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MANUAL GTZ AUTOMATIZACIÓN

134877079 manual-gtz

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Page 1: 134877079 manual-gtz

MANUAL GTZ

AUTOMATIZACIÓN

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Índice Capítulo 1: Fuerzas - Paralelogramo de fuerzas

Capítulo 2: Momentos de giro, palanca simple

Capítulo 3: Velocidad - Velocidad circular

Capítulo 4: Potencia mecánica – Rendimiento

Capítulo 5: Plano inclinado – Cuna

Capítulo 6: Poleas – Aparejos

Capítulo 7: Transmisiones por engranajes

Capítulo 8: Transmisiones Múltiples

Capítulo 9: Rueda dentada – Cremallera – Engranaje helicoidal

Capítulo 10: Troneado cónico

Capítulo 11: Presión sobre líquidos – Amplificador de fuerzas

Capítulo 12: Tensión y resistencia a la tracción

Capítulo 13: Tensión por compresión – Presión del vástago

Capítulo 14: Tensión de corte – Uniones remachadas

Capítulo 15: Corte - Perforación

Capítulo 2:

Momentos de giro, palanca simple

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Índice Capítulo 1: Fuerzas

Capítulo 2: Trabajo

Capítulo 3:

Capítulo 4:

Capítulo 5:

Capítulo 2:

Momentos de giro, palanca simple

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2000

3000

250

150

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21 72

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40000 181.81

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80 1920

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117.64 12

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43.64 76.36 11.43 8.57

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2083.33 2916.67 6315.78

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7000 5000 4000 8000

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7291.67 6708.33 25.6 14.4

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CAPÍTULO 31.4

v = s

t

s = v.t

s = 120 km . 1 h

h 4

s = 30 km

1 )

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v = s

t

v = 12km (4)

3.h

v = 16km = 16000m = 4.4m

h 3600 s s

2.)

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vm = s

t

vm = 200mm

0.6(60min)

vm = 4.17mm = 0.25m

min s

vm = 15m

min

3.)

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v = s

t

t = s

v

t = 800mm.min

60mm

t = 13.3min

4.)

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v = s

t

t = s

v

t = 20m.s

0.15m

t = 133s

5.)

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v = S / t

t = s / v

t = 0.160 m x min

8 m

t = 0.02 min = 1.2 s

6.)

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v = s / t

s = v x t

s = 16 m x 16 min

60 min

s = 4.267 m

7.)

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v = s / t

t = s / v

t = 20 m x s

4m

t = 5 s

8.)

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CAPITULO 31.5

v = D x π x n

v = 0.6 m x 3.14 x 1061

v = 33.3 m/s = 33.3 Km x 3600

1000h

v = 120 Km / h

1.)

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v = D x π x n

v = 0.12 m x 3.14 x 160

1 min

v = 60.3 m/min = 60.3 m

60 s

v = 1 m/s

2.)

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v = D x π x n

D = v

π x n

D = 25 m x 60 s

3.14 x 2000

D = 0.239 m = 239 mm

3.)

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v = d. π.n

n = v

d. π

n = 25 m g

min(0.016m)(3.14)

n = 498 1

min

4.)

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v = d. π.n

n = __v__

d. π

n = ______40m______

(0.012m)(3.14)(min.)

n = 1062

min.

5.)

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v = d. π.n

v = (0.08m)(3.14)(90)

min.

v = 22.6m

min.

6.)

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v = d. π.n

n = __v__

d. π

n = _____40 m______

(0.4m)(3.14)(min.)

n = 31.8

min.

7.)

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v = d. π.n

v = (0.15m)(3.14)(2400)

min.

v = 1130m

min.

v = 1130m

60min.

v = 18.8m

s

8.)

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CAPÍTULO 32.3

1.kg. = 10 N

G = 600N + 400N

G = 1000N

P = F.s

t

P = (1000N)(5m)

15s

P = 333Nm

s

P = 333W

1.)

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P = F.v

v = 20_m_

min.

v = 0.33_m_

s

P = (28000N)(0.333m)

s

P = 9324Nm

S

P = 9.324kW

2.)

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3.)

m = 1 T = 1 000 kg

G = 10 000 N

P = F x s

t

P = 10 000 N x 4 m

5 s

P = 8 000 Nm = 8 000 W

s

P = 8 kW

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4.)

v = d x π x n

v = 0.1 m x 3.14 x 420 x 1

60 s

v = 2.2 m/s

P = F x v

P = 1 455 N x 2.2 m/s

P = 3 201 W = 3.201 KW

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5.)

P = F x s

t

P = 200 N x 6 m

12 s

P = 100 Nm

s

P = 100 W

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6.)

P = F x s

t

P = 20 000 N x 20 m

40 s

P = 10 000 Nm = 10 000 W

s

P = 10 kW

Page 54: 134877079 manual-gtz

7.)

v = 24 m/min = 0.4 m/s

P = F x v

F = P

v

F = 3 000 Ws (1W = 1 N m)

0.4 m s

F = 7 500 N

Page 55: 134877079 manual-gtz

8.)

700 m3 = 700 000 dm3 → P = 7 000 000 N

n n t = 3 600 s

P = F x s

t

P = 7 000 000 N x 200 m

3 600 s

P = 388 888 Nm = 388 888 W

s

P = 389 kW

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a)

Solución

20

m

33.1

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b)

Solución

12

0 m

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c)

Solución

10

m

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a)

Solución

33.2

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b)

Solución

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c)

Solución

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a)

Solución

33.3

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b)

Solución

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c)

Solución

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1)

Solución

33.4

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2)

Solución

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3)

Solución

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4)

Solución

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5)

Solución

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6)

Solución

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7)

Solución

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8)

Solución

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33.5

1)

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2)

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4)

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5)

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6)

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7)

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34.1

a)

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34.2

1)

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2)

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3)

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4)

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5)

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6)

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7)

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8)

Solución

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35.1

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SOLUCION

a)

d=m*z

d= 1.75*16

d= 28mm

h=13/6m

h=13/6*1.75

h=3.79mm

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b)

d=m*z

d= 1.75*12

d= 21mm

h=13/6m

h=13/6*1.75

h=3.79mm

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c)

α=360º/72º =5

z= 3*5=15

d=m*z

d= 15*4

d=60 mm

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35.2

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SOLUCION

a)

a = (d1/2) + (d2/2)

a = (72/2) + (112/2)

a = 92 mm

b)

a = (m.z1)/2 + (m.z2)/2

a = (5*19)/2 + (5*30)/2

a = 122.5

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c)

a = (d1/2) + d2 + (d3/2)

d2 = m . z2 = 2.5*36 = 90

a = (46/2) + 90 + (20/2) = 123

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35.3

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35.4

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SOLUCION

1)

d=m*z ha= m = 4 mm

d= 4*28

d= 112mm

h=13/6m

h=13/6*4

h=8.67mm

Page 107: 134877079 manual-gtz

2)

z= 24

d =m*z

d= 5*24

d= 120 mm

da= d + 2m

da=120+2*5

da=130 mm

df=120-(14/6)*5

df=108.33mm

Page 108: 134877079 manual-gtz

3)

z= 16

ha=m

ha=1.75mm

hf=7/6 m

hf=(7*1.75)/6 mm

hf=2.04mm

Page 109: 134877079 manual-gtz

4)

da= d+2m d= z*m

da= z*m + 2m d=2.5*32 mm

da= m(z+2) d=80mm

m= da/(z+2) df=d-(14/6)*m

m=85/(32+2) df=80-(14/6)*2.5

m=2.5mm df=74.17mm

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5)

d1=m*z1 a=(d1/2)+(d2/2)

z1=d1/m a=(75mm/2) +(159mm/2) z1=75mm/3mm a=117mm

z1=25

d2=m*z2

z2=d2/m

z2=159mm/3mm

z2=53

Page 111: 134877079 manual-gtz

6) d1=m*z1

d1=2.5*31

d1=77.5mm

d2=m*z2

d2=2.5*59

d2=147.5mm

a=(d1/2)+(d2/2)

a=(77.5mm/2) +(147.5mm/2)

a=112.5mm

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7)

d1=m*z1

d1=4*31

d1=124 mm

d2=m*z2

z2=d2/m

z2=192mm/4mm

z2=48

a=(d1/2)+(d2/2)

2a= d1+d2

d2= 2a-d1

d2= 2*156mm-124mm d2=192mm

Page 113: 134877079 manual-gtz

8)

d1=m*z1

d1=2.5*31

d1=77.5 mm

d2=m*z2

d2=2.5mm*92

d2=230mm

a=(d2/2)-(d1/2)

a= (230mm/2)-(77.5mm/2)

a=75.25mm

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35.5

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SOLUCION

1)

a = m . z1 m . z2

2 2

a = 5mm . 5 + 5mm . 15

2 2

a = 50 mm

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2)

a = m. z1 + m . z2

2 2

a = 8mm . 16 + 8mm . 12

2 2

a = 112 mm

n 1 = z2

n 2 z1

n2 = n1 . z1

z2

n2 = 700 . 16 n2 = 933 (1/min)

min . 12

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3)

1 = M2

M1

M2 = 1. M1

M2 = 2. 10 Nm

M2 = 20 Nm

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4)

a = d1 + d2

2 2

a = m . z1 + m . z2

2 2

a = 4 mm . 17 + 4 mm . 49

2 2

a = 132

i = z2

z1

i = 49

17

i = 2.88

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SOLUCION

5)

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6)

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7)

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8)

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36.1

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SOLUCION

A)

i=(z2*z4/z1*z3)

i= 24*28/12*12

i= 3

B)

i=(z2*z4/z1*z3)

i= 45*45/15*15

i= 9

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I =n1/n4

9=720/n4

n4= 720/9

n4=80

C)

i=(z2*z4/z1*z3)

Z1=(z2*z4/i*z3)

Z1= 36*36/9*12

Z1= 12

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36.2

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36.3

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SOLUCION

9)

N/n min= 21*28/7*7

N min = n/12

N min= 3000/12

N min=250

N/n max= 21*15/7*15

N max = n/3

N max= 3000/3

N max= 1000

Page 138: 134877079 manual-gtz

10)

1400/n = 120*25/80*15

N = 1400* 80*15 /120*25

N = 560

11)

1000/n min = 35*15/15*15

N min= 1000*15/35

N min= 429

Page 139: 134877079 manual-gtz

1000/n max = 35*30/15*30

N max= 1000*30/35

N max= 857

12)

700/n = 34*39/17*13

N = 700/6

N= 117

I=700/117

I=6

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SOLUCION

13)

1400/n min = 31*50/19*13

N min= 1400*19*13 /31*50

N min= 223

1400 =n max

N max = 1400

14)

N min = 1400*60*15/18*30

N = 223

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15)

N/350 = 34*30/17*15

N=350*34*30/17*15

N=1400

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16)

1400/n min= 120*31/80*15

N min= 1400*80*15/120*31

N min=452

1400/n max= 80*31/120*15

N max= 1400*120*15/80*31

N max= 1016

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Ejercicio 37.1

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s = m * z *

s = 4 mm * 12 * 3,14

s = 150,72 mm

37.1

1.

z = 12

m = 4 mm

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37.1

2.

s = m * z *

s = 5 mm * 15 * 3,14

s = 235,5 mm

z = 15

m = 5 mm

= ?

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37.1

a.

z = 12 m = 6 mm

S = 226,08 mm

s = m * z *

s = 6 mm * 12 * 3,14

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S = ?

37.1

b.

= 60º

= ?

s = 2 *40 *

s = 251.2

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37.1

c.

z = 21 m = 4 mm

s = 263,76 mm

s = m * z *

s = 4 mm * 21 * 3,14

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Ejercicio 37.2

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37.2

1.

i = 40

Z2 = 40 i = ?

Z1 =1

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37.2

2.

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37.2

a.

i = ? Z2 = 40

Z1 = 2

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37.2

b.

i = ?

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37.2

c.

i = ?

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Datos Solución

EJERCICIO 37.1

CAPÍTULO 37

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Datos Solución

EJERCICIO 37.2

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Datos Solución

EJERCICIO 37.3

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Datos Solución

EJERCICIO 37.4

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Datos Solución

EJERCICIO 37.5

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Datos Solución

EJERCICIO 37.6

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Datos Solución

EJERCICIO 37.7

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Datos Solución

EJERCICIO 37.8

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Datos Solución

EJERCICIO 37.9

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Datos Solución

EJERCICIO 37.10

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Datos Solución

EJERCICIO 37.11

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Datos Solución

EJERCICIO 37.12

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Datos Solución

EJERCICIO 37.13

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Datos Solución

EJERCICIO 37.14

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Datos Solución

EJERCICIO 37.15

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Datos Solución

EJERCICIO 37.16

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38.1

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1

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2

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a)

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b)

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c)

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38.2

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1

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2

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a)

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b)

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c)

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1 38.3

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2 38.3

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3 38.3

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4 38.3

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5 38.3

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6 38.3

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7 38.3

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8 38.3

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P = F

A

39.1

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P = F / A

F = P* A

F = (30 daN/cm2)*(12.56 cm2)

F = 377 daN

Solución:

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Solución:

P = 1000 daN = 20 bar

50 cm2

a)

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b)

Solución:

P = 1000 daN = 10 bar

100 cm2

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c)

Solución:

P = 62.8 daN

P = 20 bar*π* (2cm / 2)^2

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F1

* A2

F2

* A1

F2

A1

39.2

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Solución:

F1 = F2 F1 = 8000N * 3.14 cm2

A1 A2 28.26 cm2

F1 = P2 * A1

A2

F1 = 250 N

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Solución:

F1 = F2

A1 A2

F1 = P2 * A1

A2

F1 = 1 000N * 4 cm2

16 cm2

F1 = 250 N

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Solución:

F1 = F2

A1 A2

F1 = P2 * A1

A2

A2 = 200 N * 4 cm2

50 N

A2 = 16 cm2

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F1 = 50 N * 400 cm2

100cm2

F1 = 200 N

Solución:

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Solución:

F1 = 8 daN * 12.6 cm2

cm2

F1 = 1008 N

F = P * A

39.3

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Solución:

P = 500 daN * 100 mm2

628 mm2 * 1cm2

P = 79.62 bar

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Solución:

F = P * A

F = 12 bar * π * (2cm)^2

F = 150.78 daN

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Solución:

F1 = F2

A1 A2

F1 = P2 * A1

A2

F2 = 120 N * (36 cm)^2 * π

(12 cm)^2 * π

F2 = 1080 N

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Solución: A = 200 daN *cm2 63.7 bar

A = 3.14 cm2

A = π r^2

r=1cm

d = 20 mm

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Solución:

F1 = 120 daN * 28.26 cm2

cm2

F1 = 33.9 KN

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Solución:

P = F/ A 25 bar = F/A

25 daN/cm2 = F/ (π*2.83cm)^2

F = 157.25 daN

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Solución:

(r1)^2 = 80N * (20 mm)^2 * π

320 N * π 2r1 = 20 mm

r1 =10mm

d1 = 20 mm

P = F

A

P = 320 N

(2 cm)^2 * π

P = 25.47 bar

Page 210: 134877079 manual-gtz

PROBLEMA 39.4 – 9

P = F

A

F = P.A

F =4,5 daN.254 cm2

cm2

F = 1143 daN

m = 1143 Kg

Page 211: 134877079 manual-gtz

PROBLEMA 39.4 – 10

A = (D2 - d2 ). 3,14

4

A = (62 cm2 – 22 cm2 ). 3,14

4

A = 25,13 cm2

P = F

A

F = F

(D2 - d2 ). 0,785

F = P. (D2 - d2 ). 0,785

F = 25 daN. (62 - 22 ). 0,785 cm2

cm2 F = 628 daN

Page 212: 134877079 manual-gtz

PROBLEMA 39.4 – 11

F2 = F1

A2 A1

F2 = F1 . A2

A1

F2 =25N. 3,62 . 0,785cm2

1,22 . 0,785cm2

F2 = 225 N

Page 213: 134877079 manual-gtz

PROBLEMA 39.4 – 12

P = F

A

F = P.A

F =4,5 daN. 62 . 0,785 cm2

cm2

F = 1272 daN

F = 12,72 KN

Page 214: 134877079 manual-gtz

PROBLEMA 39.4 – 13

P = F

A

P = 100 daN

22 . 0,785 cm2

P = 31,8 daN

cm2

F = 31,8 bar

Page 215: 134877079 manual-gtz

PROBLEMA 39.4 – 14

F2 = F1

A2 A1

F2 = F1 . A2

A1

F2 = 70N. 12,56cm2

3,14cm2

F2 = 280 N

Page 216: 134877079 manual-gtz

PROBLEMA 39.4 – 15

P = F

A

F = P.A

F =24 daN. (2,832 - 22 )0,785 cm2

cm2

F = 7,55 daN

F = 75,5 N

Page 217: 134877079 manual-gtz

PROBLEMA 39.4 – 16

P = F

A

F = P.A

F =50 daN. 10,2 cm2

cm2

F = 816 daN

m = 816 kg

Page 218: 134877079 manual-gtz

PROBLEMAS

40.1

Page 219: 134877079 manual-gtz

PROBLEMAS 40.2

Page 220: 134877079 manual-gtz

PROBLEMAS 40.3

Page 221: 134877079 manual-gtz

1

2

Page 222: 134877079 manual-gtz

3

4

A

F

2200

8000

mm

N

Page 223: 134877079 manual-gtz

PROBLEMAS 40.3

Page 224: 134877079 manual-gtz

5

6

*2

Page 225: 134877079 manual-gtz

A

F

7

A

F

8

Page 226: 134877079 manual-gtz

PROBLEMAS 40.4

Page 227: 134877079 manual-gtz

9.-

σ = F / A

σ = 800 N

( 45 – 15 ) mm * 15 mm

σ = 17.8 N/ mm2

10.-

A = 100 mm2 * 3.14 * 0.25

A = 78.5 mm2

Rm = Fm / A

Fm = Rm * A

Fm = 370 N/ mm2 * 78.5 mm2

Fm = 29045 N

Page 228: 134877079 manual-gtz

11.-

σ = F / A

F = σ * A

F = 85 N/ mm2 * ( 120 - 13 )mm *

15mm

F = 136.4 KN

Page 229: 134877079 manual-gtz

12.-

m = 600 Kg

G = 6000 N

σ1 = G / A

σ1 = 6000 N * 4

144 mm2 * 3.14

σ1 = 53 N / mm2

2 F22 = G2

F2 = ( G2 / 2 )1/2

F2 = G / 21/2

F2 = 4243 N

σ2 = F2 / A

σ2 = 4243 N * 4

144 mm2 * 3.14

σ2 = 37.5 N / mm2

Page 230: 134877079 manual-gtz

PROBLEMAS 40.4

Page 231: 134877079 manual-gtz

13.-

800 Kg = 8000 N

σ = G / A

σ = 8000 N * 4

225 mm2 * 3.14

σ = 45 N / mm2

14.-

σ = F / A

F = σ * A

A = 5mm (40mm – 10mm)

A = 150 mm2

F = 100 N / mm2 * 150 mm2

F = 15000 N

Page 232: 134877079 manual-gtz

15.-

4t = 40000 N

G = 40000 N

F = u * G

F = 0.3 * 40000 N

F = 12000 N

σ = F / A

σ = 12000 N * 4

256 mm2 * 3.14

σ = 60 N/ mm2

Page 233: 134877079 manual-gtz

16.-

σ = F / A

σ = 800 N * 4

2 * 64 mm2 * 3.14

σ = 8 N/ mm2

Page 234: 134877079 manual-gtz

PROBLEMAS 41.1

Page 235: 134877079 manual-gtz

PROBLEMAS 41.2

Page 236: 134877079 manual-gtz

PROBLEMAS 41.3

Page 237: 134877079 manual-gtz

PROBLEMAS 41.3

Page 238: 134877079 manual-gtz
Page 239: 134877079 manual-gtz

PROBLEMAS 41.4

Page 240: 134877079 manual-gtz

PROBLEMAS 41.4

Page 241: 134877079 manual-gtz
Page 242: 134877079 manual-gtz
Page 243: 134877079 manual-gtz

42.1

Page 244: 134877079 manual-gtz

42.1

2

2

23.90

133

12000

mm

N

mm

N

A

F

Page 245: 134877079 manual-gtz

42.1

2

2

5,63

10000

5,157

mmA

A

N

mm

N

Page 246: 134877079 manual-gtz

42.1

2

2

2

2

)11.(

84

130

16000

130

2

mm

N

mm

N

mmA

A

Page 247: 134877079 manual-gtz

42.2

Page 248: 134877079 manual-gtz

42.2

2

2

2

2

)15.(

85

353

30000

353

2

mm

N

mm

N

mmA

A

Page 249: 134877079 manual-gtz

42.2

Page 250: 134877079 manual-gtz

2

2

2

2

)11.(

105

130

20000

130

2

mm

N

mm

N

mmA

A

Page 251: 134877079 manual-gtz

42.2

2

2

2

2

8,18

8,1061

20000

8,1061

2

)13.(.4

mm

N

mm

N

mmA

A

Page 252: 134877079 manual-gtz

42.3

2

2

2

4

)10.(

153

5,78

12000

5,78

2

mm

N

mm

N

mmA

A

Page 253: 134877079 manual-gtz

42.3

KNF

NF

mmmm

NF

AF

A

F

mmA

A

04,9

9040

113.80

.

113

2

2

2

4

)12.( 2

Page 254: 134877079 manual-gtz

42.3

KNF

NF

mmmm

NF

AF

A

F

mmA

A

85,7

7850

157.50

.

157

.2

2

2

2

4

)10.( 2

Page 255: 134877079 manual-gtz

42.3

2

.2.4

4.16000

116

2,4

450

10

50

1

10

4

2

mm

N

A

F

mmd

mmmmd

mm

mmd

N

Page 256: 134877079 manual-gtz

42.3

2

22

127

.5

4.2500

2500

02,0

50

.

mm

N

mm

N

A

F

NF

m

NmF

r

MF

rFM

Page 257: 134877079 manual-gtz

42.3

3125

8

500.50

8

500.1

500.18.

F

NF

mm

mmFF

mmFmmF

2

2

2

2

124

12,25

3125

12,25

4

.4.2

4

..2

2

mm

N

mm

N

A

F

mmA

mmA

dA

Page 258: 134877079 manual-gtz

42.3

2

2

226

100

.22600

mmA

N

mmNA

FA

A

F

mmd

mmd

Ad

Ad

dA

12

.2

226.4

.2

.4

.2

.4

4

..2

2

2

2

Page 259: 134877079 manual-gtz

2

2

226

100

.22600

mmA

N

mmNA

FA

A

F

mmd

mmd

Ad

Ad

dA

12

.2

226.4

.2

.4

.2

.4

4

..2

2

2

2

Page 260: 134877079 manual-gtz

42.3

NF

NF

FF

mm

mmFF

mmFmmF

25002

500.52

1.52

20

100.12

100.120.2

2

22

2

25

.8,2

4.2500

..2

.

mm

N

mm

N

d

dF

Page 261: 134877079 manual-gtz

42.4

2

22

1326

.19

4.8000

mm

N

mm

N

A

F

228

15.19

8000

mm

NP

mmmm

NP

A

FP

Page 262: 134877079 manual-gtz

42.4

NF

mmmm

NF

AF

A

F

13267

4

1..13.100

.

22

2

2128

13.6

13267

mm

NP

mmmm

NP

A

FP

Page 263: 134877079 manual-gtz

42.4

P-3

= P/A

= 15000N x 4

2x172mm2(π)

= 33N/mm2

P = F/A

P = . 15000N .

17mmx12mm

P = 74 N/mm2

Page 264: 134877079 manual-gtz

P-4

= P/A

40 N/mm2= 18000N

A

A = 450mm2

2(450mm2)

π

A = 2(d2)(π)

4

d =

d = 17 mm

Page 265: 134877079 manual-gtz

P-5

= P/A

= 54000N x 4

2x3x132mm2(π)

= 80N/mm2

Page 266: 134877079 manual-gtz

P-6

= P/A

= Fx4

2d2(π)

F = 80N(132mm2)(π)

mm2(2)

F = 21226N = 21,226KN

Page 267: 134877079 manual-gtz

P-7

= P/A

= Fx4

2(4)d2(π)

= 60000N(4)

2(4)132mm2(π)

F = 56,5N /mm2

Page 268: 134877079 manual-gtz

P-8

= P/A

F = d2(π)

F = 100N/mm2(152mm2)(π)

F = 70650N = 70,65KN

P = F/A

P = 70650N

4(15mm)(6mm)

P = 196 N/mm2

Page 269: 134877079 manual-gtz

43.1

= Fm /A

Fm =

Fm = 100N/mm2(4mm2)

Fm = 400N

(A)

= Fm /A

Fm =

Fm = 200N/mm2(30x5mm2)

Fm = 30KN

(A)

= Fm /A

Fm =

Fm = 160N/mm2(20xπx2)mm2

Fm = 20,1KN

(A)

Page 270: 134877079 manual-gtz

43.2

P-1

= Fm/A

Fm= (A)

Fm = 320N/mm2(20mm)(π)(3mm)

Fm = 60288N = 60,288KN

Page 271: 134877079 manual-gtz

P-2

= Fm /A

A = 45000N.mm2

240N

A = 187,5 mm2

A = 30mm(π)(X)

X = 187,5mm2

30mm(π)

X = 2mm

Page 272: 134877079 manual-gtz

P-3

(A)

= Fm /A

Fm =

Fm = 200N/mm2(502mm2)(π)1/4

Fm = 392500N = 392,5KN

Page 273: 134877079 manual-gtz

P-4

= Fm /A

Fm =

Fm = 160N/mm2(21mm)(π)(2,5mm)

Fm = 26376N = 392,5KN

(A)

Page 274: 134877079 manual-gtz

P-5

= Fm /A

Fm =

Fm = 180N/mm2(2x100+ 2x80)mm(4mm)

Fm = 259200N= 259,2KN

(A)

Page 275: 134877079 manual-gtz

P-6

= Fm /A

Fm =

Fm = 200N/mm2(640mm2)

Fm = 128000N = 128KN

(A)

A = (2x50+ 2x30)mm(4mm)

A = 640mm2

Page 276: 134877079 manual-gtz

P-7

X2= 242+402

X =

X = 46,6mm

A = (24+40+46,6)mm(3mm)

A = 332mm2

242+402

= Fm /A

Fm =

Fm = 160N/mm2(332mm2)

Fm = 53088N = 53KN

(A)

Page 277: 134877079 manual-gtz

P-8 A1= 10,5mm(π)(2mm)

A1= 66mm2

A2= 21mm(π)(2mm)

A2= 132 mm2

= Fm 1/A

Fm 1= 180N/mm2(66mm2)

Fm1 = 11,9KN

Fm 1= (A)

= Fm2 /A

Fm2 =

Fm2 = 180N/mm2(132mm2)

Fm 2=23,8KN

(A)

Page 278: 134877079 manual-gtz

Ejercicio – Pág. 27.1

N6258.2

)5.3(5001F

)5.3(2F)8.2(1F

NF

F

66.6662

)3(2)2(1000

NF

F

5001

)250(100)50(1

b. a. c.

Page 279: 134877079 manual-gtz

Ejercicio Nº 1- 2– Pág. 27.2

N9090.90220

50*4001F

50*400220*1F

2d*2F1d*1F

5.2621200

420*7501F

420*7501200*1F

2d*G1d*1F

2. 1.

Page 280: 134877079 manual-gtz

Ejercicio Nº 3 - 4 – Pág. 27.2

KN25.6400

500*51F

500*5400*2F

1d*1F2d*2F

N6667.1066300

80*40001F

80*G300*1F

N4000GN10Kg1

4. 3.

Page 281: 134877079 manual-gtz

Ejercicio Nº 5- 6 – Pág. 27.2

KN12200

300*81F

300*8200*1F

2d*2F1d*1F

KN9240

180*121F

180*12240*1F

2d*2F1d*1F

6. 5.

Page 282: 134877079 manual-gtz

Ejercicio Nº 7 - 8 – Pág. 27.2

daN33.83120

400*251F

400*25120*2F

1d*1F2d*2F

KN03.398.197

300*22F

300*298.197*2F

1d*1F2d*2F

98.1972d

45cos*2802d

280/2d45cos

8. 7.

Page 283: 134877079 manual-gtz

Ejercicio Nº 1 - 2 – Pág. 28.2

N600F

2000*3.0F

G*F

N320F

4000*08.0F

G*FN4000G

Kg400m

200200m

2m1mm

2. 1.

Page 284: 134877079 manual-gtz

Ejercicio Nº 3 - 4 – Pág. 28.2

04545.0

2200/100

G*FN2200G

Kg220m

7010050m

3m2m1mm

KN144.0F

8.1*08.0F

G*F

4. 3.

Page 285: 134877079 manual-gtz

Ejercicio Nº 5 - 6 – Pág. 28.2

4.0*2

200Fn

2

GFn

Fn*2*G

KN75.3F

15*25.0F

Fn*F

6. 5.

Page 286: 134877079 manual-gtz

Ejercicio Nº 7 – Pág. 28.2

N160Fn

)1600(80)8000(Fn

KN40F

N160*25.0F

Fn*F

Nm3M

075.0*N40M

*FM

c. a.

b.

Page 287: 134877079 manual-gtz

Ejercicio Nº 8 – Pág. 28.2

Nm6M

03.0*N200M

*FM

KN2.0F

KN5*04.0F

Fn*F

Page 288: 134877079 manual-gtz

29.2 - 1

W=G.s

W=9000N.2m

W=18000Nm

W=18000J

Page 289: 134877079 manual-gtz

29.2 - 2

W=G.s

W=45N.3m

W=135Nm

W=135J

Page 290: 134877079 manual-gtz

29.2 - 3

W=G.s

W=3000N.3m

W=9000Nm

W=9000J

Page 291: 134877079 manual-gtz

29.2 - 4

W=G.s

W=2000N.2m

W=4000Nm

W=4000J

Page 292: 134877079 manual-gtz

29.2 - 5

W=G.s

G=h/s

G=200000Nm/6m

G=25000N

10N=1kg

M=2500kg=2,5T

Page 293: 134877079 manual-gtz

29.2 - 6

m=m1+m2

m=25kg+70kg

m=95kg

W=G.s

W=950N.2000m

W=1900000Nm=

1900000J=1900kJ

Page 294: 134877079 manual-gtz

29.2 - 7

m=V.f

V=2dm.4dm.10dm

V=80dm3

m=80x7,8

m=624kg

W=G.s

W=6240N.6m

W=37440Nm

W=37440J=37,44kJ

Page 295: 134877079 manual-gtz

29.2 - 8

m=V.f

V=1x3,14 x 40dm

4

V=31,4dm3

m=31,44x7,8

m=245kg=0,245T

W=G.s

s=W/G

s=4900Nm/2450N

s=2m

Page 296: 134877079 manual-gtz

29.3 - 9

W=G.s

s=W/G

s=5000000Nm

500000N

s=10m

Page 297: 134877079 manual-gtz

W=G.s

W=1000000KN.20m

W=20 Mio KJ

29.3 - 10

Page 298: 134877079 manual-gtz

W=F.s

W=2KN.1,2m

W=2.4 KJ

29.3 - 11

Page 299: 134877079 manual-gtz

F.400mm=G.r

F= GR

400mm

F=120N.200mm

400mm

F=60

W=G.s

W=120N.6m

W=720Nm=720J

29.3 - 12

Page 300: 134877079 manual-gtz

W=G.s

W=80N.12m

W=960Nm

W=960J

29.3 - 13

Page 301: 134877079 manual-gtz

W=F.s

F=µ .G

F=0.3.1000N

F=300N

W=300N.8m

W=24000Nm=2400=2,

4kJ

29.3 - 14

Page 302: 134877079 manual-gtz

W=G.s

W=1000N.1.8m

W=18000Nm

W=18000J=18J

29.3 - 15

Page 303: 134877079 manual-gtz

W=F.s

W=1500N.10000

m

W=15000 KJ

29.3 - 16

Page 304: 134877079 manual-gtz

NF

mm

mmNF

r

PFF

PFrF

ax

ax

16

250..2

5.500

..2

.

...2.

30.1 - a

Page 305: 134877079 manual-gtz

NF

mm

mmNF

r

PFF

PFrF

ax

ax

20

100..2

4.3140

..2

.

...2.

30.1 - b

Page 306: 134877079 manual-gtz

NF

mm

mmNF

P

rFF

rFPF

ax

ax

ax

ax

47100

4

250.2.120

..2.

..2..

30.1 - c

Page 307: 134877079 manual-gtz

NF

mm

mmNF

P

rFF

rFPF

ax

ax

ax

ax

40192

5

200.2.160

..2.

..2..

30.1 - 1

Page 308: 134877079 manual-gtz

NF

mm

mmNF

r

PFF

PFrF

ax

ax

4

240..2

5,1.4000

..2

.

...2.

30.1 - 2

Page 309: 134877079 manual-gtz

30.2 - 3

Fax*P=F*2Pi*r

P=F*2Pi*r

Fax

P=100N.2Pi.300mm

37680N

P=5mm

Page 310: 134877079 manual-gtz

30.2 - 4

Fax*P=F*2Pi*r

F=Fax*P

2Pi*r

F= 5000N*3mm

2*3,14*320mm

F=7,46N

Page 311: 134877079 manual-gtz

30.2 - 5

Fax*240mm=9000N*360mm

Fax=9000N*360mm

240mm

Fax=13500N

Fax*P=F*2Pi*r

F=Fax*P

2Pi*r

F= 13500N*6mm

2*3,14*230mm

F=56N

Page 312: 134877079 manual-gtz

30.2 - 6

Fax*P=F*2Pi*r

Fax=80N*2Pi*140mm

1,25mm

Fax=56269N

Page 313: 134877079 manual-gtz

30.2 - 7

Fax*P=F*2Pi*r

Fax=120N*2Pi*27mm

5mm

Fax=40694N

Page 314: 134877079 manual-gtz

30.2 - 8

2*Fax*P=F*2Pi*r

Fax=F*2Pi*r

2*P

Fax=80N.2Pi.400mm

2,2mm

Fax=50240N