de Estructuras II(1)

K' =

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 5

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

Page 1324: Trabajo Final de Estructuras II(1)

ELEMENTO 6

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 7

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Page 1325: Trabajo Final de Estructuras II(1)

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 9

Ɵ = 1.570796

T =

0 1-1 00 00 00 00 0

K' =

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 10

Ɵ = 0.000000

Page 1326: Trabajo Final de Estructuras II(1)

T =

1 00 10 00 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 11

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 12

Ɵ = 0.000000

T =

1 00 10 0

Page 1327: Trabajo Final de Estructuras II(1)

T =0 00 00 0

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 13

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 14

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

Page 1328: Trabajo Final de Estructuras II(1)

K' =

49779.5 0.00.0 417.70.0 684.0

-49779.5 0.00.0 -417.70.0 684.0

ELEMENTO 15

Ɵ = 0.000000

T =

1 00 10 00 00 00 0

K' =

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

VERIFICACIÓN DEL EQUILIBRIO

ELEMENTO 10

F' =

0.00-1.23-2.65

+0.001.23

Page 1329: Trabajo Final de Estructuras II(1)

F' =

-1.36

ELEMENTO 12

F' =

0.00-0.70-1.03

+0.000.70-1.28

ELEMENTO 14

F' =

0.00-2.39-7.48

+0.002.39-0.36

N hn ∆re

3 2.80 cm 0.0007 cm

2 2.80 cm 0.0002 cm

1 3.00 cm 0.0003 cm

Page 1330: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

0.35 m 0.35 m

0.25 m 0.25 m

A= 0.08750 A= 0.08750Ic= 0.00046 Ic= 0.00046

0.25 cm 0.25 cm

0.30 cm

Iv0.0006 cm

Av0.07500 cm

3.275 3.725

B

2

5

814 15

12 13

1110

2

5

8

Page 1331: Trabajo Final de Estructuras II(1)

U1y 0.0000Ɵ1x 0.0000U2y 0.0000Ɵ2x 0.0000U3y 0.0000Ɵ3x 0.0000U4y 0.0000Ɵ4x 0.0000U5y 0.0000Ɵ5x F= 0.0000

= U6y 0.0000Ɵ6x 0.0000U7y 0.0000Ɵ7x 0.0000U8y 0.0000Ɵ8x 0.0000U9y 0.0000Ɵ9x 0.0000Uz1 0.0864Uz2 0.1653Uz3 0.1762

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 11

10

3.275

R= 16.375 R=M= 8.938 M=

Page 1332: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

11

3.275

R= 18.013 R=M= 9.832 M=

ELEMENTO N° 15

20

3.275

R= 32.750 R=M= 17.876 M=

6.313020833 11.56302083

-51.375

-4.043802083 13.875625

Page 1333: Trabajo Final de Estructuras II(1)

-40.3625

-2.625 11.56302083

-35

-16.4-8.9

-35.0-2.6

-18.611.6-18.0-9.8

-40.4F= -4.0

-22.413.9-32.8-17.9-51.46.3

-18.611.60.10.20.2

Page 1334: Trabajo Final de Estructuras II(1)

ELEMENTO N° 1

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 2

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

Page 1335: Trabajo Final de Estructuras II(1)

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 3

raz = 63399.773

raax = 440.276

rabx = rbax = 660.414

r11x = r22x = 1320.829

r12x = r21x = 660.414

0 -63399.773 0

660.414 0 -440.276

1320.829 0 -660.414

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _12 ]=

Page 1336: Trabajo Final de Estructuras II(1)

0 63399.773 0

-660.414 0 440.276

660.414 0 -660.414

440.28 0.00 660.410.00 63399.8 0.00

660.41 0.00 1320.83

ELEMENTO N° 4

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _22 ]=

[ 〖�^1 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

Page 1337: Trabajo Final de Estructuras II(1)

-67928.3 0.000.00 707.59

ELEMENTO N° 5

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 6

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1338: Trabajo Final de Estructuras II(1)

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 7

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1339: Trabajo Final de Estructuras II(1)

758.129758.1291.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 8

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1340: Trabajo Final de Estructuras II(1)

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 9

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

1.00

1415.174

707.587

0 -67928.328 0

758.129 0 -541.520

1415.174 0 -758.129

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 1341: Trabajo Final de Estructuras II(1)

0 67928.328 0

-758.129 0 541.520

707.587 0 -758.129

0.00 -758.1367928.3 0.00

0.00 1415.17

0.00 758.13-67928.3 0.00

0.00 707.59

ELEMENTO N° 10

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

Page 1342: Trabajo Final de Estructuras II(1)

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 11

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1343: Trabajo Final de Estructuras II(1)

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 13

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1344: Trabajo Final de Estructuras II(1)

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

ELEMENTO N° 14

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

0.00

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1345: Trabajo Final de Estructuras II(1)

1493.386

746.693

0 -49779.538 0

683.994 0 -417.706

1493.386 0 -683.994

0 49779.538 0

-683.994 0 417.706

746.693 0 -683.994

0.00 0.00417.7 683.99

683.99 1493.39

0.00 0.00-417.7 -683.99683.99 746.69

ELEMENTO N° 15

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

0.00

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1346: Trabajo Final de Estructuras II(1)

0 -43765.903 0

528.716 0 -283.874

1312.977 0 -528.716

0 43765.903 0

-528.716 0 283.874

656.489 0 -528.716

0.00 0.00283.9 528.72

528.72 1312.98

0.00 0.00-283.9 -528.72528.72 656.49

CÁLCULO DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

2 32y 2x 3z 3y 3x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.4E+04 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+020.0E+00 0.0E+00 4.5E+04 8.0E-12 -9.8E+01-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-14

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

Page 1347: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

2 32y 2x 3z 3y 3x

-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+001.3E+05 -1.6E+02 0.0E+00 -2.8E+02 5.3E+02-1.6E+02 5.5E+03 0.0E+00 -5.3E+02 6.6E+02-2.8E+02 -5.3E+02 8.0E-12 1.3E+05 -5.3E+025.3E+02 6.6E+02 -9.8E+01 -5.3E+02 4.0E+030.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 0.0E+004.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 -4.6E-140.0E+00 0.0E+00 -7.6E+02 4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 9.8E+02 8.0E-12 -9.8E+01-4.1E-12 7.6E+02 -5.4E+02 -4.1E-12 7.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

3 4 53y 3x 4y 4x 5y

0.0E+00 0.0E+00 -6.8E+04 4.6E-14 0.0E+000.0E+00 0.0E+00 -4.6E-14 7.1E+02 0.0E+00-2.8E+02 5.3E+02 0.0E+00 0.0E+00 -6.8E+04-5.3E+02 6.6E+02 0.0E+00 0.0E+00 -4.6E-141.3E+05 -5.3E+02 0.0E+00 0.0E+00 0.0E+00-5.3E+02 4.0E+03 0.0E+00 0.0E+00 0.0E+00

Page 1348: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 1.4E+05 6.8E+02 -4.2E+020.0E+00 0.0E+00 6.8E+02 4.3E+03 -6.8E+020.0E+00 0.0E+00 -4.2E+02 -6.8E+02 1.4E+050.0E+00 0.0E+00 6.8E+02 7.5E+02 -1.6E+02-6.8E+04 -4.6E-14 0.0E+00 0.0E+00 -2.8E+024.6E-14 7.1E+02 0.0E+00 0.0E+00 5.3E+020.0E+00 0.0E+00 -6.8E+04 -4.6E-14 0.0E+000.0E+00 0.0E+00 4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -6.8E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.0E-12 -9.8E+01 -4.1E-12 -7.6E+02 -4.1E-12-4.1E-12 7.6E+02 8.3E-12 0.0E+00 8.3E-120.0E+00 0.0E+00 -4.1E-12 7.6E+02 -4.1E-12

3 4 53y 3x 4y 4x 5y

-8.8E-08 -1.1E-06 1.6E-05 -3.2E-06 3.2E-078.6E-07 6.0E-05 -3.4E-06 -2.1E-05 2.1E-061.7E-07 -1.6E-06 3.2E-07 1.8E-06 1.5E-051.9E-06 -7.3E-07 -2.5E-06 2.8E-05 5.0E-071.6E-05 2.7E-06 -1.4E-07 1.4E-06 2.8E-072.7E-06 3.2E-04 -1.6E-06 2.1E-05 -1.2E-06-1.4E-07 -1.6E-06 3.0E-05 -6.1E-06 5.5E-071.4E-06 2.1E-05 -6.1E-06 3.1E-04 3.8E-062.8E-07 -1.2E-06 5.5E-07 3.8E-06 2.9E-052.0E-06 2.8E-05 -4.7E-06 -5.9E-06 9.3E-071.6E-05 2.8E-06 -2.5E-07 2.3E-06 4.8E-072.6E-06 -2.3E-05 -3.0E-06 5.9E-05 -2.1E-06-1.7E-07 -1.6E-06 3.0E-05 -6.1E-06 6.6E-077.3E-07 3.2E-08 -7.6E-06 -3.5E-05 6.2E-063.3E-07 -1.3E-06 6.6E-07 3.3E-06 2.9E-052.0E-06 -3.1E-06 -4.8E-06 3.7E-05 9.4E-071.6E-05 2.8E-06 -3.0E-07 2.8E-06 5.8E-073.4E-06 1.2E-05 -1.9E-06 2.6E-05 -4.6E-06-2.7E-06 -1.9E-04 3.7E-06 -1.4E-05 -7.2E-07-8.1E-06 -3.8E-04 1.4E-05 -2.0E-04 -2.7E-06-1.4E-05 -3.9E-04 2.7E-05 -3.8E-04 -5.1E-06

Page 1349: Trabajo Final de Estructuras II(1)

U1y -0.000991Ɵ1x -0.002103U2y -0.002118Ɵ2x -0.000378U3y -0.000889Ɵ3x 0.002575U4y -0.001692Ɵ4x -0.000913U5y -0.003550Ɵ5x -0.001251U6y = -0.001457Ɵ6x 0.002719U7y -0.002139Ɵ7x -0.007195U8y -0.004374Ɵ8x 0.002331U9y -0.001698Ɵ9x 0.003335Uz1 0.000277Uz2 0.000184Uz3 0.000746

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0

Page 1350: Trabajo Final de Estructuras II(1)

660.4 0.0 -440.3 660.41320.8 0.0 -660.4 660.4

0.0 63399.8 0.0 0.0-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -63399.8 0.0 0.0660.4 0.0 -440.3 660.4

1320.8 0.0 -660.4 660.40.0 63399.8 0.0 0.0

Page 1351: Trabajo Final de Estructuras II(1)

-660.4 0.0 440.3 -660.4660.4 0.0 -660.4 1320.8

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1352: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1353: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

0 0 0 00 0 0 01 0 0 00 0 1 00 -1 0 00 0 0 1

0.0 -67928.3 0.0 0.0758.1 0.0 -541.5 758.1

1415.2 0.0 -758.1 707.60.0 67928.3 0.0 0.0

-758.1 0.0 541.5 -758.1707.6 0.0 -758.1 1415.2

Page 1354: Trabajo Final de Estructuras II(1)

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 0

Page 1355: Trabajo Final de Estructuras II(1)

0 1 0 00 0 1 00 0 0 1

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

Page 1356: Trabajo Final de Estructuras II(1)

0.0 -49779.5 0.0 0.0684.0 0.0 -417.7 684.0

1493.4 0.0 -684.0 746.70.0 49779.5 0.0 0.0

-684.0 0.0 417.7 -684.0746.7 0.0 -684.0 1493.4

0 0 0 00 0 0 01 0 0 00 1 0 00 0 1 00 0 0 1

0.0 -43765.9 0.0 0.0528.7 0.0 -283.9 528.7

1313.0 0.0 -528.7 656.50.0 43765.9 0.0 0.0

-528.7 0.0 283.9 -528.7656.5 0.0 -528.7 1313.0

VERIFICACIÓN DEL EQUILIBRIO

0.00 0.000016.38 15.14928.94

=6.2868

0.00 0.000016.38 17.6008

Page 1357: Trabajo Final de Estructuras II(1)

8.94 7.5749

0.00 0.000018.01 17.30889.83

=8.8057

0.00 0.000018.01 18.71629.83 8.5533

0.00 0.000032.75 30.356917.88

=10.4009

0.00 0.000032.75 35.143117.88 17.5138

∆tr ∆rr

0.0006 cm 0.0045 cm 0.0034 cm

-0.0001 cm 0.0011 cm -0.0006 cm

0.0003 cm 0.0017 cm 0.0017 cm

∆te

Page 1358: Trabajo Final de Estructuras II(1)

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

2.8

2.8

3

3.725

C

3

6

9

9

6

3

Page 1359: Trabajo Final de Estructuras II(1)

ELEMENTO N° 11

10

3.725

18.625 R= 18.62511.563 M= 11.563

Page 1360: Trabajo Final de Estructuras II(1)

ELEMENTO N° 13

12

3.725

22.350 R= 22.35013.876 M= 13.876

ELEMENTO N° 15

10

3.725

18.625 R= 18.62511.563 M= 11.563

-18.625

Page 1361: Trabajo Final de Estructuras II(1)

-22.35

-18.625

Page 1362: Trabajo Final de Estructuras II(1)

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

Page 1363: Trabajo Final de Estructuras II(1)

1320.8291320.829

660.414

0

660.414

660.414

0

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

0

660.414

660.414

Page 1364: Trabajo Final de Estructuras II(1)

0

-660.414

1320.829

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.13

Page 1365: Trabajo Final de Estructuras II(1)

0.00 67928.3 0.00758.13 0.00 1415.17

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1366: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1367: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

Page 1368: Trabajo Final de Estructuras II(1)

0

758.129

707.587

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

758.129

707.587

Page 1369: Trabajo Final de Estructuras II(1)

0

-758.129

1415.174

-541.52 0.00 -758.130.00 -67928.3 0.00

758.13 0.00 707.59

541.52 0.00 758.130.00 67928.3 0.00

758.13 0.00 1415.17

0

683.994

746.693

0

-683.994

1493.386

Page 1370: Trabajo Final de Estructuras II(1)

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.72

Page 1371: Trabajo Final de Estructuras II(1)

0.00 -528.72 1312.98

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 1372: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

Page 1373: Trabajo Final de Estructuras II(1)

0

683.994

746.693

0

-683.994

1493.386

-49779.54 0.00 0.000.00 -417.7 683.990.00 -683.99 746.69

49779.54 0.00 0.000.00 417.7 -683.990.00 -683.99 1493.39

Page 1374: Trabajo Final de Estructuras II(1)

0

528.716

656.489

0

-528.716

1312.977

-43765.90 0.00 0.000.00 -283.9 528.720.00 -528.72 656.49

43765.90 0.00 0.000.00 283.9 -528.720.00 -528.72 1312.98

4 54z 4y 4x 5z 5y

-5.4E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+005.1E+04 8.3E-12 0.0E+00 -5.0E+04 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+02-5.0E+04 0.0E+00 0.0E+00 9.5E+04 8.3E-120.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 -4.4E+04 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+02

Page 1375: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-5.4E+02 -4.1E-12 7.6E+02 0.0E+00 0.0E+00-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -5.4E+02 -4.1E-120.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

4 54z 4y 4x 5z 5y

-4.1E-12 -6.8E+04 4.6E-14 0.0E+00 0.0E+007.6E+02 -4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 7.6E+02 -4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+008.3E-12 1.4E+05 6.8E+02 0.0E+00 -4.2E+020.0E+00 6.8E+02 4.3E+03 0.0E+00 -6.8E+020.0E+00 -4.2E+02 -6.8E+02 8.3E-12 1.4E+050.0E+00 6.8E+02 7.5E+02 0.0E+00 -1.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 -2.8E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 5.3E+02-4.1E-12 -6.8E+04 -4.6E-14 0.0E+00 0.0E+00-7.6E+02 4.6E-14 7.1E+02 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -4.1E-12 -6.8E+040.0E+00 0.0E+00 0.0E+00 -7.6E+02 4.6E-140.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-5.4E+02 -4.1E-12 -7.6E+02 -5.4E+02 -4.1E-121.1E+03 8.3E-12 0.0E+00 1.1E+03 8.3E-12-5.4E+02 -4.1E-12 7.6E+02 -5.4E+02 -4.1E-12

5 6 75x 6y 6x 7y 7x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -6.8E+04 4.6E-14 0.0E+00 0.0E+000.0E+00 -4.6E-14 7.1E+02 0.0E+00 0.0E+00

Page 1376: Trabajo Final de Estructuras II(1)

6.8E+02 0.0E+00 0.0E+00 -6.8E+04 4.6E-147.5E+02 0.0E+00 0.0E+00 -4.6E-14 7.1E+02-1.6E+02 -2.8E+02 5.3E+02 0.0E+00 0.0E+005.6E+03 -5.3E+02 6.6E+02 0.0E+00 0.0E+00-5.3E+02 1.4E+05 -5.3E+02 0.0E+00 0.0E+006.6E+02 -5.3E+02 4.1E+03 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 6.8E+04 6.8E+020.0E+00 0.0E+00 0.0E+00 6.8E+02 2.9E+03-4.6E-14 0.0E+00 0.0E+00 -4.2E+02 -6.8E+027.1E+02 0.0E+00 0.0E+00 6.8E+02 7.5E+020.0E+00 -6.8E+04 -4.6E-14 0.0E+00 0.0E+000.0E+00 4.6E-14 7.1E+02 0.0E+00 0.0E+00-7.6E+02 -4.1E-12 -7.6E+02 0.0E+00 0.0E+000.0E+00 8.3E-12 0.0E+00 -4.1E-12 -7.6E+027.6E+02 -4.1E-12 7.6E+02 4.1E-12 7.6E+02

5 6 75x 6y 6x 7y 7x

-2.5E-06 -1.4E-07 -1.8E-06 1.6E-05 -4.0E-062.8E-05 1.2E-06 2.1E-05 -3.4E-06 1.2E-054.9E-07 2.8E-07 -8.3E-07 3.7E-07 3.2E-06-1.6E-05 2.0E-06 2.8E-05 -2.5E-06 -3.1E-062.0E-06 1.6E-05 2.6E-06 -1.7E-07 7.3E-072.8E-05 2.8E-06 -2.3E-05 -1.6E-06 3.2E-08-4.7E-06 -2.5E-07 -3.0E-06 3.0E-05 -7.6E-06-5.9E-06 2.3E-06 5.9E-05 -6.1E-06 -3.5E-059.3E-07 4.8E-07 -2.1E-06 6.6E-07 6.2E-062.2E-04 3.8E-06 -1.9E-06 -4.8E-06 4.2E-053.8E-06 3.0E-05 5.0E-06 -3.0E-07 1.4E-06-1.9E-06 5.0E-06 3.2E-04 -3.6E-06 2.6E-05-4.8E-06 -3.0E-07 -3.6E-06 4.5E-05 -1.1E-054.2E-05 1.4E-06 2.6E-05 -1.1E-05 4.3E-049.4E-07 5.7E-07 -1.4E-06 8.1E-07 9.7E-06-2.7E-05 3.9E-06 3.7E-05 -7.1E-06 -5.1E-053.9E-06 3.0E-05 5.0E-06 -3.6E-07 1.6E-064.2E-05 6.5E-06 -3.9E-05 -2.1E-06 6.6E-05-2.0E-05 -3.0E-06 -1.3E-05 3.8E-06 -4.3E-06-1.4E-04 -1.1E-05 -2.0E-04 1.4E-05 -2.4E-05-2.6E-04 -2.2E-05 -3.9E-04 3.0E-05 -2.5E-04

Page 1377: Trabajo Final de Estructuras II(1)

u =

uaz 0.0000

u' =

uay 0.0000uax 0.0000u1z 0.0003u1y -0.0010u1x -0.0021

F' =

F'ay 62.81

Page 1378: Trabajo Final de Estructuras II(1)

F' =

F'az -1.27F'ax -1.21F'1y -62.81F'1z 1.27F'1x -2.59

u =

ubz 0.0000

u' =

uby 0.0000ubx 0.0000u2z 0.0003u2y -0.0021u2x -0.0004

F' =

F'by 134.29F'bz -0.13F'bx -0.07F'2y -134.29F'2z 0.13F'2x -0.32

u =

ucz 0.0000

u' =

ucy 0.0000ucx 0.0000u3z 0.0003u3y -0.0009u3x 0.0026

F' =

F'cy 56.37F'cz 1.82F'cx 1.88F'3y -56.37

Page 1379: Trabajo Final de Estructuras II(1)

F' =F'3z -1.82F'3x 3.58

u =

u1z 0.0003

u' =

u1y -0.0010u1x -0.0021u4z 0.0002u4y -0.0017u4x -0.0009

F' =

F'1y 47.67F'1z -2.34F'1x -3.69F'4y -47.67F'4z 2.34F'4x -2.85

u =

u2z 0.0003

u' =

u2y -0.0021u2x -0.0004u5z 0.0002u5y -0.0035u5x -0.0013

F' =

F'2y 97.25F'2z -1.28F'2x -1.49F'5y -97.25F'5z 1.28F'5x -2.11

Page 1380: Trabajo Final de Estructuras II(1)

u =

u3z 0.0003

u' =

u3y -0.0009u3x 0.0026u6z 0.0002u6y -0.0015u6x 0.0027

F' =

F'3y 38.56F'3z 3.96F'3x 5.50F'6y -38.56F'6z -3.96F'6x 5.60

u =

u4z 0.0002

u' =

u4y -0.0017u4x -0.0009u7z 0.0007u7y -0.0021u7x -0.0072

F' =

F'4y 30.36F'4z -5.84F'4x -5.96F'7y -30.36F'7z 5.84F'7x -10.40

Page 1381: Trabajo Final de Estructuras II(1)

u =

u5z 0.0002

u' =

u5y -0.0035u5x -0.0013u8z 0.0007u8y -0.0044u8x 0.0023

F' =

F'5y 56.00F'5z 1.12F'5x 0.31F'8y -56.00F'8z -1.12F'8x 2.84

u =

u6z 0.0002

u' =

u6y -0.0015u6x 0.0027u9z 0.0007u9y -0.0017u9x 0.0033

F' =

F'6y 16.39F'6z 4.89F'6x 6.63F'9y -16.39F'9z -4.89F'9x 7.07

Page 1382: Trabajo Final de Estructuras II(1)

u =

u1z 0.0003

u' =

u1y -0.0010u1x -0.0021u2z 0.0003u2y -0.0021u2x -0.0004

F' =

F'1y 0.00F'1z -1.23F'1x -2.65F'2y 0.00F'2z 1.23F'2x -1.36

u =

u2z 0.0003

u' =

u2y -0.0021u2x -0.0004u3z 0.0003u3y -0.0009u3x 0.0026

F' =

F'2y 0.00F'2z 0.81F'2x 0.54F'3y 0.00F'3z -0.81F'3x 2.48

u =

u4z 0.0002

u' =

u4y -0.0017u4x -0.0009

Page 1383: Trabajo Final de Estructuras II(1)

u = u5z 0.0002 u' =u5y -0.0035u5x -0.0013

F' =

F'4y 0.00F'4z -0.70F'4x -1.03F'5y 0.00F'5z 0.70F'5x -1.28

u =

u5z 0.0002

u' =

u5y -0.0035u5x -0.0013u6z 0.0002u6y -0.0015u6x 0.0027

F' =

F'5y 0.00F'5z 0.18F'5x -0.96F'6y 0.00F'6z -0.18F'6x 1.64

u =

u7z 0.0007

u' =

u7y -0.0021u7x -0.0072u8z 0.0007u8y -0.0044u8x 0.0023

Page 1384: Trabajo Final de Estructuras II(1)

F' =

F'7y 0.00F'7z -2.39F'7x -7.48F'8y 0.00F'8z 2.39F'8x -0.36

u =

u8z 0.0007

u' =

u8y -0.0044u8x 0.0023u9z 0.0007u9y -0.0017u9x 0.0033

F' =

F'8y 0.00F'8z 2.24F'8x 3.83F'9y 0.00F'9z -2.24F'9x 4.49

ELEMENTO 11

F' =

0.00 0.000.81 18.630.54

+11.56

0.00 0.00-0.81 18.63

Page 1385: Trabajo Final de Estructuras II(1)

F' =

2.48 11.56

ELEMENTO 13

F' =

0.00 0.000.18 22.35-0.96

+13.88

0.00 0.00-0.18 22.351.64 13.88

ELEMENTO 15

F' =

0.00 0.002.24 18.633.83

+11.56

0.00 0.00-2.24 18.634.49 11.56

∆rr D

0.0034 cm 0.00121

-0.0006 cm -0.00020

0.0017 cm 0.00055

Page 1386: Trabajo Final de Estructuras II(1)
Page 1387: Trabajo Final de Estructuras II(1)
Page 1388: Trabajo Final de Estructuras II(1)
Page 1389: Trabajo Final de Estructuras II(1)
Page 1390: Trabajo Final de Estructuras II(1)
Page 1391: Trabajo Final de Estructuras II(1)
Page 1392: Trabajo Final de Estructuras II(1)
Page 1393: Trabajo Final de Estructuras II(1)
Page 1394: Trabajo Final de Estructuras II(1)
Page 1395: Trabajo Final de Estructuras II(1)
Page 1396: Trabajo Final de Estructuras II(1)
Page 1397: Trabajo Final de Estructuras II(1)
Page 1398: Trabajo Final de Estructuras II(1)
Page 1399: Trabajo Final de Estructuras II(1)
Page 1400: Trabajo Final de Estructuras II(1)
Page 1401: Trabajo Final de Estructuras II(1)
Page 1402: Trabajo Final de Estructuras II(1)

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-7.6E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 -5.4E+026.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+020.0E+00 -4.4E+04 0.0E+00 0.0E+00 0.0E+00-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+000.0E+00 4.5E+04 8.3E-12 0.0E+00 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+00

Page 1403: Trabajo Final de Estructuras II(1)

6.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 5.0E+040.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+027.6E+02 0.0E+00 0.0E+00 0.0E+00 -5.0E+04-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -5.4E+02 -4.1E-12 7.6E+02 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00

5 6 75x 6z 6y 6x 7z

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 4.6E-14 0.0E+000.0E+00 7.6E+02 -4.6E-14 7.1E+02 0.0E+006.8E+02 0.0E+00 0.0E+00 0.0E+00 -4.1E-127.5E+02 0.0E+00 0.0E+00 0.0E+00 7.6E+02-1.6E+02 0.0E+00 -2.8E+02 5.3E+02 0.0E+005.6E+03 0.0E+00 -5.3E+02 6.6E+02 0.0E+00-5.3E+02 8.3E-12 1.4E+05 -5.3E+02 0.0E+006.6E+02 0.0E+00 -5.3E+02 4.1E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 7.6E+02-4.6E-14 0.0E+00 0.0E+00 0.0E+00 0.0E+007.1E+02 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 -4.1E-12 -6.8E+04 -4.6E-14 0.0E+000.0E+00 -7.6E+02 4.6E-14 7.1E+02 0.0E+00-7.6E+02 -5.4E+02 -4.1E-12 -7.6E+02 0.0E+000.0E+00 1.1E+03 8.3E-12 0.0E+00 -5.4E+027.6E+02 -5.4E+02 -4.1E-12 7.6E+02 5.4E+02

8 98y 8x 9y 9x Z1

0.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+010.0E+00 0.0E+00 0.0E+00 0.0E+00 8.0E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -9.8E+01

Page 1404: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 -4.1E-120.0E+00 0.0E+00 0.0E+00 0.0E+00 -7.6E+02-6.8E+04 4.6E-14 0.0E+00 0.0E+00 -4.1E-12-4.6E-14 7.1E+02 0.0E+00 0.0E+00 -7.6E+020.0E+00 0.0E+00 -6.8E+04 4.6E-14 -4.1E-120.0E+00 0.0E+00 -4.6E-14 7.1E+02 -7.6E+02-4.2E+02 6.8E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+02 7.5E+02 0.0E+00 0.0E+00 0.0E+006.9E+04 -1.6E+02 -2.8E+02 5.3E+02 0.0E+00-1.6E+02 4.2E+03 -5.3E+02 6.6E+02 0.0E+00-2.8E+02 -5.3E+02 6.8E+04 -5.3E+02 0.0E+005.3E+02 6.6E+02 -5.3E+02 2.7E+03 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 2.9E+03-4.1E-12 -7.6E+02 -4.1E-12 -7.6E+02 -1.6E+034.1E-12 7.6E+02 4.1E-12 7.6E+02 0.0E+00

8 98y 8x 9y 9x Z1

3.7E-07 -2.5E-06 -1.7E-07 -9.7E-07 3.4E-062.2E-06 -2.8E-06 1.2E-06 -1.6E-07 -1.8E-041.5E-05 4.9E-07 3.3E-07 -2.4E-06 -6.6E-075.0E-07 7.9E-06 2.0E-06 -3.5E-06 -1.0E-043.3E-07 2.0E-06 1.6E-05 3.4E-06 -2.7E-06-1.3E-06 -3.1E-06 2.8E-06 1.2E-05 -1.9E-046.6E-07 -4.8E-06 -3.0E-07 -1.9E-06 3.7E-063.3E-06 3.7E-05 2.8E-06 2.6E-05 -1.4E-052.9E-05 9.4E-07 5.8E-07 -4.6E-06 -7.2E-079.4E-07 -2.7E-05 3.9E-06 4.2E-05 -2.0E-055.7E-07 3.9E-06 3.0E-05 6.5E-06 -3.0E-06-1.4E-06 3.7E-05 5.0E-06 -3.9E-05 -1.3E-058.1E-07 -7.1E-06 -3.6E-07 -2.1E-06 3.8E-069.7E-06 -5.1E-05 1.6E-06 6.6E-05 -4.3E-064.4E-05 1.4E-06 7.1E-07 -7.5E-06 -7.2E-071.4E-06 2.8E-04 5.7E-06 -4.6E-05 -1.0E-067.1E-07 5.7E-06 4.5E-05 9.6E-06 -3.0E-06-7.5E-06 -4.6E-05 9.6E-06 4.6E-04 -4.2E-06-7.2E-07 -1.0E-06 -3.0E-06 -4.2E-06 9.9E-04-2.7E-06 -2.4E-05 -1.1E-05 -2.2E-05 1.2E-03-5.7E-06 -1.3E-04 -2.5E-05 -2.6E-04 1.3E-03

Page 1405: Trabajo Final de Estructuras II(1)

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y -0.0010u'1z -0.0003u'1x -0.0021

Page 1406: Trabajo Final de Estructuras II(1)

u'by 0.0000u'bz 0.0000u'bx 0.0000u'2y -0.0021u'2z -0.0003u'2x -0.0004

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y -0.0009u'3z -0.0003u'3x 0.0026

Page 1407: Trabajo Final de Estructuras II(1)

u'1y -0.0010u'1z -0.0003u'1x -0.0021u'4y -0.0017u'4z -0.0002u'4x -0.0009

u'2y -0.0021u'2z -0.0003u'2x -0.0004u'5y -0.0035u'5z -0.0002u'5x -0.0013

Page 1408: Trabajo Final de Estructuras II(1)

u'3y -0.0009u'3z -0.0003u'3x 0.0026u'6y -0.0015u'6z -0.0002u'6x 0.0027

u'4y -0.0017u'4z -0.0002u'4x -0.0009u'7y -0.0021u'7z -0.0007u'7x -0.0072

Page 1409: Trabajo Final de Estructuras II(1)

u'5y -0.0035u'5z -0.0002u'5x -0.0013u'8y -0.0044u'8z -0.0007u'8x 0.0023

u'6y -0.0015u'6z -0.0002u'6x 0.0027u'9y -0.0017u'9z -0.0007u'9x 0.0033

Page 1410: Trabajo Final de Estructuras II(1)

u'1y 0.0003u'1z -0.0010u'1x -0.0021u'2y 0.0003u'2z -0.0021u'2x -0.0004

u'2y 0.0003u'2z -0.0021u'2x -0.0004u'3y 0.0003u'3z -0.0009u'3x 0.0026

u'4y 0.0002u'4z -0.0017u'4x -0.0009

Page 1411: Trabajo Final de Estructuras II(1)

u'5y 0.0002u'5z -0.0035u'5x -0.0013

u'5y 0.0002u'5z -0.0035u'5x -0.0013u'6y 0.0002u'6z -0.0015u'6x 0.0027

u'7y 0.0007u'7z -0.0021u'7x -0.0072u'8y 0.0007u'8z -0.0044u'8x 0.0023

Page 1412: Trabajo Final de Estructuras II(1)

u'8y 0.0007u'8z -0.0044u'8x 0.0023u'9y 0.0007u'9z -0.0017u'9x 0.0033

0.000019.4376

=12.10740.000017.8124

Page 1413: Trabajo Final de Estructuras II(1)

14.0456

0.000022.5323

=12.91200.000022.167715.5181

0.000020.8608

=15.39780.000016.389216.0566

Page 1414: Trabajo Final de Estructuras II(1)
Page 1415: Trabajo Final de Estructuras II(1)
Page 1416: Trabajo Final de Estructuras II(1)
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Page 1430: Trabajo Final de Estructuras II(1)

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -5.4E+02 -4.1E-12 -7.6E+020.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

Page 1431: Trabajo Final de Estructuras II(1)

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+004.1E-12 7.6E+02 -5.0E+04 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+020.0E+00 0.0E+00 9.4E+04 4.1E-12 7.6E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 -4.4E+04 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+02

7 87y 7x 8z 8y 8x

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-6.8E+04 4.6E-14 0.0E+00 0.0E+00 0.0E+00-4.6E-14 7.1E+02 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 -4.1E-12 -6.8E+04 4.6E-140.0E+00 0.0E+00 7.6E+02 -4.6E-14 7.1E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+000.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+006.8E+04 6.8E+02 0.0E+00 -4.2E+02 6.8E+026.8E+02 2.9E+03 0.0E+00 -6.8E+02 7.5E+02-4.2E+02 -6.8E+02 4.1E-12 6.9E+04 -1.6E+026.8E+02 7.5E+02 7.6E+02 -1.6E+02 4.2E+030.0E+00 0.0E+00 0.0E+00 -2.8E+02 -5.3E+020.0E+00 0.0E+00 0.0E+00 5.3E+02 6.6E+020.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00-4.1E-12 -7.6E+02 -5.4E+02 -4.1E-12 -7.6E+024.1E-12 7.6E+02 5.4E+02 4.1E-12 7.6E+02

Z2 Z3-4.1E-12 0.0E+00 1y

17.6E+02 0.0E+00 1x-4.1E-12 0.0E+00 2y

27.6E+02 0.0E+00 2x-4.1E-12 0.0E+00 3y

37.6E+02 0.0E+00 3x

Page 1432: Trabajo Final de Estructuras II(1)

8.3E-12 -4.1E-12 4y4

0.0E+00 7.6E+02 4x8.3E-12 -4.1E-12 5y

50.0E+00 7.6E+02 5x8.3E-12 -4.1E-12 6y

60.0E+00 7.6E+02 6x-4.1E-12 4.1E-12 7y

7-7.6E+02 7.6E+02 7x-4.1E-12 4.1E-12 8y

8-7.6E+02 7.6E+02 8x-4.1E-12 4.1E-12 9y

9-7.6E+02 7.6E+02 9x-1.6E+03 0.0E+00 Z13.2E+03 -1.6E+03 Z2-1.6E+03 1.6E+03 Z3

Z2 Z31.0E-05 1.7E-05 1y

1-3.6E-04 -3.8E-04 1x-2.0E-06 -3.3E-06 2y

2-2.2E-04 -2.4E-04 2x-8.1E-06 -1.4E-05 3y

3-3.8E-04 -3.9E-04 3x1.4E-05 2.7E-05 4y

4-2.0E-04 -3.8E-04 4x-2.7E-06 -5.1E-06 5y

5-1.4E-04 -2.6E-04 5x-1.1E-05 -2.2E-05 6y

6-2.0E-04 -3.9E-04 6x1.4E-05 3.0E-05 7y

7-2.4E-05 -2.5E-04 7x-2.7E-06 -5.7E-06 8y

8-2.4E-05 -1.3E-04 8x-1.1E-05 -2.5E-05 9y

9-2.2E-05 -2.6E-04 9x1.2E-03 1.3E-03 Z12.5E-03 2.8E-03 Z22.8E-03 4.2E-03 Z3

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99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1z10.0E+00 0.0E+00 0.0E+00 1y

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2z

20.0E+00 0.0E+00 0.0E+00 2y0.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3z

30.0E+00 0.0E+00 0.0E+00 3y0.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4z

40.0E+00 0.0E+00 0.0E+00 4y0.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5z

50.0E+00 0.0E+00 0.0E+00 5y0.0E+00 0.0E+00 0.0E+00 5x-5.4E+02 -4.1E-12 -7.6E+02 6z

6-4.1E-12 -6.8E+04 4.6E-14 6y

Page 1459: Trabajo Final de Estructuras II(1)

7.6E+02 -4.6E-14 7.1E+02 6x6

0.0E+00 0.0E+00 0.0E+00 7z70.0E+00 0.0E+00 0.0E+00 7y

0.0E+00 0.0E+00 0.0E+00 7x-4.4E+04 0.0E+00 0.0E+00 8z

80.0E+00 -2.8E+02 5.3E+02 8y0.0E+00 -5.3E+02 6.6E+02 8x4.4E+04 4.1E-12 7.6E+02 9z

94.1E-12 6.8E+04 -5.3E+02 9y7.6E+02 -5.3E+02 2.7E+03 9x

99z 9y 9x

0.0E+00 0.0E+00 0.0E+00 1y1

0.0E+00 0.0E+00 0.0E+00 1x0.0E+00 0.0E+00 0.0E+00 2y

20.0E+00 0.0E+00 0.0E+00 2x0.0E+00 0.0E+00 0.0E+00 3y

30.0E+00 0.0E+00 0.0E+00 3x0.0E+00 0.0E+00 0.0E+00 4y

40.0E+00 0.0E+00 0.0E+00 4x0.0E+00 0.0E+00 0.0E+00 5y

50.0E+00 0.0E+00 0.0E+00 5x-4.1E-12 -6.8E+04 4.6E-14 6y

67.6E+02 -4.6E-14 7.1E+02 6x0.0E+00 0.0E+00 0.0E+00 7y

70.0E+00 0.0E+00 0.0E+00 7x0.0E+00 -2.8E+02 5.3E+02 8y

80.0E+00 -5.3E+02 6.6E+02 8x4.1E-12 6.8E+04 -5.3E+02 9y

97.6E+02 -5.3E+02 2.7E+03 9x0.0E+00 0.0E+00 0.0E+00 Z1-5.4E+02 -4.1E-12 -7.6E+02 Z25.4E+02 4.1E-12 7.6E+02 Z3

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