Diseño Presa Trabajo Final

8/12/2019 Diseño Presa Trabajo Final

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DETERMINAR:

A) DISTRIBUCION DE ESFUERZOS NORMALES VERTICALES

B) DISTRIBUCION DE ESFUERZOS CORTANTES

C) DISTRIBUCION DE ESFUERZOS NORMALES HORIZONTALES

D) ESFUERZOS PRINCIPALES Y DIRECCIONES PRINCIPALES DE ESFUERZOS

SEGUIR LAS RECOMENDACIONES DE:

DESIGN STANDARDS NO.2 GRAVITY DAMS, USBR

DESIGN OF GRAVITY DAMS, USBR

TEXTO DE VARSHNEY (COPIAS PROPORCIONADAS)PRESENTACION:

EL TRABAJO DEBE COMPRENDER LA PRESENTACION DE UNA PLANTILLA GENERICA EN EXCEL

QUE PERMITA RESOLVER CUALQUIER CASO PRACTICO, CON SOLO MODIFICAR EL AREA DE

DATOS. SE HARA USO DE LOS MACROS QUE PUEDAN SER REQUERIDOS.

DEBERA PRESENTARSE UNA SALIDA GRAFICA QUE MUESTRE VECTORES A ESCALA CON LOS

ESFUERZOS PRINCIPALES Y DIRECCIONES PRINCIPALES DE ESFUERZOS.

CRITERIOS DE CALIFICACION:

A) DISTRIBUCION DE ESFUERZOS NORMALES VERTICALES DETERMINADOS: 2 PUNTOS

B) DISTRIBUCION DE ESFUERZOS CORTANTES DETERMINADOS: 3 PUNTOS

C) DISTRIBUCION DE ESFUERZOS NORMALES HORIZONTALES DETERMINADOS: 4 PUNTOS

D) ESFUERZOS Y DIRECCIONES PRINCIPALES DETERMINADOS: 3 PUNTOS

E) PRESENTACION GRAFICA DE LOS ESFUERZOS Y DIRECCIONES PRINCIPALES: 3 PUNTOS

F) CARACTERISTICA GENERICA DE LA PLANTILLA: 3 PUNTOS

G) SUSTENTACION DEL TRABAJO: 2 PUNTOS

TRABAJO CALIFICADO



Datos:

T1 = 16 m

T2 = 10 m

T3 = 146.7 m

T = T1+T2+T3 172.7 m

Posición drenes = 21 m (desde extremo izquierdo)

Cota fondo = 630 msnm

Cota sedim = 681 msnm

Cota S.L. = 797 msnm

Cota quiebre arr = 792 msnm

Cota quiebre ab. = 793 msnm

Cota cresta = 802 msnm

aSH

= 0.15 g

aSV = 0.075 g

glodo horiz = 1.4 t/m3

glodo (verti) = 1.92 t/m3

DETERMINACION DE LOS ESFUERZOS NORMALES Y CORTANTES COTA : 630

A) Determinar factor de seguridad al volteo (FSV) y factor de deslizamiento ( f ) :

Momentos respecto al punto "O"



Descripción Fuerza (t) Distancia (m) Mo opuestos al volteo Mo activos al volteo

Peso propio (Wi):W1 = 3,110.40 162.03 503,988.48

W2= 4,128.00 151.70 626,217.60

W3 = 28,694.52 97.80 2,806,324.06

Peso del agua (Wai):

x = 5.04 y = (T1-x) = 10.96

Wa1 = 584.30 170.18 99,436.41

Wa2 = 54.81 162.18 8,889.95

Wa3 = 608.44 164.01 99,790.15

Peso del lodo (Ws):

Ws = 246.61 171.02 42,176.06

Subpresión (Us):

U1 = 1,169.00 162.20 189,611.80

U2 = 1,169.00 165.70 193,703.30

U3 = 4,222.32 101.13 427,016.96

Fuerza del agua:

Fa = 6,728.00 89.67 603,277.33

Flodo1 = 5,916.00 25.50 150,858.00

Flodo2 = 1,820.70 17.00 30,951.90

Fuerza de sismo horizontal (FIHi):

FIH(W1) = 466.56 54.00 25,194.24

FIH(W2) = 619.20 86.00 53,251.20

FIH(W3) = 4,304.18 54.33 233,860.34FIH(Wa1) = 43.82 109.00 4,776.62

FIH(Wa2) = 4.11 164.50 676.28

FIH(Wa3) = 45.63 128.33 5,856.28



FIH(Ws) = 18.50 34.00 628.86

Fuerza de sismo vertical (FIVi):

FIV(W1) = 233.28 162.03 37,799.14

FIV(W2) = 309.60 151.70 46,966.32

FIV(W3) = 2,152.09 97.80 210,474.30

FIV(Wa1) = 43.82 170.18 7,457.73

FIV(Wa2) = 4.11 162.18 666.75

FIV(Wa3) = 45.63 164.01 7,484.26

FIV(Ws) = 18.50 171.02 3,163.20

Fuerza hidrodinámica (Fx, Fy):

Fx = 2,104.01 68.78 144,710.00

Fy = 201.58 165.91 33,443.83

Suma Momentos 4,220,266.52 2,378,384.81

Dim. Horiz (T1) = 16.00 m

Dim. Vertical (SL-fon 167.00 m

Angulo (q ) = 5.47 º Metodo de Zangar:

Cm = 0.70

CE = 0.70

PE = 17.43 t/m2

Cm = g(q) = 0.0193(90°-q)0.808

PE = CE HgwH H= aSH /g

+

H

y

H

y

H

y

H

yC C m E 22

2



F = 0.726*PEy

M = 0.299*PEy2

Fhidr.sismo (F) = 2,113.64 t

Mo Fhidr. Sismo (M) 145,372.65 t-m

d (lìnea de acción) = 68.78 m

∑Mo de fuerzas opuestas al volteo

∑Mo de fuerzas activas al volteo

FSV = 1.77

∑F H

∑F V

∑F H = 22,070.71

∑F V = 33,875.39

f = 0.65

FSV =

f =

( f > 1.5), para el caso de

combinaciones usual e inusual

(0.65 < f < 0.75 ), para el casode combinaciones usual e

inusual



B) Cálculo de los esfuerzos smax y smín en la base de la presa:

Momentos respecto al punto "P" (ubicado a T/2) :



Descripción Fuerza (t) Distancia (m) Momento (t.m) Sentido

Peso propio (Wi):

W1 = 3,110.40 75.68 235,405.44 antihorario

W2= 4,128.00 65.35 269,764.80 antihorario

W3 = 28,694.52 11.45 328,552.25 antihorario


x = 5.04 m y = (T1-x) = 10.96

Wa1 = 584.30 83.83 48,982.42 antihorario

Wa2 = 54.81 75.83 4,156.69 antihorario

Wa3 = 608.44 77.66 47,250.97 antihorarioPeso del lodo (Ws):

Ws = 246.61 84.67 20,880.99 antihorario

Subpresión (Us):

U1 = 1,169.00 75.85 -88,668.65 horario

U2 = 1,169.00 79.35 -92,760.15 horario

U3 = 4,222.32 14.78 -62,419.91 horario

Fuerza del agua:

Fa = 6,728.00 89.67 -603,277.33 horario

Flodo1 = 5,916.00 25.50 -150,858.00 horario

Flodo2 = 1,820.70 17.00 -30,951.90 horario


FIH(W1) = 466.56 54.00 -25,194.24 horario

FIH(W2) = 619.20 86.00 -53,251.20 horario

FIH(W3) = 4,304.18 54.33 -233,860.34 horario

FIH(Wa1) = 43.82 109.00 -4,776.62 horarioFIH(Wa2) = 4.11 164.50 -676.28 horario

FIH(Wa3) = 45.63 128.33 -5,856.28 horario

FIH(Ws) = 18.50 34.00 -628.86 horario




FIV(W1) = 233.28 75.68 17,655.41 antihorario


FIV(W3) = 2,152.09 11.45 24,641.42 antihorario

FIV(Wa1) = 43.82 83.83 3,673.68 antihorario

FIV(Wa2) = 4.11 75.83 311.75 antihorario


FIV(Ws) = 18.50 84.67 1,566.07 antihorario


Fx = 2,104.01 68.78 -144,710.00 horario

Fy = 201.58 79.56 16,037.25 antihorario

Suma Momentos -471,271.68

Donde:

B = T 172.7 m

W =∑F V = 33,875.39 t

H = ∑F H = 22,070.71 t

M = ∑F Mo = -471,271.68 t-m

I = 429,235.63 m4

smin = 101.35 ton/m2

>0 (ok)

smax = 290.96 ton/m2 29.10 kg/cm

2

sadm (arenisca) = c = 32.00 kg/cm2

FS esf = Esfuerzo adm is ib le del m ater ial (

material ) Esfuerzo admisible del m aterial ( ma x )

FS esf = 1.10

2minmax/ B

M6

B

V

s

2minmax/

6

B

M

B

F V

s



C) Distribución de Esfuerzos Normales Verticales (sz):

a = szD = 290.96 t/m2

a = szD = W/T - 6M/T2

szU = 101.35 t/m2 szU = W/T + 6M/T

2

b= -1.09793 b = 12M/T3

sz = 290.96 + -1.09793 y

De acuerdo a la notación: Factor de fricción por corte (SSF):szU = 101.35 t/m

2

szD = 290.96 t/m2

M = -471,271.68 t-m

W =∑V = 33,875.39 t tanf = 0.75

H = ∑H = -22,070.71 t SFF = 3.66

T = A = 172.70 m

tan fU = 0.10

tan fD = 0.90

P = 187.40 t/m2

PE = 17.43 t/m2

PU = 204.83 t/m2

P' = 0.00

P'E = 0.00

PD = 0.00 t/m2

t zU =tz U = 10.22 t/m

2

t zU = -(szU - PU)*tanfU

t zD =tz D = 261.86 t/m2

t zD = (szD - PD)*tanfD

sz = a + by

H

tanVcASFF

f+



D) Distribución de Esfuerzos Cortantes (tyz):

a1 = 261.86 t/m2

a1 = tyzD

b1 = -1.74 t/m2

b1 =-(2/T)*[ 3H/T + tyzU + 2tyzD ]

c1 = 0.00166 t/m2

c1 =(3/T2)*[ 2H/T + tyzU + tyzD ]

Por lo tanto:

tyz = 261.86 + -1.74 y + 0.00166 y2

Para y = T = 172.70 m

t z = 10.22 t/m2

E) Distribución de Esfuerzos Normales Horizontales (sy):

s D = 235.68 t/m2 s D = szDtanfD

a2 = s D = 235.68 t/m2

b2 = a1/z + b1tanfD + k -------- (a) Igualando:

b2 = tanfD(zD/z) + b1tanfD + k -------- (b) a1/z = tanfD(zD/z) -------- (c)

b1tanfD = -1.569

k = -0.36

zD/z = wc + tanfU[ 12M/T3 + 2W/T

2 - 2PU/T ] + tanfD[ 12M/T

3 - 4W/T

2 + 4PD/T ] - 6H/T

2

wc = 2.4 t/m3

zD/z = 1.6446

Remplazando en (c):

a1/z = 1.4802

Remplazando en (a):

b2 = -0.44898

sy = a2 + b2y + c2y2+ d2y

3

tyz = a1 + b1y + c1y2



c2 = 1/2(b1/z + 2c1tanfD) -------- (d)

H/z = ( PD - PU ) + kT -------- (e)

H/z = -267.005

t zU/z = -(szU - PU)*tan U/z tan U(szU/z PU/z) -------- (f)

t zU/z = tanfU(szU/z PU/z) -------- (g)

tanfU/z 0 entonces: tanfU constante

PU/z w - k - cawh/z ------- (h) w = 1 t/m2

cawh/z = awh/z{(z/h)*(2-z/h) + [(z/h)*(2-z/h)]1/2}

cawh/z = awh{2/h - 2z/h2 + (2/h - 2z/h

2)/[(z/h)*(2-z/h)]

1/2} -------- (i)

cawh/z = 0 z = h de la base

Reemplazando valores en (h):

PU/z 1.36

szU/z = szD/z + (12/T2)M/z - (24/T

3M)*T/z

szU/z = szD/z + (12/T2)[ H + (T/2)*(PUtanfU - PDtanfD)] + (W/2)*(-tanfU + tanfD)] + (24/T

3M)T/z -------- (j)

T/z = tanfU + tan 1.00

szU/z = -3.26544

Reemplazando valores en (g):

tyzU/z = 0.46

tyzD/z = tanfD*szD/z -------- (k)t zD/z = 1.48017

Deribando la ecuación de "b1" se tiene:

b1/z = -(6/T2)H/z + (12H/T

3)T/z - (2/T)tyzU/z + (2/T

2)tyzUT/z - (4/T)tyzD/z + (4/T

2)tyzDT/z

b1/z = -0.00145

Calculamos "c2" de la ecuación (d):

c2 = 0.000765

d2 = (1/T3)*[2H/z - T/z(2t zU+2t zD + 6H/T)] + (1/T

2)*[t zU/z + t zD/z]

d2 = 0.0000044

Remplazando los valores de a2, b2, c2 y d2 en la ecuación cubica tenemos:

s = 235.68 + -0.44898 y + 0.000765 y2 + 0.0000044 y3



Para y = T = 172.70 m

s U = 203.82 t/m2

También, se puede determinar con:

syU = (szU - PU)*tan2fU + PU

syU = 203.82 t/m2

E) Determiniación de los Esfuerzos Cortantes (tyz) en la base:

Cálculo de los esfuerzos cortantes en diferentes puntos y secciones horizontales de la sección de desdoblamiento

Condición = F.R.L. + sismo

tyz = 261.86 + -1.74 y + 0.00166 y2

SecciónDistancia (m) al pto de

origen = y

a1 b1 b1y c1 c1y2

tyz

1 2 3 4 5 6 7 8

0.0 261.86 0.00 0.00 261.86

20.0 261.86 -34.87 0.66 227.66

30.0 261.86 -52.31 1.49 211.05

40.0 261.86 -69.74 2.65 194.78

60.0 261.86 -104.61 5.97 163.22

74.5 261.86 -129.89 9.20 141.18

80.0 261.86 -139.48 10.61 133.00

R.L. 630.00 94.2 261.86 -1.74 -164.24 0.00166 14.72 112.34

100.0 261.86 -174.35 16.58 104.10

116.7 261.86 -203.47 22.59 80.98

120.0 261.86 -209.22 23.88 76.52

139.7 261.86 -243.57 32.37 50.66

. 140.0 261.86 -244.09 32.50 50.28

149.7 261.86 -261.00 37.16 38.02156.7 261.86 -273.21 40.72 29.38

160.0 261.86 -278.96 42.45 25.36

172.7 261.86 -301.10 49.46 10.22



H) Determinación de la Magnitud (sP1 ysP2) y direccón de los Esfuerzos ( ) en la base:


Elevac. Horiz.

de sección

Distancia (m) al pto de

origen = y sz sy sz sy sz + sy (sz + sy)/2 (sz sy)/2 (sz sy)2/4 tyz

1 2 3 4 5 6 7 8 9 10

0.00 290.96 235.68 55.28 526.63 263.32 27.64 764.03 261.86

20.00 269.00 227.04 41.96 496.04 248.02 20.98 440.19 227.66

30.00 258.02 223.02 35.00 481.04 240.52 17.50 306.33 211.05

40.00 247.04 219.23 27.82 466.27 233.13 13.91 193.42 194.78

60.00 225.08 212.45 12.63 437.53 218.77 6.32 39.89 163.22

74.50 209.16 208.31 0.85 417.47 208.74 0.43 0.18 141.18

80.00 203.12 206.93 -3.80 410.05 205.03 -1.90 3.62 133.00

R.L. 630.00 94.20 187.53 203.88 -16.35 391.42 195.71 -8.18 66.84 112.34

100.00 181.16 202.87 -21.71 384.03 192.02 -10.85 117.78 104.10

116.70 162.83 200.76 -37.93 363.59 181.79 -18.96 359.63 80.98120.00 159.21 200.49 -41.28 359.70 179.85 -20.64 426.06 76.52

139.70 137.58 199.99 -62.41 337.57 168.78 -31.21 973.86 50.66

140.00 137.25 200.00 -62.75 337.25 168.62 -31.38 984.41 50.28

149.70 126.60 200.50 -73.91 327.10 163.55 -36.95 1,365.55 38.02

156.70 118.91 201.19 -82.28 320.10 160.05 -41.14 1,692.45 29.38

160.00 115.29 201.61 -86.32 316.90 158.45 -43.16 1,862.86 25.36

172.70 101.35 203.82 -102.48 305.17 152.58 -51.24 2,625.47 10.22



0, -291.0

-30, -258.0

-74.5, -209.2

-94.2, -187.5

-116.7, -162.8

-139.7, -137.6

-149.7, -126.6-156.7, -118.9

-172.7, -101.3

y = -1.0979x - 290.96

-291.0

-241.0

-191.0

-141.0

-91.0

-41.0

-172.7 -152.7 -132.7 -112.7 -92.7 -72.7 -52.7 -32.7 -12.7

z ( T o n / m 2 )

Distancia horizontal (m)Distribución de Esfuerzos Normales Verticales en la base (sz):



Variables reales Para graficar

y sz = a + by y sz = a + by

0 291.0 0 -291.0

30 258.0 -30 -258.0

74.5 209.2 -74.5 -209.2

94.2 187.5 -94.2 -187.5116.7 162.8 -116.7 -162.8

139.7 137.6 -139.7 -137.6

149.7 126.6 -149.7 -126.6

156.7 118.9 -156.7 -118.9

172.7 101.3 -172.7 -101.3



0.0, -261.86

-20.0, -227.66

-30.0, -211.05

-40.0, -194.78

-60.0, -163.22

-74.5, -141.18

-80.0, -133.00

-94.2, -112.34

-100.0, -104.10

-116.7, -80.98-120.0, -76.52

-139.7, -50.66-140.0, -50.28

-149.7, -38.02

-156.7, -29.38-160.0, -25.36

-172.7, -10.22

y = -0.0017x2 - 1.7435x - 261.86

-280.00

-240.00

-200.00

-160.00

-120.00

-80.00

-40.00

0.00

-190.0 -170.0 -150.0 -130.0 -110.0 -90.0 -70.0 -50.0 -30.0 -10.0

z ( T o n / m 2 )

Distancia horizontal (m)

Distribución de Esfuerzos Cortante (tz):



tz = 261.86 - 1.74y + 0.00166y2

Valres reales Para graficar y tzy y tzy

0.0 261.86 0.0 -261.86

20.0 227.66 -20.0 -227.66

30.0 211.05 -30.0 -211.05

40.0 194.78 -40.0 -194.78

60.0 163.22 -60.0 -163.22

74.5 141.18 -74.5 -141.18

80.0 133.00 -80.0 -133.00

94.2 112.34 -94.2 -112.34

100.0 104.10 -100.0 -104.10

116.7 80.98 -116.7 -80.98

120.0 76.52 -120.0 -76.52

139.7 50.66 -139.7 -50.66

140.0 50.28 -140.0 -50.28149.7 38.02 -149.7 -38.02

156.7 29.38 -156.7 -29.38

160.0 25.36 -160.0 -25.36

172.7 10.22 -172.7 -10.22



tyz2 (9) + (11) (12)

1/2 sP1 =

(7)+(13)

sP2 =

(7) - (13)2tyz

tan2f =

-(16)/(5)2f f

11 12 13 14 15 16 17 18 19

68,571.85 69,335.88 263.32 526.63 0.00 523.72 -9.47 -83.97 -41.99

51,827.04 52,267.23 228.62 476.64 19.40 455.31 -10.85 -84.73 -42.37

44,541.96 44,848.30 211.77 452.29 28.74 422.10 -12.06 -85.26 -42.63

37,937.49 38,130.92 195.27 428.40 37.86 389.55 -14.00 -85.92 -42.96

26,641.48 26,681.36 163.34 382.11 55.42 326.44 -25.84 -87.78 -43.89

19,930.56 19,930.74 141.18 349.91 67.56 282.35 -331.43 -89.83 -44.91

17,687.82 17,691.44 133.01 338.04 72.02 265.99 69.91 89.18 44.59

12,620.29 12,687.13 112.64 308.35 83.07 224.68 13.74 85.84 42.92

10,835.91 10,953.69 104.66 296.68 87.36 208.19 9.59 84.05 42.02

6,557.88 6,917.51 83.17 264.96 98.62 161.96 4.27 76.82 38.41

5,855.70 6,281.76 79.26 259.11 100.59 153.05 3.71 74.90 37.45

2,566.43 3,540.30 59.50 228.28 109.28 101.32 1.62 58.37 29.18

2,527.69 3,512.09 59.26 227.89 109.36 100.55 1.60 58.03 29.02

1,445.85 2,811.40 53.02 216.57 110.53 76.05 1.03 45.82 22.91

862.99 2,555.44 50.55 210.60 109.50 58.75 0.71 35.53 17.76

642.94 2,505.81 50.06 208.51 108.39 50.71 0.59 30.43 15.22

104.47 2,729.94 52.25 204.83 100.34 20.44 0.20 11.28 5.64



Datos:

T1 = 10.96 mT2 = 10 m

T3 = 100.80 m

T = T1+T2+T3 121.76 m

Posición drenes = 15.96 m (desde extremo izquierdo)







aSH = 0.15 g

aSV = 0.075 g

glodo horiz = 1.4 t/m3






Peso propio (Wi):

W1 = 1,460.27 114.45 167,133.83

W2= 2,904.00 105.80 307,243.20

W3 = 13,547.52 67.20 910,393.34


x = 0.00 y = (T1-x) = 10.96

Wa1 = 0.00 121.76 0.00

Wa2 = 54.81 116.28 6,373.95

Wa3 = 608.44 118.11 71,862.55

Peso del lodo (Ws):

Ws = 0.00 121.76 0.00

Subpresión (Us):

U1 = 0.00 113.78 0.00

U2 = 0.00 116.44 0.00

U3 = 0.00 70.53 0.00

Fuerza del agua:

Fa = 6,728.00 38.67 260,149.33

Flodo1 = 0.00 0.00 0.00

Flodo2 = 0.00 0.00 0.00

Fuerza de sismo horizontal (FIHi):FIH(W1) = 219.04 37.00 8,104.48

FIH(W2) = 435.60 60.50 26,353.80

FIH(W3) = 2,032.13 37.33 75,866.11

FIH(Wa1) = 0.00 58.00 0.00

FIH(Wa2) = 4.11 113.50 466.61

FIH(Wa3) = 45.63 77.33 3,528.98

FIH(Ws) = 0.00 0.00 0.00




FIV(W1) = 109.52 114.45 12,535.04

FIV(W2) = 217.80 105.80 23,043.24

FIV(W3) = 1,016.06 67.20 68,279.50

FIV(Wa1) = 0.00 121.76 0.00

FIV(Wa2) = 4.11 116.28 478.05

FIV(Wa3) = 45.63 118.11 5,389.69

FIV(Ws) = 0.00 121.76 0.00


Fx = 1,015.99 47.77 48,538.09

Fy = 96.02 117.04 11,238.57

Suma Momentos 1,474,245.44 532,732.92




Cm = 0.70

CE = 0.70

PE = 12.12 t/m2

Cm = g(q) = 0.0193(90°-q)0.808

F = 0.726*PEy

M = 0.299*PEy2

Fhidr.sismo (F) = 1,020.52 t

Mo Fhidr. Sismo (M) 48,754.37 t-m




FSV = 2.77

∑F H

∑F V

FSV =

PE = CE HgwH

H= aSH /g

f =



(0.65 < f < 0.75 ), para el caso

de combinaciones usual e

inusual

+

H

y

H

y

H

y

H

yC C m E 22

2



∑F H = 10,480.50

∑F V = 20,064.19

f = 0.52






Peso propio (Wi):

W1 = 1,460.27 53.57 78,230.63 antihorario

W2= 2,904.00 44.91851852 130,443.38 antihorario

W3 = 13,547.52 6.318518519 85,600.26 antihorario


x = 0.00 m y = (T1-x) = 10.96Wa1 = 0.00 60.88 0.00 antihorario

Wa2 = 54.81 55.40 3,036.74 antihorario

Wa3 = 608.44 57.23 34,819.55 antihorario

Peso del lodo (Ws):

Ws = 0.00 60.88 0.00 antihorario

Subpresión (Us):

U1 = 0.00 52.9 0.00 horario

U2 = 0.00 55.56049383 0.00 horario

U3 = 0.00 9.65 0.00 horario

Fuerza del agua:

Fa = 6,728.00 38.67 -260,149.33 horario

Flodo1 = 0.00 0.00 0.00 horario

Flodo2 = 0.00 0.00 0.00 horario


FIH(W1) = 219.04 37.00 -8,104.48 horarioFIH(W2) = 435.60 60.50 -26,353.80 horario

FIH(W3) = 2,032.13 37.33 -75,866.11 horario

FIH(Wa1) = 0.00 58.00 0.00 horario

FIH(Wa2) = 4.11 113.50 -466.61 horario

FIH(Wa3) = 45.63 77.33 -3,528.98 horario

FIH(Ws) = 0.00 0.00 0.00 horario






FIV(W3) = 1,016.06 6.318518519 6,420.02 antihorario




FIV(Ws) = 0.00 60.88 0.00 antihorario


Fx = 1,015.99 47.77 -48,538.09 horario

Fy = 96.02 56.16 5,392.76 antihorario

Suma Momentos -65,967.06

Donde:

B = T 121.76 m

W =∑F V = 20,064.19 t

H = ∑F H = 10,480.50 t

M = ∑F Mo = -65,967.06 t-m

I = 150,440.36 m4

smin = 138.08 ton/m2

>0 (ok)

smax = 191.48 ton/m2 19.15 kg/cm

2


2minmax/ BM6BV s

2minmax/

6

B

M

B

F V

s



FS esf = Esfuerzo adm is ib le del m ater ial ( material )

Esfuerzo admisib le del m ater ial ( ma x )

FS esf = 1.67


a = szD =191.48

t/m

2

a = szD = W/T - 6M/T

2

szU = 138.08 t/m2 szU = W/T + 6M/T

2

b= -0.43849 b = 12M/T3

sz = 191.48 + -0.43849 y

De acuerdo a la notación: Factor de fricción por corte (SSF):

szU = 138.08 t/m2

szD = 191.48 t/m2

M = -65,967.06 t-m

W =∑V = 20,064.19 t tan = 0.75

H = ∑H = -10,480.50 t SFF = 5.15

T = A = 121.76 m

tan U = 0.10

tan fD = 0.90

P = 116.00 t/m2

PE = 12.12 t/m2

PU = 128.12 t/m2

P' = 0.00

P'E = 0.00

PD = 0.00 t/m2

sz = a + by

H

tanVcASFF

f+



t zU =tz U = -0.98 t/m2

t zU = -(szU - PU)*tanfU

t zD =tz D = 172.33 t/m2

t zD = (szD - PD)*tan D


a1 = 172.33 t/m2

a1 = t zD

b1 = -1.40 t/m2

b1 =-(2/T)*[ 3H/T + t zU + 2t zD ]

c1 = -0.00016 t/m2

c1 =(3/T2)*[ 2H/T + tyzU + tyzD ]

Por lo tanto:

tyz = 172.33 + -1.40 y + -0.00016 y2

Para y = T = 121.76 m

tyz = -0.98 t/m2


syD = 155.10 t/m2 syD = szDtanfD

a2 = syD = 155.10 t/m2

b2 = a1/z + b1tanfD + k -------- (a) Igualando:


b1tan D = -1.263

k = -0.36


2 - 2PU/T ] + tanfD[ 12M/T

3 - 4W/T

2 + 4PD/T ] - 6H/T

2

wc = 2.4 t/m3

zD/z = 1.3910

Remplazando en (c):

a1/z = 1.2519Remplazando en (a):

b2 = -0.37135

c2 = 1/2(b1/z + 2c1tan D) -------- (d)

H/z = ( PD - PU ) + kT -------- (e)

H/z = -171.953

t zU/z = -(szU - PU)*tanfU/z tanfU(szU/z PU/z) -------- (f)

t zU/z = tan U(szU/z PU/z) -------- (g)


sy = a2 + b2y + c2y2+ d2y

3

tyz = a1 + b1y + c1y2



PU/z w - k - cawh/z ------- (h) w = 1 t/m2


cawh/z = awh{2/h - 2z/h2 + (2/h - 2z/h

2)/[(z/h)*(2-z/h)]

1/2} -------- (i)



PU/z 1.36

szU/z = szD/z + (12/T2)M/z - (24/T

3M)*T/z

szU/z = szD/z + (12/T2

)[ H + (T/2)*(PUtanfU - PDtanfD)] + (W/2)*(-tanfU + tanfD)] + (24/T3

M)T/z -------- (j)T/z = tanfU + tan 1.00

szU/z = -0.83822


t zU/z = 0.22

tyzD/z = tanfD*szD/z -------- (k)

tyzD/z = 1.25191


b1/z = -(6/T2)H/z + (12H/T3)T/z - (2/T)tyzU/z + (2/T2)tyzUT/z - (4/T)tyzD/z + (4/T2)tyzDT/z

b1/z = 0.00162


c2 = 0.000663

d2 = (1/T3)*[2H/z - T/z(2t zU+2t zD + 6H/T)] + (1/T

2)*[t zU/z + t zD/z]

d2 = 0.0000047


s =155.10 + -0.37135 y + 0.000663 y2 + 0.0000047 y3

Para y = T = 121.76 m

s U = 128.22 t/m2


syU = (szU - PU)*tan2fU + PU

s U = 128.22 t/m2






tyz = 172.33 + -1.40 y + -0.00016 y2


origen = ya1 b1 b1y c1 c1y

2 tyz

1 2 3 4 5 6 7 8

0.00 172.33 0.00 0.00 172.33

20.00 172.33 -28.07 -0.06 144.19

30.00 172.33 -42.11 -0.15 130.07

40.00 172.33 -56.15 -0.26 115.92

60.00 172.33 -84.22 -0.58 87.53

74.50 172.33 -104.57 -0.90 66.86

80.00 172.33 -112.29 -1.04 59.00

R.L. 630.00 94.20 172.33 -1.40 -132.22 -0.00016 -1.44 38.67

100.00 172.33 -140.36 -1.62 30.35

116.70 172.33 -163.80 -2.21 6.32

120.00 172.33 -168.44 -2.33 1.56

121.76 172.33 -170.91 -2.40 -0.98

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

G) Determiniación de los Esfuerzos Normales Verticales (sy) en la base:

Cálculo de los esfuerzos Normales Horizontales en diferentes puntos y planos verticales en la sección de desdoblamiento




sy = 155.10 + -0.37135 y + 0.000663 y2 + 0.0000047 y3

Localizac. de

sección Horiz.


origen = yconstantes b2y y

2 c2y2

y3 d2y

3sy

1 2 3 4 5 6 7 8 9

0.0 a2 = 0.00 0.00 0.00 0.00 0.00 155.10

20.0 -7.43 400.00 0.27 8,000.00 0.04 147.97

30.0 155.10 -11.14 900.00 0.60 27,000.00 0.13 144.68

40.0 -14.85 1600.00 1.06 64,000.00 0.30 141.60

60.0 -22.28 3600.00 2.39 216,000.00 1.02 136.22

74.5 b2 = -27.67 5550.25 3.68 413,493.63 1.95 133.06

80.0 -29.71 6400.00 4.25 512,000.00 2.41 132.04

R.L. 630.00 94.2 -0.37135 -34.98 8873.64 5.89 835,896.89 3.94 129.94

100.0 -37.14 10000.00 6.63 1,000,000.00 4.71 129.30

116.7 c2 = -43.34 13618.89 9.03 1,589,324.46 7.48 128.28

120.0 -44.56 14400.00 9.55 1,728,000.00 8.14 128.22

121.8 0.000663 -45.22 14826.22 9.83 1,805,284.37 8.50 128.22

0.0 0.00 0.00 0.00 0.00 0.00 0.00

0.0 d2 = 0.00 0.00 0.00 0.00 0.00 0.00

0.0 0.00000471 0.00 0.00 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00 0.00 0.000.0 0.00 0.00 0.00 0.00 0.00 0.00



H) Determinación de la Magnitud (sP1 y sP2) y direccón de los Esfuerzos ( ) en la base:


Elevac. Horiz.

de sección


origen = y sz sy sz sy sz + sy (sz + sy)/2 (sz sy)/2 (sz sy)2/4 tyz

1 2 3 4 5 6 7 8 9 10

0.00 191.48 155.10 36.38 346.57 173.29 18.19 330.89 172.33

20.00 182.71 147.97 34.73 330.68 165.34 17.37 301.63 144.19

30.00 178.32 144.68 33.64 323.00 161.50 16.82 282.95 130.07

40.00 173.94 141.60 32.33 315.54 157.77 16.17 261.34 115.92

60.00 165.17 136.22 28.95 301.39 150.69 14.47 209.48 87.53

74.50 158.81 133.06 25.75 291.87 145.93 12.87 165.76 66.86

80.00 156.40 132.04 24.35 288.44 144.22 12.18 148.27 59.00

R.L. 630.00 94.20 150.17 129.94 20.23 280.11 140.05 10.12 102.35 38.67

100.00 147.63 129.30 18.32 276.93 138.47 9.16 83.94 30.35

116.70 140.30 128.28 12.03 268.58 134.29 6.01 36.16 6.32

120.00 138.86 128.22 10.63 267.08 133.54 5.32 28.27 1.56

121.76 138.08 128.22 9.87 266.30 133.15 4.93 24.35 -0.98

0.00 191.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 191.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 191.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 191.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 191.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00



0.00, -200.42

-20.00, -179.82

-30.00, -169.53

-40.00, -159.23

-60.00, -138.64

-74.50, -123.70-80.00, -118.04

-94.20, -103.42-100.00, -97.45

y = -1.0297x - 200.42

-290.96

-240.96

-190.96

-140.96

-90.96

-40.96

-172.70 -152.70 -132.70 -112.70 -92.70 -72.70 -52.70 -32.70 -12.70

z ( T o n / m 2 )


Distribución de Esfuerzos Normales Verticales en la base (sz):





0.00 191.48 0.00 -200.42

20.00 182.71 -20.00 -179.82

30.00 178.32 -30.00 -169.53

40.00 173.94 -40.00 -159.23

60.00 165.17 -60.00 -138.64

74.50 158.81 -74.50 -123.70

80.00 156.40 -80.00 -118.04

94.20 150.17 -94.20 -103.42

100.00 147.63 -100.00 -97.45

116.70 140.30 -116.70 -80.25

120.00 138.86 -120.00 -76.85

121.48 138.21 -121.48 -75.33



0.00, -179.87

-20.00, -165.90

-30.00, -159.69

-40.00, -153.99

-60.00, -144.13

-74.50, -138.27-80.00, -136.33

-94.20, -132.04-100.00, -130.58

-116.70, -127.35-120.00, -126.89-121.48, -126.69

-180.00

-160.00

-140.00

-120.00

-100.00

-140.00 -120.00 -100.00 -80.00 -60.00 -40.00 -20.00 0.00

z ( T o n / m 2 )





tzy = 261.86 - 1.74y + 0.00166y2

Valres reales Para graficar

y tzy y tzy

0.00 172.33 0.00 -179.87

20.00 164.19 -20.00 -165.90

30.00 160.07 -30.00 -159.69

40.00 155.92 -40.00 -153.99

60.00 147.53 -60.00 -144.13

74.50 141.36 -74.50 -138.27

80.00 139.00 -80.00 -136.33

94.20 132.87 -94.20 -132.04

100.00 130.35 -100.00 -130.58

116.70 123.02 -116.70 -127.35

120.00 121.56 -120.00 -126.89

121.48 120.50 -121.48 -126.69

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.000.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00



Datos:

T1 = 0 m

T2 = 10 m

T3 = 0.90 m

T = T1+T2+T3 10.90 m

Posición drenes = 5.00 m (desde extremo izquierdo)







aSH = 0.15 g

aSV = 0.075 g

lodo horiz = 1.4 t/m3





A) Determinar factor de seguridad al volteo (FSV) y factor de deslizamiento ( f ) :

Momentos respecto al punto "O"




Peso propio (Wi):

W1 = 0.00 10.90 0.00

W2= 240.00 5.90 1,416.00

W3 = 1.08 0.60 0.65


x = 0.00 y = (T1-x) = 0.00

Wa1 = 0.00 10.90 0.00

Wa2 = 0.00 10.90 0.00

Wa3 = 0.00 10.90 0.00

Peso del lodo (Ws):

Ws = 0.00 10.90 0.00

Subpresión (Us):

U1 = 0.00 8.40 0.00

U2 = 0.00 9.23 0.00

U3 = 0.00 3.93 0.00Fuerza del agua:

Fa = 12.50 1.67 20.83

Flodo1 = 0.00 0.00 0.00

Flodo2 = 0.00 0.00 0.00


FIH(W1) = 0.00 3.33 0.00

FIH(W2) = 36.00 5.00 180.00

FIH(W3) = 0.16 0.33 0.05

FIH(Wa1) = 0.00 2.50 0.00

FIH(Wa2) = 0.00 7.50 0.00

FIH(Wa3) = 0.00 3.33 0.00

FIH(Ws) = 0.00 0.00 0.00



Fuerza de sismo vertical (FIV i):

FIV(W1) = 0.00 10.90 0.00

FIV(W2) = 18.00 5.90 106.20

FIV(W3) = 0.08 0.60 0.05

FIV(Wa1) = 0.00 10.90 0.00

FIV(Wa2) = 0.00 10.90 0.00

FIV(Wa3) = 0.00 10.90 0.00

FIV(Ws) = 0.00 10.90 0.00


Fx = 1.99 2.06 4.10

Fy = 0.00 10.90 0.00

Suma Momentos 1,416.65 311.24




Cm = 0.73

CE = 0.73

PE = 0.55 t/m2

Cm = g(q) = 0.0193(90°-q)0.808

PE = CE HgwH

H= aSH /g

+

H

y

H

y

H

y

H

yC C m E 22

2



F = 0.726*PEy

M = 0.299*PEy2

Fhidr.sismo (F) = 1.99 t

Mo Fhidr. Sismo (M) 4.10 t-m




FSV = 4.55

∑F H

∑F V

∑F H = 50.66

∑F V = 259.16

f = 0.20

FSV =

f =



(0.65 < f < 0.75 ), para el caso

de combinaciones usual e

inusual



Peso propio (Wi):

W1 = 0.00 5.45 0.00 antihorario

W2= 240.00 0.45 108.00 antihorario

W3 = 1.08 -4.85 -5.24 antihorario


x = 0.00 m y = (T1-x) = 0.00

Wa1 = 0.00 5.45 0.00 antihorario

Wa2 = 0.00 5.45 0.00 antihorario

Wa3 = 0.00 5.45 0.00 antihorarioPeso del lodo (Ws):

Ws = 0.00 5.45 0.00 antihorario

Subpresión (Us):

U1 = 0.00 2.95 0.00 horario

U2 = 0.00 3.78 0.00 horario

U3 = 0.00 -1.52 0.00 horario

Fuerza del agua:

Fa = 12.50 1.67 -20.83 horario

Flodo1 = 0.00 0.00 0.00 horario

Flodo2 = 0.00 0.00 0.00 horario


FIH(W1) = 0.00 3.33 0.00 horario

FIH(W2) = 36.00 5.00 -180.00 horario

FIH(W3) = 0.16 0.33 -0.05 horario

FIH(Wa1

) = 0.00 2.50 0.00 horario

FIH(Wa2) = 0.00 7.50 0.00 horario

FIH(Wa3) = 0.00 3.33 0.00 horario

FIH(Ws) = 0.00 0.00 0.00 horario




FIV(W1) = 0.00 5.45 0.00 antihorario

FIV(W2) = 18.00 0.45 8.10 antihorario

FIV(W3) = 0.08 -4.85 -0.39 antihorarioFIV(Wa1) = 0.00 5.45 0.00 antihorario



FIV(Ws) = 0.00 5.45 0.00 antihorario


Fx = 1.99 2.06 -4.10 horario

Fy = 0.00 5.45 0.00 antihorario

Suma Momentos -94.52

Donde:

B = T 10.9 m

W =∑F V = 259.16 t

H = ∑F H = 50.66 t

M = ∑F Mo = -94.52 t-m

I = 107.92 m4

smin = 19.00 ton/m2

>0 (ok)

smax = 28.55 ton/m2 2.85 kg/cm

2


FS esf = Esfuerzo adm is ib le del material ( material )

Esfuerzo admisible del m aterial ( ma x )

FS esf = 11.21


a = szD = 28.55 t/m2

a = szD = W/T - 6M/T2

szU = 19.00 t/m2 szU = W/T + 6M/T

2

sz = a + by

2minmax/

B

M6

B

V s

2minmax/

6

B

M

B

F V

s



b= -0.87587 b = 12M/T3

sz = 28.55 + -0.87587 y

De acuerdo a la notación: Factor de fricción por corte (SSF):

szU = 19.00 t/m2

szD = 28.55 t/m2

M = -94.52 t-m

W =∑V = 259.16 t tanf = 0.75

H = ∑H = -50.66 t SFF = 72.69

T = A = 10.90 m

tan fU = 0.00

tan fD = 0.90

P = 5.00 t/m2

PE = 0.55 t/m2

PU = 5.55 t/m2

P' = 0.00

P'E = 0.00

PD = 0.00 t/m2

tyzU =tzyU = 0.00 t/m

2

tyzU = -(szU - PU)*tanfU

tyzD =tzyD = 25.69 t/m2

tyzD = (szD - PD)*tanfD


a1 = 25.69 t/m2

a1 = t zD

b1 = -6.87 t/m2

b1 =-(2/T)*[ 3H/T + t zU + 2t zD ]

c1 = 0.41411 t/m2

c1 =(3/T2)*[ 2H/T + t zU + t zD ]

Por lo tanto:

tyz = 25.69 + -6.87 y + 0.41411 y2

Para y = T = 10.90 m

t z = 0.00 t/m2


tyz = a1 + b1y + c1y2

H

tanVcASFF

f+



syD = 23.13 t/m2 syD = szDtanfD

a2 = s D = 23.13 t/m2

b2 =

a

1/

z + b

1tan

fD + k -------- (a) Igualando:


b1tanfD = -6.184

k = -0.36


2 - 2PU/T ] + tanfD[ 12M/T

3 - 4W/T

2 + 4PD/T ] - 6H/T

2

wc = 2.4 t/m3

zD/z = -3.6829

Remplazando en (c):

a1/z = -3.3146Remplazando en (a):

b2 = -9.85859

c2 = 1/2(b1/z + 2c1tanfD) -------- (d)

H/z = ( PD - PU ) + kT -------- (e)

H/z = -9.473

tyzU/z = -(szU - PU)*tanfU/z tanfU(szU/z PU/z) -------- (f)

t zU/z = tanfU(szU/z PU/z) -------- (g)


PU/z w - k - cawh/z ------- (h) w = 1 t/m2


cawh/z = awh{2/h - 2z/h2 + (2/h - 2z/h

2)/[(z/h)*(2-z/h)]

1/2} -------- (i)



PU/z 1.36

sz

U/

z =

szD/

z + (12/T2)

M/

z - (24/T

3M)*

T/

z

szU/z = szD/z + (12/T2)[ H + (T/2)*(PUtanfU - PDtanfD)] + (W/2)*(-tanfU + tanfD)] + (24/T

3M)T/z -------- (j)

T/z = tanfU + tan 0.90

szU/z = 1.40338


sy = a2 + b2y + c2y2

+ d2y3



tyzU/z = 0.00

tyzD/z = tanfD*szD/z -------- (k)

tyzD/z = -3.31457


b1/z = -(6/T2)H/z + (12H/T

3)T/z - (2/T)tyzU/z + (2/T

2)tyzUT/z - (4/T)tyzD/z + (4/T

2)tyzDT/z

b1/z = 2.05087


c2 = 1.398137

d2 = (1/T3)*[2H/z - T/z(2tyzU+2tyzD + 6H/T)] + (1/T

2)*[tyzU/z + tyzD/z]

d2 = -0.0588638


s = 23.13 + -9.85859 y + 1.398137 y2 + -0.0588638

Para y = T = 10.90 m

s U = 5.55 t/m2


s U = (szU - PU)*tan2fU + PU

syU = 5.55 t/m2




tyz = 25.69 + -6.87 y + 0.41411 y2


origen = ya1 b1 b1y c1 c1y

2tyz

1 2 3 4 5 6 7 8

0.00 25.69 0.00 0.00 25.69

10.90 25.69 -74.90 49.20 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00



0.0 0.00 0.00 0.00 0.00

R.L. 630.00 0.0 0.00 -6.87113 0.00 0.41411 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

. 0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

0.0 0.00 0.00 0.00 0.00

G) Determiniación de los Esfuerzos Normales Verticales (sy) en la base:

Cálculo de los esfuerzos Normales Horizontales en diferentes puntos y planos verticales en la sección de desdoblamiento


sy = 23.13 + -9.85859 y + 1.398137 y2 + -0.0588638

Localizac. de

sección Horiz.


origen = yconstantes b2y y

2 c2y2

y3 d2y

3sy

1 2 3 4 5 6 7 8 9

0.00 a2 = 0.00 0.00 0.00 0.00 0.00 23.13

10.90 -107.46 118.81 166.11 1,295.03 -76.23 5.55

0.00 23.13 0.00 0.00 0.00 0.00 0.00 23.13

0.00 0.00 0.00 0.00 0.00 0.00 23.13

0.00 0.00 0.00 0.00 0.00 0.00 23.13

0.00 b2 = 0.00 0.00 0.00 0.00 0.00 23.13

0.00 0.00 0.00 0.00 0.00 0.00 23.13

R.L. 630.00 0.00 -9.85859 0.00 0.00 0.00 0.00 0.00 23.130.00 0.00 0.00 0.00 0.00 0.00 23.13

0.00 c2 = 0.00 0.00 0.00 0.00 0.00 23.13

0.00 0.00 0.00 0.00 0.00 0.00 23.13

0.00 1.398137 0.00 0.00 0.00 0.00 0.00 23.13



0.00 0.00 0.00 0.00 0.00 0.00 23.13

0.00 d2 = 0.00 0.00 0.00 0.00 0.00 23.13

0.00 -0.05886375 0.00 0.00 0.00 0.00 0.00 23.130.00 0.00 0.00 0.00 0.00 0.00 23.13

0.00 0.00 0.00 0.00 0.00 0.00 23.13

H) Determinación de la Magnitud (sP1 ysP2) y direccón de los Esfuerzos ( ) en la base:


Elevac. Horiz.

de sección


origen = y sz sy sz sy sz + sy (sz + sy)/2 (sz sy)/2 (sz sy)2/4

1 2 3 4 5 6 7 8 9

0.00 28.55 3.54 25.45 6.26 23.06 8.35 21.24

10.90 19.00 11.91 18.12 12.68 17.45 13.27 16.93

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

R.L. 630.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00



0, -28.5-10.9, -19.0

0, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.0

y = 1.416x - 3.5687

-291.0

-241.0

-191.0

-141.0

-91.0

-41.0

-172.7 -152.7 -132.7 -112.7 -92.7 -72.7 -52.7 -32.7 -12.7

z ( T o n / m 2 )







0 28.5 0 -28.5

10.9 19.0 -10.9 -19.0

0 0.0 0 0.0

0 0.0 0 0.0

0 0.0 0 0.0

0 0.0 0 0.00 0.0 0 0.0

0 0.0 0 0.0

0 0.0 0 0.0



y3



tyz tyz2 (9) + (11) (12)

1/2 sP1 =

(7)+(13)

sP2 =

(7) - (13)2tyz

tan2f =

-(16)/(5)2f f

10 11 12 13 14 15 16 17 18 19

9.95 19.84 11.18 18.76 12.12 17.94 12.84 17.30 13.39 16.82

13.72 16.53 14.07 16.22 14.34 15.99 14.54 15.81 14.70 15.67

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Diseño Presa Trabajo Final

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