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

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

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

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=

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

1.863 m

δ C.A δ CONT δ ENL

PSERV=

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

18.260 Tn

10.590 Tn

7. PESO DE COLUMNAS

4.410 Tn

8.820 Tn

9.135 Tn

DENSIDAD = 0.876 Tn/m2

V= 37.305 Tn

δ C.A=

δ TAB.R=

δ COL.3=

δ COL.2=

δ COL.1=

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

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

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

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

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

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

18.260 Tn

10.452 Tn

7. PESO DE COLUMNAS

3.528 Tn

7.056 Tn

7.308 Tn

δ C.A=

δ TAB.R=

δ COL.3=

δ COL.2=

δ COL.1=

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

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

PREDIMENSIONAMIENTO

5.000 m 2.050 m 3.875 m

L1y= 3.725 mL2y= 3.275 m

Lmáx(y) 3.725 m

14.9 m 17 cmHL-A=

12.42 cm

420.0 kg/m2 9.31 cm

9.69 cm

VS0.25 m bv

A3 A4 A5

A8 A9 A10

A13A13 A14 A15

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=

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

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

6.517 Tn

8.278 Tn

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

3.918 Tn

9.692 Tn

10.104 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 =

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

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

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

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

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

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

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

6.432 Tn

8.278 Tn

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

3.385 Tn

8.372 Tn

8.728 Tn

δ CONT=

δ COB=

δ TAB.P 3 =

δ TAB.P 2 =

δ TAB.P 1 =

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

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

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

300.0 kg/m2

250.0 kg/m2

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

1.125 m

0.738 m

A16 A17

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=

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

10 cm 35 cm

2.80 m

1.125 m

3.00 m

0.738 m

δ COL

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

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

0.250 m-3.307 m

0.35 m

0.25 m

0.35 m

0.25 m

0.35 m

0.25 m

1.125 m

3.875 m

6.679 m

3.706 m

0.00447 m4

1.125 m

0.00447 m4

3.875 m

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

0.35 m

0.25 m

0.35 m

0.25 m

1.50 m

0.25 m

1.125 m

3.875 m

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

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

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

0.250 m-2.155 m

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

1.40 m

1.50 m

δ Sis58.261 Tn79.311 Tn80.039 Tn

217.611 Tn

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

229.019 Tn

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) =

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

207.50 cm

0.468 Tn

0.439 Tn

0.229 Tn

N hn Fs

3 280 cm 0.468 Tn

2 280 cm 0.439 Tn

1 300 cm 0.229 Tn

E= 217370.65 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 = 4.0582 a= 0.6699 D= 213.6946 cm3 Kl= 7109.8360 kg/cm

207.50 cm 500.00 cm

Qs Kl ∆re

0.468 Tn 32.420 Tn/cm 0.0144 cm

0.907 Tn 32.420 Tn/cm 0.0280 cm

1.136 Tn 31.062 Tn/cm 0.0366 cm

25 cm 25 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=

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

∆tr ∆rr

0.0790 cm 0.0866 cm 0.4738 cm

0.0645 cm 0.1678 cm 0.3872 cm

0.0366 cm 0.2194 cm 0.2194 cm

Iv189843.75 189843.75

Kv Kv914.90964 379.688

Iv189843.75 189843.75

Kv Kv914.90964 379.688

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

4.4387 K = 1.53570.6894 a= 0.4343

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

4.7557 K = 1.64540.7780 a= 0.5885

205.00 cm 387.50 cm

0.08 cm

0.06 cm

0.04 cm

0.00169

0.00138

0.00073

25 cm 25 cm

lv189843.75

Kv926.067

25 cm 25 cm

lv189843.75

Kv926.067

25 cm 25 cm

lv189843.75

Kv926.067

280.00 cm

32.420 Tn/cm

280.00 cm

32.420 Tn/cm

300.00 cm

31.062 Tn/cm

lv189843.75

Kv489.919

lv189843.75

Kv489.919

lv189843.75

Kv489.919

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

f'c (kg/cm2) =

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 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

2 280 cm 0.079 Tn 0.163 Tn

1 300 cm 0.041 Tn 0.204 Tn

E= 217370.65 Kg/cm2

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

327.50 cm 372.50 cm

Qs Kl ∆re

0.084 Tn 6.282 Tn/cm 0.0134 cm 0.0673 cm

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

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

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

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

372.50 cm

∆tr ∆rr D

0.0673 cm 0.0803 cm 0.404 cm 0.00144

0.0539 cm 0.1556 cm 0.324 cm 0.00116

0.0280 cm 0.1680 cm 0.168 cm 0.00056

6.282 Tn/cm

7.292 Tn/cm

0.07 cm

0.05 cm

0.03 cm

0.00144

0.00116

0.00056

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

f'c (kg/cm2) =

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 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

2 280 cm 0.165 Tn 0.341 Tn

1 300 cm 0.086 Tn 0.428 Tn

E= 217370.65 Kg/cm2

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

327.50 cm 372.50 cm

Qs Kl ∆re

0.176 Tn 6.282 Tn/cm 0.0280 cm 0.1411 cm

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

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 0.9278

Ic= 45572.9167 cm4 kc= 162.7604 cm3

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

372.50 cm

∆tr ∆rr D

0.1411 cm 0.1682 cm 0.8464 cm 0.00302

0.1130 cm 0.3261 cm 0.6781 cm 0.00242

0.0587 cm 0.3521 cm 0.3521 cm 0.00117

6.282 Tn/cm

7.292 Tn/cm

0.14 cm

0.11 cm

0.06 cm

0.00302

0.00242

0.00117

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

f'c (kg/cm2) =

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 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

2 280 cm 0.079 Tn 0.163 Tn

1 300 cm 0.041 Tn 0.204 Tn

E= 217370.65 Kg/cm2

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

327.50 cm 372.50 cm

Qs Kl ∆re

0.084 Tn 6.282 Tn/cm 0.0134 cm 0.0673 cm

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

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 45572.9167 cm4 kc= 162.7604 cm3 K = 0.9278

Ic= 45572.9167 cm4 kc= 162.7604 cm3

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

372.50 cm

∆tr ∆rr D

0.0673 cm 0.0803 cm 0.4040 cm 0.00144

0.0539 cm 0.1556 cm 0.3237 cm 0.00116

0.0280 cm 0.1680 cm 0.1680 cm 0.00056

6.282 Tn/cm

7.292 Tn/cm

0.07 cm

0.05 cm

0.03 cm

0.00144

0.00116

0.00056

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

f'c (kg/cm2) =

K = 1.0553 a= 0.3454 D= 56.2163 cm3 Kl= 1870.3725 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

2 280 cm 0.165 Tn 0.341 Tn

1 300 cm 0.086 Tn 0.428 Tn

E= 217370.65 Kg/cm2

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

327.50 cm 372.50 cm

Qs Kl ∆re

0.176 Tn 6.833 Tn/cm 0.0258 cm 0.1137 cm

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

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

25 cmIv

Iv56250 cm4 56250 cm4

Kv Kv171.76 cm3 151.01 cm3

Ic= 195312.5000 cm4 kc= 697.5446 cm3 K = 0.2165

Ic= 195312.5000 cm4 kc= 697.5446 cm3

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

372.50 cm

∆tr ∆rr D

0.1137 cm 0.1547 cm 0.6820 cm 0.00244

0.0879 cm 0.2998 cm 0.5273 cm 0.00188

0.0379 cm 0.2275 cm 0.2275 cm 0.00076

6.833 Tn/cm

11.283 Tn/cm

0.11 cm

0.09 cm

0.04 cm

0.00244

0.00188

0.00076

METRADO DE CARGAS

1.638 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

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

METRADO DE CARGAS

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

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

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

3.275 m 3.725 m

METRADO DE CARGAS

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

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

1.125 m

0.738 m

0.54684 0.252

0.48825 0.225

0.35154 0.162

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A - COMBO 1

f'c= 210

E= 2173706.51

0.0000

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

DETERMINACIÓN DE FUERZAS DE FIJACIÓN Y MOMENTOS DE EMPOTRAMIENTO

ELEMENTO N° 10

0.54684

R= 0.895M= 0.489

ELEMENTO N° 12

0.54684

R= 0.895M= 0.489

ELEMENTO N° 14

R= 0.413M= 0.225

0.225238125

-0.41265

0.488766731

0-0.8954505

0.488766731

0-0.8954505

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS Ɵ = 0SEN Ɵ = 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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.77 0.00

0.00 -440.28

0.00 660.41

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

541.50.0

-758.1

-541.5

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

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 ]=

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

-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

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

0.00-0.06-0.13

+0.000.06

ELEMENTO 12

0.00-0.04-0.10

+0.000.04-0.05

ELEMENTO 14

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

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

814 15

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

ELEMENTO N° 11

0.54684

R= 0.895 R=M= 0.489 M=

ELEMENTO N° 13

0.54684

R= 0.895 R=M= 0.489 M=

ELEMENTO N° 15

R= 0.413 R=M= 0.225 M=

-0.06615 0.29139

-0.882

-0.1435455 0.63231

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

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

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

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

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

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

-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

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

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

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

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

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

0.00 0.00000.90 0.83050.49

=0.3550

0.00 0.00000.90 0.9604

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

0.54684

1.018 R= 1.0180.632 M= 0.632

ELEMENTO N° 13

0.54684

1.018 R= 1.0180.632 M= 0.632

ELEMENTO N° 15

0.469 R= 0.4690.291 M= 0.291

-0.46935

-1.0184895

63399.773

440.276

660.414

1320.829

660.414

660.41

-660.41

1320.83

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

660.41

-660.41

1320.83

63399.773

440.276

660.414

1320.829

660.414

660.41

-660.41

1320.83

-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

0.0 67928.3 0.0758.1 0.0 1415.2

758.129

707.587

-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

758.13

707.59

-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

758.13

707.59

-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

758.129

707.587

-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

758.129

707.587

-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

-684.0

1493.4

-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

528.716

656.489

-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

0.0 -528.7 1313.0

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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

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

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

uaz 0.0000

uay 0.0000uax 0.0000u1z 0.0000u1y 0.0000u1x -0.0001

F'ay 2.07

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

ubz 0.0000

uby 0.0000ubx 0.0000u2z 0.0000u2y -0.0001u2x 0.0000

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

ucz 0.0000

ucy 0.0000ucx 0.0000u3z 0.0000u3y 0.0000u3x 0.0001

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

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

u1z 0.0000

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

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

u2z 0.0000

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

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

u3z 0.0000

u3y 0.0000u3x 0.0001u6z 0.0000u6y -0.0001u6x 0.0001

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

u4z 0.0000

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

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

u5z 0.0000

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

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

u6z 0.0000

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

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

u1z 0.0000

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

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

u2z 0.0000

u2y -0.0001u2x 0.0000u3z 0.0000u3y 0.0000u3x 0.0001

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

u4z 0.0000

u4y -0.0001u4x -0.0001

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

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

u5z 0.0000

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

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

u7z -0.0001

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

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

u8z -0.0001

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

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

ELEMENTO 11

0.00 0.000.05 1.020.04

0.00 0.00-0.05 1.02

0.16 0.63

ELEMENTO 13

0.00 0.000.04 1.020.02

0.00 0.00-0.04 1.020.12 0.63

ELEMENTO 15

0.00 0.000.02 0.470.00

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

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

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

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

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

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

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

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

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

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

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

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

0.7905

0.00001.0576

=0.65580.00000.97930.7546

0.00000.4912

=0.29550.00000.44750.3686

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

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

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

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

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

f'c= 210

E= 2173706.51

0.0841

0.0789

0.0412

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO N° 10

0.48825

R= 0.800M= 0.436

ELEMENTO N° 12

0.48825

R= 0.800M= 0.436

ELEMENTO N° 14

R= 0.368M= 0.201

0.201105469

0.0840777207

-0.3684375

0.436398867

0.0788782281-0.799509375

0.436398867

0.0412495515-0.799509375

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

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

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.77 0.00

0.00 -440.28

0.00 660.41

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

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

43765.90.00.0

-43765.90.00.0

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

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

1 21z 1y 1x 2z

1 21y 1x 2y 2x

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 10

0.00-0.13-0.25

+0.000.13

ELEMENTO 12

0.00-0.09-0.18

+0.000.09-0.13

ELEMENTO 14

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

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

814 15

ELEMENTO N° 11

0.48825

R= 0.800 R=M= 0.436 M=

ELEMENTO N° 13

0.48825

R= 0.800 R=M= 0.436 M=

ELEMENTO N° 15

R= 0.368 R=M= 0.201 M=

-0.0590625 0.260167969

-0.7875

-0.128165625 0.564564492

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

2 32y 2x 3z 3y 3x

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

2 32y 2x 3z 3y 3x

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

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

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

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

-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

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

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

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

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

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

0.00 0.00000.80 0.66840.44

=0.1877

0.00 0.00000.80 0.9306

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

0.48825

0.909 R= 0.9090.565 M= 0.565

ELEMENTO N° 13

0.48825

0.909 R= 0.9090.565 M= 0.565

ELEMENTO N° 15

0.419 R= 0.4190.260 M= 0.260

-0.4190625

-0.909365625

63399.773

440.276

660.414

1320.829

660.414

660.41

-660.41

1320.83

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

660.41

-660.41

1320.83

63399.773

440.276

660.414

1320.829

660.414

660.41

-660.41

1320.83

758.13

707.59

-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

0.00 67928.3 0.00758.13 0.00 1415.17

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

683.994

746.693

-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

528.716

656.489

-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

0.0 -528.7 1313.0

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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 6 75x 6y 6x 7y 7x

uaz 0.0000

uay 0.0000uax 0.0000u1z 0.0002u1y 0.0000u1x -0.0002

F'ay 1.70

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

ubz 0.0000

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

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

ucz 0.0000

ucy 0.0000ucx 0.0000u3z 0.0002u3y 0.0000u3x 0.0001

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

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

u1z 0.0002

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

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

u2z 0.0002

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

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

u3z 0.0002

u3y 0.0000u3x 0.0001u6z 0.0005u6y -0.0001u6x 0.0001

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

u4z 0.0005

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

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

u5z 0.0005

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

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

u6z 0.0005

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

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

u1z 0.0002

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

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

u2z 0.0002

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

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

u4z 0.0005

u4y 0.0000u4x -0.0001

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

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

u5z 0.0005

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

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

u7z 0.0006

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

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

u8z 0.0006

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

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

ELEMENTO 11

0.00 0.00-0.01 0.91-0.06

0.00 0.000.01 0.91

0.02 0.56

ELEMENTO 13

0.00 0.00-0.01 0.91-0.05

0.00 0.000.01 0.910.02 0.56

ELEMENTO 15

0.00 0.000.00 0.42-0.03

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

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

8 98y 8x 9y 9x Z1

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

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

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

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

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

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

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

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

0.5868

0.00000.9010

=0.51010.00000.91770.5880

0.00000.4199

=0.23270.00000.41820.2909

7 87y 7x 8z 8y 8x

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

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

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

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

f'c= 210

E= 2173706.51

-0.0841

-0.0789

-0.0412

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO N° 10

0.48825

R= 0.800M= 0.436

ELEMENTO N° 12

0.48825

R= 0.800M= 0.436

ELEMENTO N° 14

R= 0.368M= 0.201

0.201105469

-0.0840777207

-0.3684375

0.436398867

-0.0788782281-0.799509375

0.436398867

-0.0412495515-0.799509375

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

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

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.773 0

0 -440.276

0 660.414

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

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

43765.90.00.0

-43765.90.00.0

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

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

1 21z 1y 1x 2z

1 21y 1x 2y 2x

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 10

0.000.020.01

+0.00-0.02

ELEMENTO 12

0.000.010.01

+0.00-0.010.04

ELEMENTO 14

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

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

814 15

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

ELEMENTO N° 11

0.48825

R= 0.800 R=M= 0.436 M=

ELEMENTO N° 13

0.48825

R= 0.800 R=M= 0.436 M=

ELEMENTO N° 15

R= 0.368 R=M= 0.201 M=

-0.0590625 0.260167969

-0.7875

-0.128165625 0.564564492

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

2 32y 2x 3z 3y 3x

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

2 32y 2x 3z 3y 3x

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

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

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

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

-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

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

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

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

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

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

0.00 0.00000.80 0.81460.44

=0.4463

0.00 0.00000.80 0.7844

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

0.48825

0.909 R= 0.9090.565 M= 0.565

ELEMENTO N° 13

0.48825

0.909 R= 0.9090.565 M= 0.565

ELEMENTO N° 15

0.419 R= 0.4190.260 M= 0.260

-0.4190625

-0.909365625

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

758.129

707.587

-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

0.00 67928.3 0.00758.13 0.00 1415.17

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

683.994

746.693

-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

528.716

656.489

-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

0.0 -528.7 1313.0

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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 6 75x 6y 6x 7y 7x

uaz 0.0000

uay 0.0000uax 0.0000u1z -0.0003u1y 0.0000u1x 0.0000

F'ay 2.00

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

ubz 0.0000

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

ucz 0.0000

ucy 0.0000ucx 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

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

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

u1z -0.0003

u1y 0.0000u1x 0.0000u4z -0.0005u4y 0.0000u4x 0.0000

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

u2z -0.0003

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

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

u3z -0.0003

u3y 0.0000u3x 0.0002u6z -0.0005u6y 0.0000u6x 0.0002

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

u4z -0.0005

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

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

u5z -0.0005

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

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

u6z -0.0005

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

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

u1z -0.0003

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

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

u2z -0.0003

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

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

u4z -0.0005

u4y 0.0000u4x 0.0000

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

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

u5z -0.0005

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

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

u7z -0.0007

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

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

u8z -0.0007

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

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

ELEMENTO 11

0.00 0.000.11 0.910.14

0.00 0.00-0.11 0.91

0.26 0.56

ELEMENTO 13

0.00 0.000.08 0.910.10

0.00 0.00-0.08 0.910.19 0.56

ELEMENTO 15

0.00 0.000.04 0.420.03

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

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

8 98y 8x 9y 9x Z1

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

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

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

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

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

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

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

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

0.8248

0.00000.9876

=0.66100.00000.83110.7596

0.00000.4572

=0.29500.00000.38100.3673

7 87y 7x 8z 8y 8x

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

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

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

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

f'c= 210

E= 2173706.51

0.0841

0.0789

0.0412

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO N° 10

0.35154

R= 0.576M= 0.314

ELEMENTO N° 12

0.35154

R= 0.576M= 0.314

ELEMENTO N° 14

R= 0.265M= 0.145

0.144795938

0.0840777207

-0.265275

0.314207184

0.0788782281-0.57564675

0.314207184

0.0412495515-0.57564675

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

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

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.773 0

0 -440.276

0 660.414

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

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.90.00.0

-43765.90.0

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.50.00.0

-49779.50.00.0

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

43765.90.00.0

-43765.90.00.0

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

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

1 21z 1y 1x 2z

1 21y 1x 2y 2x

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 10

0.00-0.11-0.22

+0.000.11

ELEMENTO 12

0.00-0.08-0.16

+0.000.08-0.11

ELEMENTO 14

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

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

814 15

ELEMENTO N° 11

0.35154

R= 0.576 R=M= 0.314 M=

ELEMENTO N° 13

0.35154

R= 0.576 R=M= 0.314 M=

ELEMENTO N° 15

R= 0.265 R=M= 0.145 M=

-0.042525 0.187320938

-0.567

-0.09227925 0.406486434

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.7 656.5

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

2 32y 2x 3z 3y 3x

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

2 32y 2x 3z 3y 3x

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

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

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

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

-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

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

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

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

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

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

0.00 0.00000.58 0.46080.31

=0.0989

0.00 0.00000.58 0.6905

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

0.35154

0.655 R= 0.6550.406 M= 0.406

ELEMENTO N° 13

0.35154

0.655 R= 0.6550.406 M= 0.406

ELEMENTO N° 15

0.302 R= 0.3020.187 M= 0.187

-0.301725

-0.65474325

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

758.129

707.587

-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

0.00 67928.3 0.00758.13 0.00 1415.17

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

683.994

746.693

-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

528.716

656.489

-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

0.0 -528.7 1313.0

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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 6 75x 6y 6x 7y 7x

uaz 0.0000

uay 0.0000uax 0.0000u1z 0.0002u1y 0.0000u1x -0.0001

F'ay 1.18

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

ubz 0.0000

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

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

ucz 0.0000

ucy 0.0000ucx 0.0000u3z 0.0002u3y 0.0000u3x 0.0000

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

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

u1z 0.0002

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

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

u2z 0.0002

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

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

u3z 0.0002

u3y 0.0000u3x 0.0000u6z 0.0005u6y 0.0000u6x 0.0000

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

u4z 0.0005

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

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

u5z 0.0005

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

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

u6z 0.0005

u6y 0.0000u6x 0.0000u9z 0.0006u9y 0.0000u9x 0.0000

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

u1z 0.0002

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

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

u2z 0.0002

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

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

u4z 0.0005

u4y 0.0000u4x -0.0001

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

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

u5z 0.0005

u5y -0.0001u5x 0.0000u6z 0.0005u6y 0.0000u6x 0.0000

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

u7z 0.0006

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

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

u8z 0.0006

u8y -0.0001u8x 0.0000u9z 0.0006u9y 0.0000u9x 0.0000

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

ELEMENTO 11

0.00 0.00-0.02 0.65-0.07

0.00 0.000.02 0.65

-0.02 0.41

ELEMENTO 13

0.00 0.00-0.02 0.65-0.06

0.00 0.000.02 0.65-0.01 0.41

ELEMENTO 15

0.00 0.000.00 0.30-0.03

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

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

8 98y 8x 9y 9x Z1

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

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

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

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

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

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

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

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

0.3892

0.00000.6366

=0.34610.00000.67290.3994

0.00000.2972

=0.15880.00000.30630.1988

7 87y 7x 8z 8y 8x

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

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

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

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

f'c= 210

E= 2173706.51

-0.0841

-0.0789

-0.0412

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO N° 10

0.35154

R= 0.576M= 0.314

ELEMENTO N° 12

0.35154

R= 0.576M= 0.314

ELEMENTO N° 14

R= 0.265M= 0.145

0.144795938

-0.0840777207

-0.265275

0.314207184

-0.0788782281-0.57564675

0.314207184

-0.0412495515-0.57564675

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

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

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.773 0

0 -440.276

0 660.414

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

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

43765.900.000.00

-43765.900.000.00

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

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

1 21z 1y 1x 2z

1 21y 1x 2y 2x

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 10

0.000.030.04

+0.00-0.03

ELEMENTO 12

0.000.030.03

+0.00-0.030.05

ELEMENTO 14

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

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

814 15

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

ELEMENTO N° 11

0.35154

R= 0.576 R=M= 0.314 M=

ELEMENTO N° 13

0.35154

R= 0.576 R=M= 0.314 M=

ELEMENTO N° 15

R= 0.265 R=M= 0.145 M=

-0.042525 0.187320938

-0.567

-0.09227925 0.406486434

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

2 32y 2x 3z 3y 3x

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

2 32y 2x 3z 3y 3x

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

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

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

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

-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

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

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

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

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

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

0.00 0.00000.58 0.60700.31

=0.3575

0.00 0.00000.58 0.5443

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

0.35154

0.655 R= 0.6550.406 M= 0.406

ELEMENTO N° 13

0.35154

0.655 R= 0.6550.406 M= 0.406

ELEMENTO N° 15

0.302 R= 0.3020.187 M= 0.187

-0.301725

-0.65474325

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

758.129

707.587

-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

0.00 67928.3 0.00758.13 0.00 1415.17

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

683.994

746.693

-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

528.716

656.489

-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

0.00 -528.72 1312.98

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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 6 75x 6y 6x 7y 7x

uaz 0.0000

uay 0.0000uax 0.0000u1z -0.0003u1y 0.0000u1x 0.0000

F'ay 1.48

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

ubz 0.0000

uby 0.0000ubx 0.0000u2z -0.0003u2y 0.0000u2x 0.0000

ucz 0.0000

ucy 0.0000ucx 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

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

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

u1z -0.0003

u1y 0.0000u1x 0.0000u4z -0.0005u4y 0.0000u4x 0.0000

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

u2z -0.0003

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

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

u3z -0.0003

u3y 0.0000u3x 0.0002u6z -0.0005u6y 0.0000u6x 0.0001

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

u4z -0.0005

u4y 0.0000u4x 0.0000u7z -0.0007u7y 0.0000u7x 0.0000

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

u5z -0.0005

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

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

u6z -0.0005

u6y 0.0000u6x 0.0001u9z -0.0007u9y 0.0000u9x 0.0001

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

u1z -0.0003

u1y 0.0000u1x 0.0000u2z -0.0003u2y 0.0000u2x 0.0000

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

u2z -0.0003

u2y 0.0000u2x 0.0000u3z -0.0003u3y 0.0000u3x 0.0002

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

u4z -0.0005

u4y 0.0000u4x 0.0000

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

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

u5z -0.0005

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

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

u7z -0.0007

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

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

u8z -0.0007

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

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

ELEMENTO 11

0.00 0.000.09 0.650.13

0.00 0.00-0.09 0.65

0.22 0.41

ELEMENTO 13

0.00 0.000.07 0.650.09

0.00 0.00-0.07 0.650.16 0.41

ELEMENTO 15

0.00 0.000.03 0.300.03

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

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

8 98y 8x 9y 9x Z1

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

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

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

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

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

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

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

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

0.6271

0.00000.7232

=0.49700.00000.58630.5709

0.00000.3344

=0.22120.00000.26910.2751

7 87y 7x 8z 8y 8x

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

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

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

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

ANÁLISIS MÉTODO MATRICIAL - PÓRTICO A-A

f'c= 210

E= 2173706.51

0.1762

0.1653

0.0864

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO N° 10

R= 16.375M= 8.938

ELEMENTO N° 12

R= 18.013M= 9.832

ELEMENTO N° 14

R= 32.750M= 17.876

17.87604167

0.1761628435

-32.75

9.831822917

0.1652686683-18.0125

8.938020833

0.0864276316-16.375

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

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

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.773 0

0 -440.276

0 660.414

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

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

43765.900.000.00

-43765.900.000.00

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

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

1 21z 1y 1x 2z

1 21y 1x 2y 2x

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 10

0.00-1.23-2.65

+0.001.23

ELEMENTO 12

0.00-0.70-1.03

+0.000.70-1.28

ELEMENTO 14

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

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

814 15

ELEMENTO N° 11

R= 16.375 R=M= 8.938 M=

ELEMENTO N° 13

R= 18.013 R=M= 9.832 M=

ELEMENTO N° 15

R= 32.750 R=M= 17.876 M=

6.313020833 11.56302083

-51.375

-4.043802083 13.875625

-40.3625

-2.625 11.56302083

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

2 32y 2x 3z 3y 3x

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

2 32y 2x 3z 3y 3x

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

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

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

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

-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

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

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

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

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

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

0.00 0.000016.38 15.14928.94

=6.2868

0.00 0.000016.38 17.6008

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

18.625 R= 18.62511.563 M= 11.563

ELEMENTO N° 13

22.350 R= 22.35013.876 M= 13.876

ELEMENTO N° 15

18.625 R= 18.62511.563 M= 11.563

-18.625

-22.35

-18.625

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

758.129

707.587

-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

0.00 67928.3 0.00758.13 0.00 1415.17

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

683.994

746.693

-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

528.716

656.489

-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

0.00 -528.72 1312.98

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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 6 75x 6y 6x 7y 7x

uaz 0.0000

uay 0.0000uax 0.0000u1z 0.0003u1y -0.0010u1x -0.0021

F'ay 62.81

F'az -1.27F'ax -1.21F'1y -62.81F'1z 1.27F'1x -2.59

ubz 0.0000

uby 0.0000ubx 0.0000u2z 0.0003u2y -0.0021u2x -0.0004

ucz 0.0000

ucy 0.0000ucx 0.0000u3z 0.0003u3y -0.0009u3x 0.0026

F'cy 56.37F'cz 1.82F'cx 1.88F'3y -56.37

F' =F'3z -1.82F'3x 3.58

u1z 0.0003

u1y -0.0010u1x -0.0021u4z 0.0002u4y -0.0017u4x -0.0009

F'1y 47.67F'1z -2.34F'1x -3.69F'4y -47.67F'4z 2.34F'4x -2.85

u2z 0.0003

u2y -0.0021u2x -0.0004u5z 0.0002u5y -0.0035u5x -0.0013

F'2y 97.25F'2z -1.28F'2x -1.49F'5y -97.25F'5z 1.28F'5x -2.11

u3z 0.0003

u3y -0.0009u3x 0.0026u6z 0.0002u6y -0.0015u6x 0.0027

F'3y 38.56F'3z 3.96F'3x 5.50F'6y -38.56F'6z -3.96F'6x 5.60

u4z 0.0002

u4y -0.0017u4x -0.0009u7z 0.0007u7y -0.0021u7x -0.0072

F'4y 30.36F'4z -5.84F'4x -5.96F'7y -30.36F'7z 5.84F'7x -10.40

u5z 0.0002

u5y -0.0035u5x -0.0013u8z 0.0007u8y -0.0044u8x 0.0023

F'5y 56.00F'5z 1.12F'5x 0.31F'8y -56.00F'8z -1.12F'8x 2.84

u6z 0.0002

u6y -0.0015u6x 0.0027u9z 0.0007u9y -0.0017u9x 0.0033

F'6y 16.39F'6z 4.89F'6x 6.63F'9y -16.39F'9z -4.89F'9x 7.07

u1z 0.0003

u1y -0.0010u1x -0.0021u2z 0.0003u2y -0.0021u2x -0.0004

F'1y 0.00F'1z -1.23F'1x -2.65F'2y 0.00F'2z 1.23F'2x -1.36

u2z 0.0003

u2y -0.0021u2x -0.0004u3z 0.0003u3y -0.0009u3x 0.0026

F'2y 0.00F'2z 0.81F'2x 0.54F'3y 0.00F'3z -0.81F'3x 2.48

u4z 0.0002

u4y -0.0017u4x -0.0009

u = u5z 0.0002 u' =u5y -0.0035u5x -0.0013

F'4y 0.00F'4z -0.70F'4x -1.03F'5y 0.00F'5z 0.70F'5x -1.28

u5z 0.0002

u5y -0.0035u5x -0.0013u6z 0.0002u6y -0.0015u6x 0.0027

F'5y 0.00F'5z 0.18F'5x -0.96F'6y 0.00F'6z -0.18F'6x 1.64

u7z 0.0007

u7y -0.0021u7x -0.0072u8z 0.0007u8y -0.0044u8x 0.0023

F'7y 0.00F'7z -2.39F'7x -7.48F'8y 0.00F'8z 2.39F'8x -0.36

u8z 0.0007

u8y -0.0044u8x 0.0023u9z 0.0007u9y -0.0017u9x 0.0033

F'8y 0.00F'8z 2.24F'8x 3.83F'9y 0.00F'9z -2.24F'9x 4.49

ELEMENTO 11

0.00 0.000.81 18.630.54

+11.56

0.00 0.00-0.81 18.63

2.48 11.56

ELEMENTO 13

0.00 0.000.18 22.35-0.96

+13.88

0.00 0.00-0.18 22.351.64 13.88

ELEMENTO 15

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

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

8 98y 8x 9y 9x Z1

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y -0.0010u'1z -0.0003u'1x -0.0021

u'cy 0.0000u'cz 0.0000u'cx 0.0000u'3y -0.0009u'3z -0.0003u'3x 0.0026

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

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

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

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

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

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

14.0456

0.000022.5323

=12.91200.000022.167715.5181

0.000020.8608

=15.39780.000016.389216.0566

7 87y 7x 8z 8y 8x

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

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

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

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

f'c= 210

E= 2173706.51

0.0841

0.0789

0.0412

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U= U5y

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO N° 10

R= 16.375M= 8.938

ELEMENTO N° 12

R= 18.013M= 9.832

ELEMENTO N° 14

R= 32.750M= 17.876

17.87604167

0.0840777207

-32.75

9.831822917

0.0788782281-18.0125

8.938020833

0.0412495515-16.375

ELEMENTO N° 1

A = 63399.773B = 440.276Ɵ = 1.5707963268

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

ELEMENTO N° 2

A = 63399.773B = 440.276Ɵ = 1.5707963268

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^1 〗 _11 ]=

[ 〖�^1 〗 _21 ]=

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

ELEMENTO N° 3

A = 63399.773B = 440.276Ɵ = 1.5707963268

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 ]=

-63399.773 0

0 -440.276

0 660.414

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

541.520.00

-758.13

-541.52

[ 〖�^1 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

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

541.520.00

-758.13

-541.520.00

-758.13

ELEMENTO N° 6

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

67928.328 0

0 541.520

0 758.129

-67928.328 0

0 -541.520

0 758.129

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 ]=

-67928.328 0

0 -541.520

0 758.129

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

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

43765.900.000.00

-43765.900.00

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

49779.540.000.00

-49779.540.000.00

ELEMENTO N° 13

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

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

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 ]=

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

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 ]=

43765.903 0

0 283.874

0 528.716

-43765.903 0

0 -283.874

0 528.716

43765.900.000.00

-43765.900.000.00

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

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

[ 〖�^3 〗 _11 ]=

[ 〖�^3 〗 _21 ]=

1 21z 1y 1x 2z

1 21y 1x 2y 2x

U1zU1y

U2zU2y

U3zU3y

U4zU4y

U5zU= U5y =

U6zU6y

U7zU7y

U8zU8y

U9zU9y

ELEMENTO 1

Ɵ = 1.570796

0 1-1 00 00 00 00 0

63399.8 0.0

0.0 440.30.0 660.4

-63399.8 0.00.0 -440.30.0 660.4

ELEMENTO 2

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

63399.8 0.00.0 440.30.0 660.4

-63399.8 0.0

0.0 -440.30.0 660.4

ELEMENTO 4

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 6

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

67928.3 0.00.0 541.50.0 758.1

-67928.3 0.00.0 -541.50.0 758.1

ELEMENTO 8

Ɵ = 1.570796

0 1-1 00 00 00 00 0

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

0 1-1 00 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 0

T =0 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

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

1 00 10 00 00 00 0

43765.9 0.00.0 283.90.0 528.7

-43765.9 0.00.0 -283.90.0 528.7

ELEMENTO 10

0.00-1.15-2.51

+0.001.15

ELEMENTO 12

0.00-0.64-0.92

+0.000.64-1.19

ELEMENTO 14

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

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

814 15

ELEMENTO N° 11

R= 16.375 R=M= 8.938 M=

ELEMENTO N° 13

R= 18.013 R=M= 9.832 M=

ELEMENTO N° 15

R= 32.750 R=M= 17.876 M=

6.313020833 11.56302083

-51.375

-4.043802083 13.875625

-40.3625

-2.625 11.56302083

-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

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 ]=

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 ]=

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

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 ]=

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

-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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

67928.328Ɵ = 1.5708

541.520COS Ɵ = 0.00SEN Ɵ = 1.00

758.1290.00

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 〗 _22 ]=

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

1415.174

707.587

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

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 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

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

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 〗 _12 ]=

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

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 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

528.72 656.49

ELEMENTO N° 12

49779.538Ɵ = 0.0000

417.706COS Ɵ = 1.00SEN Ɵ = 0.00

683.9941.00

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 〗 _22 ]=

43765.903Ɵ = 0.0000

283.874COS Ɵ = 1.00SEN Ɵ = 0.00

528.7161.00

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

COS2 Ɵ =

SEN2 Ɵ =

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

1312.977

656.489

COS2 Ɵ =

SEN2 Ɵ =

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

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

2 32y 2x 3z 3y 3x

[ 〖�^3 〗 _22 ]=

[ 〖�^3 〗 _12 ]=

[ 〖�^3 〗 _22 ]=

2 32y 2x 3z 3y 3x

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

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

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

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

-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

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

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

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

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

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

0.00 0.000016.38 15.22938.94

=6.4284

0.00 0.000016.38 17.5207

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

0.35 m

0.25 m

A= 0.08750Ic= 0.00046

0.30 cm

Iv0.00056 cm

Av0.07500 cm

ELEMENTO N° 11

18.625 R= 18.62511.563 M= 11.563

ELEMENTO N° 13

22.350 R= 22.35013.876 M= 13.876

ELEMENTO N° 15

18.625 R= 18.62511.563 M= 11.563

-18.625

-22.35

-18.625

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

1320.8291320.829

660.414

-660.414

1320.829

63399.773

440.276

660.414

1320.829

660.414

-660.414

1320.829

758.129

707.587

-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

0.00 67928.3 0.00758.13 0.00 1415.17

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

758.129

707.587

-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

683.994

746.693

-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

528.716

656.489

-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

0.00 -528.72 1312.98

683.994

746.693

-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

528.716

656.489

-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

683.994

746.693

-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

528.716

656.489

-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 6 75x 6y 6x 7y 7x

uaz 0.0000

uay 0.0000uax 0.0000u1z 0.0000u1y -0.0010u1x -0.0020

F'ay 62.98

F'az -1.34F'ax -1.33F'1y -62.98F'1z 1.34F'1x -2.67

ubz 0.0000

uby 0.0000ubx 0.0000u2z 0.0000u2y -0.0021u2x -0.0003

ucz 0.0000

ucy 0.0000ucx 0.0000u3z 0.0000u3y -0.0009u3x 0.0027

F'cy 56.24F'cz 1.76F'cx 1.76F'3y -56.24

F' =F'3z -1.76F'3x 3.51

u1z 0.0000

u1y -0.0010u1x -0.0020u4z -0.0004u4y -0.0017u4x -0.0009

F'1y 47.75F'1z -2.39F'1x -3.75F'4y -47.75F'4z 2.39F'4x -2.93

u2z 0.0000

u2y -0.0021u2x -0.0003u5z -0.0004u5y -0.0035u5x -0.0012

F'2y 97.24F'2z -1.37F'2x -1.60F'5y -97.24F'5z 1.37F'5x -2.23

u3z 0.0000

u3y -0.0009u3x 0.0027u6z -0.0004u6y -0.0015u6x 0.0028

F'3y 38.49F'3z 3.92F'3x 5.44F'6y -38.49F'6z -3.92F'6x 5.53

u4z -0.0004

u4y -0.0017u4x -0.0009u7z 0.0001u7y -0.0021u7x -0.0072

F'4y 30.38F'4z -5.87F'4x -5.98F'7y -30.38F'7z 5.87F'7x -10.45

u5z -0.0004

u5y -0.0035u5x -0.0012u8z 0.0001u8y -0.0044u8x 0.0023

F'5y 56.00F'5z 1.08F'5x 0.25F'8y -56.00F'8z -1.08F'8x 2.77

u6z -0.0004

u6y -0.0015u6x 0.0028u9z 0.0001u9y -0.0017u9x 0.0034

F'6y 16.37F'6z 4.87F'6x 6.61F'9y -16.37F'9z -4.87F'9x 7.03

u1z 0.0000

u1y -0.0010u1x -0.0020u2z 0.0000u2y -0.0021u2x -0.0003

F'1y 0.00F'1z -1.15F'1x -2.51F'2y 0.00F'2z 1.15F'2x -1.24

u2z 0.0000

u2y -0.0021u2x -0.0003u3z 0.0000u3y -0.0009u3x 0.0027

F'2y 0.00F'2z 0.88F'2x 0.65F'3y 0.00F'3z -0.88F'3x 2.61

u4z -0.0004

u4y -0.0017u4x -0.0009

u = u5z -0.0004 u' =u5y -0.0035u5x -0.0012

F'4y 0.00F'4z -0.64F'4x -0.92F'5y 0.00F'5z 0.64F'5x -1.19

u5z -0.0004

u5y -0.0035u5x -0.0012u6z -0.0004u6y -0.0015u6x 0.0028

F'5y 0.00F'5z 0.23F'5x -0.88F'6y 0.00F'6z -0.23F'6x 1.74

u7z 0.0001

u7y -0.0021u7x -0.0072u8z 0.0001u8y -0.0044u8x 0.0023

F'7y 0.00F'7z -2.37F'7x -7.43F'8y 0.00F'8z 2.37F'8x -0.33

u8z 0.0001

u8y -0.0044u8x 0.0023u9z 0.0001u9y -0.0017u9x 0.0034

F'8y 0.00F'8z 2.26F'8x 3.87F'9y 0.00F'9z -2.26F'9x 4.54

ELEMENTO 11

0.00 0.000.88 18.630.65

+11.56

0.00 0.00-0.88 18.63

2.61 11.56

ELEMENTO 13

0.00 0.000.23 22.35-0.88

+13.88

0.00 0.00-0.23 22.351.74 13.88

ELEMENTO 15

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

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

8 98y 8x 9y 9x Z1

u'ay 0.0000u'az 0.0000u'ax 0.0000u'1y -0.0010u'1z 0.0000u'1x -0.0020

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

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

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

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

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

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

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

14.1760

0.000022.5797

=12.99470.000022.120315.6121

0.000020.8812

=15.43200.000016.368816.0984