Presa Gravedad

8/22/2019 Presa Gravedad

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Diseo presa de gravedad

CALCULOS

tan f = 0.78

C= 24 Kg / cm2

t = 340 mm / s2

Espesor hielo = 0.2 cm

T = 5.9 C

B= 3 m

d B1 - d

H3

2

1

4

3

B1

H2H1

B2

H4

B

R

g H3j*g * (H1 - H3) + g * H3

g * (H1 - H3) - j g * ( H1 -H3 )

h0

a b


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H1 = 22 m

H2 = 15 m

H3 = 0 m

H4 = 23 m

h0 = 4 m

R = 3 m

d= 0.5 m

a = 82.4054

b = 53.5308

gh = 1 T/m3

gs = 1.8 T/m3

g's = 1.8 T/m3

j = 0.33333

gH = 2.08 T/m3

1. Calculo de la base

B1 = 08 * ( H1+R ) = 20 m

BASE = 22Asum. B2 = 2 m

2. Calculo de la fuerza hidraulica

1 Forma

F' = g * 1 / 2*( H1 - H2 )2

F' = 24.5 [ T ]

F'' = g * [( H1 - H2 )+ H2 / 2 ] * ( H2 / sen a )F'' = 219.42 [ T ]

F'' = F''seno a Fv1 = F'' cos a

F' = 217.5 [ T ] Fv1 = 29.00 [ T ]

F1 = F' + F'''

F1 = 242 [ T ] ycp = 15.96 m

2 Forma

H4

F'

F'''F''

F1

F1'

Fv1


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F1 = g * 1 / 2*( H1 )2

F1 = 242 [ T ]

F' 1 = g * 1 / 2*( H3 )2

F'1 = 0

3. Calculo de la fuerza hidraulica vertical

X =( H2 - h0 ) / tang a X = 1.47 m

Fv' = g *( H1 - H2 ) * X Fv' = 10.27 [ T ]

Fv'' = g / 2 * ( H2 - h0 ) * X Fv'' = 8.07 [ T ]

F8 = Fv' + Fv'' F8 = 18.33 [ T ]

Punto de aplicacin en 1.16 m

4. Calculo de la fuerza de Sedimentos

Fh2 = 1/2* h02

* gs

Fh2 = 14.4 [ T ]

Fv2 = 1/2*( B2- X ) * h0

* g's

Fv2 = 1.92 [ T ]

5. Calculo de la fuerza de subprecin

U1 = 0.00 T/m

U2 = 18.33 T/m

U3 = 71.50 T/m

U4 = 18.33 T/m

Fv

Fv''

Fh

Fv'X


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F7 = 108.17 T/m brazo= 6.30

6. Calculo del peso propio

W1 = V1 * gH W1 = 31.2 T/m

W2 = V2 * gH W2 = 156 T/m

W3 = V3 *gH W3 = 406.64 T/m

F9 = 593.84 T/m

7. Calculo de la fuerza del hielo

Para :

e = 0.2 cm

T = 5.9 C

F3 = 9.8 T/m

8. Calculo de la fuerza ssmica

F5 = 0.0001 * t * m * b * W

Para :

Roca sana b = 0.7

estructura alta m = 2

t = 340 mm / s2

W = 593.84 T/m

F5 = 28.27 T/m

F4 = 14.13 T/m

9. Calculo de la fuerza dinamica del agua

F6 = 0.726 * c * a *gh * h2

c= 0.76

F4 = F5 / 2

a = t / g

W W W


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F6 = 9.26 T/m

10. Calculo del centro de gravedad

Elemento Xi Yi Wi Xi * Wi Yi * Wi

1 1.33 5.00 31.20 41.60 156.00

2 3.50 12.50 156.00 546.00 1950.00

3 10.67 7.67 406.64 4337.49 3117.57

593.84 4925.09 5223.57

X = 8.29 m

Y = 8.80 m


FuerzaFv

iX

iX

i *F

i

W1 31.20 1.33 41.60

W2 156.00 3.50 546.00

W3 406.64 10.67 4337.5

Fv2 1.92 0.18 0.34

F4 0.00 8.29 0.00

F8 18.33 1.16 21.25

614.09 4946.685

Z = ( S Xi * Fi + S Yi * Fi ) / S Fv

Fuerza Fhi Yi Xi * Fi

F1 242.00 7.33 1774.67 Z = 11.905 m

F'1 0.00 0.00 0.00

Fh2 14.40 2.67 38.40

F3 9.80 22.00 215.60

F5 28.27 8.80 248.64

F6 9.26 9.35 86.54

303.72 2363.849


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12. Calculo de la excentricidad

e = 0.90 m

13. Calculo de esfuerzos verticales

smin = S w * (1 - 6e/Base) / (Base * 1)

smin = 20.33 T / m2

smax =S w * (1+ 6e/Base) / (Base * 1)

smax = 33.65 T / m2

14. Esfuerzos en el paramento seco

tXL = sXL * cot b

tXL = 26.34

sYL = sXL cot2b

sYL = 20.61 T / m2

15. Esfuerzos principales en el paramento seco

s1 = 1/2 [ (sXL + sYL ) + (( sXL - sYL)2

+ 4 tXL2))

1/2]

s1 = 54.26 T / m2

s2 = 1/2 [ (sXL + sYL ) - (( sXL - sYL)2

+ 4 tXL2))

1/2]

s2 = 0.00 T / m2

16. Esfuerzos en el paramento mojado

tYW = (sXW - g Y ) * cot a

tYW = -0.22

sYW =Y g + ( sXW - Y g ) cot2a

sYW = 21.97 T / m2

17. Esfuerzos principales en el paramento mojado

eZ

( B2 + B1 ) / 2 ( B2 + B1 ) / 2

eZ

( B2 + B1 ) / 2 ( B2 + B1 ) / 2


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s1 = 1/2 [ (sXW + sYW ) + ((sXW +sYW)2

+ 4tXW2))

1/2]

s1 = 22.000 T / m2

s2 = 1/2 [ (sXW + sYW ) - ((sXW +sYW)2

+ 4tXW2))

1/2]

s2 = 20.304 T / m2

16. Calculo del coeficiente de seguiridad al vuelco

Mi Fuerza Fvi Xi Xi * Fi

M1 W1 31.20 20.67 644.80

M2 W2 156.00 18.50 2886.00

M3 W3 406.64 11.33 4608.6

M4 Fv2 1.92 21.82 41.90

M5 F4 14.13 13.71 193.72

M6 F7 108.17 15.70 1697.97

M7 F8 18.33 20.84 382.08

Mi Fuerza Fhi Yi Xi * Fi

M'1 F1 242.00 7.33 1774.67

M'2 F'1 0.00 0.00 0.00

M'3 Fh2 14.40 2.67 38.40

M'4 F3 9.80 22.00 215.60

M'5 F5 28.27 8.80 248.64

M'6 F6 9.26 9.35 86.54

S MR = M1 + M2 + M3 + M4 + M5 + M8 + M'2S MR = 8649.9

S MA = M'1 + M'3 + M'4 + M'5 + M'6 + M6 + M7S MA = 4255.5

Fv =S MR / S MA

Fv = 2.03 > 2 OK

17. Calculo del coeficiente de deslisamiento

fD-1

= ( S Fv - U ) / S FH

fD = 0.600 < 3 OK

18. Calculo del coeficiente de seguridad

fS = f ' / FD

fS = f ' * SV / SH (Para presas pequeas)

Para f S = 1.25

f ' = fS *fd

f ' = 0.75


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19. Calculo del coeficiente por corte y rozamiento

fCR= f ' * ( SV + B *t ) / SH

compresin del H fck= 560 T/m2

t=1 / 5 * fckt= 112 T/m2

fCR= 7.61 > 4 Ok

20. Calculo del esfuerzo mnimo a al compresin

j = 0.4 sU = j *g* H - ft / fSfS = 3

sU = -2.866667

fct = 35.00 T/m2

-2.866667 < 35 Ok

21Esfuerzo al corte en el cuello de la presa

t = SFH/(A N)

SFH= F1+F3

F3 = 9.8

FI=1/2(R)^2*g

F1= 4.5

SFH= 14.3 A= 3

t = 4.8 < 112

21. Calculo de dentellones

Pa un coeficiente de lane 1.6

Trayectoria de corrimiento pesada= Wp=B/3= 7.333333

H= 22

Carga efectiva=

Wp/H_= 0.244444

pero Wp/H> 1.6


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Wp necesario= 35.2

ancho dentellon= 1

Dentelon aguas abajo 10

Dentellon aguas arriba 9

Longitud del conlchon 0

Trayectoria de corrimiento pesada= Wp= 45.33333

Wp/H_= 2.060606

Fuerza de corte en el dentellon

t = SFH/(A N) N= 2

t = 151.86 < 112

Calculo del gasto de filtracin

Metodo de la red de flujo

Q=k(nf/nd)Hd

nf= 1.75

nd= 20

Hd= 22 m

k= 3.00E-03 m/s

Q= 0.006 m^3/s

Metodo de darcy

Q=kia

i=Hd/Wp= 0.49

a=3*1= 3

Q= 0.004


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Diseo presa de gravedad

d B1 - d

2

1

4

3

B1

H2H1

B2

H4

B

R

j*g * (H1 - H3) + g * H3

g * (H1 - H3) - j g * ( H1 -H3 )

h0

a b

d B1 - d

2

1

4

3

B1

H2H1

B2

H4

B

R

j*g * (H1 - H3) + g * H3

g * (H1 - H3) - j g * ( H1 -H3 )

h0

a b


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CALCULOS

tan f = 0.65

C= 25 Kg / cm2

t = 350 mm / s2


T = 16.5 C

B= 3 m

H1 = 30 m

H2 = 10 m

H3 = 0 m

H4 = 30 m

h0 = 5.3 m

R = 5.5 m

d= 0.5 m

a = 84.28941

b = 49.74652 gh = 1 T/m

3

gs = 1.36 T/m3

g's = 1.92 T/m3

j = 0.333333

gH = 2.4 T/m3


B1 = 08 * ( H1+R ) = 28.4 m

Asum. B2 = 1 m


F'

F'''F''

F1

Fv1

F'

F'''F''

F1

Fv1


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1 Forma

F' = g * 1 / 2*( H1 - H2 )2

F' = 200 [ T ]

F'' = g * [( H1 - H2 )+ H2 / 2 ] * ( H2 / sen a )

F'' = 251.25 [ T ]


F' = 250 [ T ] Fv1 = 25.00

F1 = F' + F'''

F1 = 450 [ T ] ycp = 25.46

2 Forma

F1 = g * 1 / 2*( H1 )2

F1 = 450 [ T ]

F' 1 = g * 1 / 2*( H3 )2

F'1 = 0


Fv

Fv''

Fh

Fv'X

Fv

Fv''

Fh

Fv'X

Fv

Fv''

Fh

Fv'X

Fv

Fv''

Fh

Fv'X


13/35

X =( H2 - h0 ) / tang a X = 0.47 m

Fv' = g *( H1 - H2 ) * X Fv' = 9.40 [ T ]

Fv'' = g / 2 * ( H2 - h0 ) * X Fv'' = 1.10 [ T ]

F8 = Fv' + Fv'' F8 = 10.50 [ T ]

Punto de aplicacin en 0.76

4. Calculo de la fuerza de cedimentos

Fh2 = 1/2* h02

* gs

Fh2 = 19.1012 [ T ]

Fv2 = 1/2*( B2- X ) * h0

* g's

Fv2 = 2.70 [ T ]


U1 = 0.00 T/mU2 = 15.00 T/m

U3 = 139.50 T/m

U4 = 15.00 T/m

F7 = 169.50 T/m brazo= 9.00


W1 = V1 * gH W1 = 12 T/m

W2 = V2 * gH W2 = 255.6 T/m

W3 = V3 *gH W3 = 914.4 T/m

W1W3

W2

W1W3

W2

W1W3

W2

W1W3

W2


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F9 = 1182 T/m


Para :

e = 0.45 cmT = 16.5 C

F3 = 9.8 T/m


F5 = 0.0001 * t * m * b * W

Para :

Roca sana b = 0.7


t = 350 mm / s2

W = 1182 T/m

F5 = 57.92 T/m

F4 = 28.96 T/m


F6 = 0.726 * c * a *gh * h2

c= 0.76

F6 = 17.72 T/m


Elemento Xi Yi Wi Xi * Wi Yi * Wi

1 0.67 3.33 12.00 8.00 40.00

2 3.75 17.75 255.60 958.50 4536.90

3 12.47 10.00 914.40 11399.52 9144.00

1182.00 12366.02 13720.90

X = 10.46 m

Y = 11.61 m


F4 = F5 / 2

a = t / g


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Fuerza Fvi Xi Xi * Fi

W1 12.00 0.67 8.00

W2 255.60 2.50 639.00

W3 914.40 14.13 12923.5

Fv2 2.70 0.18 0.48

F4 0.00 10.46 0.00F8 10.50 0.76 7.95

1195.20 13578.95

Z = ( S Xi * Fi + S Yi * Fi


F1 450.00 10.00 4500.00 Z = 16.180

F'1 0.00 0.00 0.00

Fh2 19.10 3.53 67.49

F3 9.80 30.00 294.00

F5 57.92 11.61 672.32

F6 17.72 12.75 225.89

554.54 5759.708


e = 1.48 m


smin = S w * (1 - 6e/Base) / (Base * 1)

smin = 28.06 T / m2

smax =S w * (1+ 6e/Base) / (Base * 1)

smax = 52.35 T / m2


eZ

( B2 + B1 ) / 2 ( B2 + B1 ) / 2

eZ

( B2 + B1 ) / 2 ( B2 + B1 ) / 2

eZ

( B2 + B1 ) / 2 ( B2 + B1 ) / 2

eZ

( B2 + B1 ) / 2 ( B2 + B1 ) / 2


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tXL = sXL * cot b

tXL = 46.07

sYL = sXL cot2b

sYL = 40.54 T / m2


s1 = 1/2 [ (sXL + sYL ) + (( sXL - sYL)2

+ 4 tXL2))

1/2]

s1 = 92.89 T / m2

s2 = 1/2 [ (sXL + sYL ) - (( sXL - sYL)2

+ 4 tXL2))

1/2]

s2 = 0.00 T / m2



tYW = -0.19


sYW = 29.98 T / m2


s1 = 1/2 [ (sXW + sYW ) + ((sXW +sYW)2

+ 4tXW2))

1/2]

s1 = 30.000 T / m2

s2 = 1/2 [ (sXW + sYW ) - ((sXW +sYW)2

+ 4tXW2))

1/2]

s2 = 28.039 T / m2



M1 W1 12.00 28.73 344.80

M2 W2 255.60 26.90 6875.64M3 W3 914.40 15.27 13959.8

M4 Fv2 2.70 29.22 78.80

M5 F4 28.96 18.94 548.43

M6 F7 169.50 20.40 3457.95

M7 F8 10.50 28.64 300.88


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M'1 F1 450.00 10.00 4500.00

M'2 F'1 0.00 0.00 0.00

M'3 Fh2 19.10 3.53 67.49

M'4 F3 9.80 30.00 294.00

M'5 F5 57.92 11.61 672.32M'6 F6 17.72 12.75 225.89

S MR = M1 + M2 + M3 + M4 + M5 + M8 + M'2S MR = 21785.9

S MA = M'1 + M'3 + M'4 + M'5 + M'6 + M6 + M7S MA = 9766.1

Fv =S MR / S MA

Fv = 2.23 > 2 OK


fD-1

= ( S Fv - U ) / S FH

fD = 0.541 < 0.7 OK


fS = f ' / FD

fS = f ' * SV / SH (Para presas pequeas)

Para f S = 1.25

f ' = fS *fd

f ' = 0.68


fCR= f ' * ( SV + B *t ) / SH

compresin del H fck= 560 T/m2

t=1 / 5 * fckt= 112 T/m2

fCR= 5.47 > 4 Ok


18/35

20. Calculo del esfuerzo mnimo a al compresin

j = 0.4 sU = j *g* H - ft / fSfS = 3

sU = 0.333333

fct = 35.00 T/m2

0.333333 < 35 Ok


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H3

g H3

H3

g H3


20/35

H

' H'


21/35

[ T ]

m


22/35

m


23/35


24/35

) / S Fv

m


25/35

4045.5

4040

d B1 - d

H3

2

1

4

3

B1

H2H1

B2

H4

B

R

g H3j*g * (H1 - H3) + g * H3

g * (H1 - H3) - j g * ( H1 -H3 )

h0

a b


26/35

CALCULOS

tan f = 0.65

C= 25 Kg / cm2

t = 200 mm / s2


T = 10.5 CB= 3 m

H1 = 30 m

H2 = 15 m

H3 = 0 m

H4 = 30 m

h0 = 8 m

R = 5 m

d= 0.5 m

a = 78.69007

b = 50.19443

gh = 1 T/m3

gs = 1.36 T/m3

g's = 1.92 T/m3

j = 0.333

gH = 2.4 T/m3


B1 = 0.8 * ( H1 + R ) = 28 m

Asum. B2 = 3 m


1 Forma

H4

F'

F'''F''

F1

F1'

Fv1


27/35

F' = g * 1 / 2*( H1 - H2 )2

F' = 112.5 [ T ]

F'' = g * [( H1 - H2 )+ H2 / 2 ] * ( H2 / sen a )

F'' = 344.184 [ T ]


F' = 337.5 [ T ] Fv1 = 67.50 [ T ]

F1 = F' + F'''

F1 = 450 [ T ] ycp = 23.83 m

2 Forma

F1 = g * 1 / 2*( H1 )2

F1 = 450 [ T ]

F' 1 = g * 1 / 2*( H3 )2

F'1 = 0


X =( H2 - h0 ) / tang a X = 1.40 m

Fv' = g *( H1 - H2 ) * X Fv' = 21.00 [ T ]

Fv'' = g / 2 * ( H2 - h0 ) * X Fv'' = 4.90 [ T ]

F8 = Fv' + Fv'' F8 = 25.90 [ T ]

Punto de aplicacin en X = 2.26 m

4. Calculo de la fuerza de cedimentos

Fh2 = 1/2* h02* gs

Fh2 = 43.52 [ T ]

Fv2 = 1/2*( B2- X ) * h0

* g's

Fv

Fv''

Fh

Fv'X


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Fv2 = 12.29 [ T ]


U1 = 0.00 T/m

U2 = 35.00 T/m

U3 = 137.50 T/mU4 = 35.00 T/m

F7 = 207.50 T/m brazo= 8.89


W1 = V1 * gH W1 = 54 T/m

W2 = V2 * gH W2 = 252 T/m

W3 = V3 *gH W3 = 900 T/m

F9 = 1206 T/m


Para :

e = 0.55 cm

T = 10.5 C

F3 = 9.8 T/m


F5 = 0.0001 * t * m * b * W

Para :

Roca sana b = 0.7


W1W3

W2


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t = 200 mm / s2

W = 1206 T/m

F5 = 33.77 T/m

F4 = 16.88 T/m


F6 = 0.726 * c * a *gh * h2

c= 0.76

F6 = 10.12 T/m


Elemento Xi Yi Wi Xi * Wi Yi * Wi1 2.00 5.00 54.00 108.00 270.00

2 5.50 17.50 252.00 1386.00 4410.00

3 14.33 10.00 900.00 12900.00 9000.00

1206.00 14394.00 13680.00

X = 11.94 m

Y = 11.34 m


Fuerza Fvi Xi Xi * Fi

W1 54.00 2.00 108.00W2 252.00 4.50 1134.00

W3 900.00 15.67 14100.0

Fv2 12.29 0.53 6.55

F4 0.00 11.94 0.00

F8 25.90 2.26 58.43

1244.19 15406.98

Z = ( S Xi * Fi + S Yi * Fi ) / S Fv


F1 450.00 10.00 4500.00 Z = 16.834 m

F'1 0.00 0.00 0.00

Fh2 43.52 5.33 232.11

F3 9.80 30.00 294.00F5 33.77 11.34 383.04

F6 10.12 12.75 129.08

547.21 5538.2281


F4 = F5 / 2

a = t / g

e


30/35

e = 1.33 m


smin= S w * (1 - 6e/Base) / (Base * 1)

smin= 28.86 T / m2

smax=S w * (1+ 6e/Base) / (Base * 1)

smax = 48.95 T / m2


tXL = sXL * cot b

tXL = 42.42

sYL = sXL cot2b

sYL = 36.77 T / m2


s1 = 1/2 [ (sXL + sYL ) + (( sXL - sYL)2+ 4 tXL

2))

1/2]

s1 = 85.72 T / m2

s2 = 1/2 [ (sXL + sYL ) - (( sXL - sYL)2+ 4 tXL

2))

1/2]

s2 = 0.00 T / m2



tYW= -0.23


sYW = 29.95 T / m2


s1 = 1/2 [ (sXW + sYW ) + ((sXW +sYW)2

+ 4tXW2))

1/2]

Z

( B2 + B1 ) / 2 ( B2 + B1 ) / 2


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s1 = 30.000 T / m2

s2 = 1/2 [ (sXW + sYW ) - ((sXW +sYW)2

+ 4tXW2))

1/2]

s2 = 28.810 T / m2



M1 W1 54.00 29.00 1566.00

M2 W2 252.00 26.50 6678.00

M3 W3 900.00 15.33 13800.0

M4 Fv2 12.29 30.47 374.37

M5 F4 16.88 19.06 321.89

M6 F7 207.50 22.11 4588.75

M7 F8 25.90 28.74 744.47


M'1 F1 450.00 10.00 4500.00M'2 F'1 0.00 0.00 0.00

M'3 Fh2 43.52 5.33 232.11

M'4 F3 9.80 30.00 294.00

M'5 F5 33.77 11.34 383.04

M'6 F6 10.12 12.75 129.08

S MR = M1 + M2 + M3 + M4 + M5 + M8 + M'2S MR = 23291.9

S MA = M'1 + M'3 + M'4 + M'5 + M'6 + M6 + M7S MA = 10448.87

Fv =S MR / S MA

Fv = 2.23 > 2 OK


fD-1

= ( S Fv - U ) / S FH

fD = 0.528 < 0.7 OK


fS = f ' / FD

fS = f ' * SV / SH

Para f S = 1.25

f ' = fS *( SV - U ) / SH


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f ' = 2.84


fCR= f ' * ( SV + B *t ) / SH

compresin del H 560 T/m2

t= 112 T/m2

fCR= 23.42 > 4 Ok

20. Calculo del esfuerzo mnico a al compresin

j = 0.4 sU = j *g* H - ft / fSfS = 3

sU = 0.3333333

ft = 35 T/m2

0.333333333 < 35 Ok

21Esfuerzo al corte en el cuello de la presa

t = SFH/(A N)

SFH= F1+F3

F3 = 9.8

FI=1/2(R)^2*g

F1= 12.5

SFH= 22.3 A= 3

t = 7.4 < 112

21. Calculo de dentellones

Pa un coeficiente de lane 1.6

Trayectoria de corrimiento pesada= Wp=B/3= 10.333333

H= 30

Carega efectiva=

Esfuerzo permitido en el concreto


33/35

Wp/H_= 0.3444444

pero Wp/H> 1.6

Wp necesario= 48

ancho dentellon= 1

Dentelon aguas abajo 10Dentellon aguas arriba 8

Longitud del conlchon 0

Trayectoria de corrimiento pesada= Wp= 46.333333

Wp/H_= 1.54

Fuerza de corte en el dentellon

t = SFH/(A N) N= 2

t = 273.61 < 112

Calculo del gasto de filtracin

Metodo de la red de flujo

Q=k(nf/nd)Hd

nf= 1.9

nd= 21

Hd= 30 m

k= 3.00E-03 m/s

Q= 0.008 m^3/s

Metodo de darcy

Q=kia

i=Hd/Wp 0.65

a=3*1= 3

Q= 0.006 m^3/s


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Presa Gravedad