Problemas Propuestos Capitulo 6

Captulo 6

Esfuerzo Cortante y Momento Flector

Solucionario Resistencia de Materiales Schaum

53

Problemas Propuestos Capitulo 6: Esfuerzo Cortante y Momento Flector

16.-

100 Kg 200 Kg

X

0.5 m 0.5m

D.C.L.

100 Kg 200 Kg

1 2 M

1 Ax

1 0.5 m 2 0.5m Ay

1. Anlisis por corte 1

100 Kg

v M

n

x 1

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2. Anlisis por Corte 2

100 Kg 200 Kg

v M

n

0.5 m 2

x

Diagrama Cortante

V(x)

0.5 m 1 m V(x) = -100 kg

V(x) = -300 kg

-100 kg

-300 kg

Diagrama Momento flector

M(x)

0.5 m 1 m M(x) = -100x [kg-m]

M(x) = -100x -200(x-0.5) [kg-m]

-50 kg-m

-200 kg-m

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17.-

200 kg/m

X

1.5 m 1.5 m

D.C.L.

200 kg/m

M

Ax

1.5 m 1.5 m Ay


200*x

v M

n

1

x/2 x

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300 kg

0.75m v M

n

1.5 m 2

x

Diagrama Cortante.

V(x)

1.5 m 3 m V(x) = -200x kg

V(x) = -300 kg

-300 kg

Diagrama Momento Flector.

M(x)

1.5 m 3 m M(x) = -100x2 [kg-m]

M(x) = -300x -225 [kg-m]

-225 kg-m

-675 kg-m

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18.-

500 Kg-m 600 Kg/m

X

1.5 m 2 m

D.C.L.

500 Kg-m 600 Kg/m

1 2

X

1 2

1.5 m 2 m


500 Kg-m

V M

n

1

x

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2. anlisis por Corte 2

500 Kg-m 600*x

V M

n

1.5 m x/2 2

x

Diagrama Cortante

V(x)

1.5 m 3.5 m V(x) = 0

V(x) = -600x + 900 kg

-1200 kg

Diagrama Momento Flector

M(x)

1.5 m 3.5 m M(x) = -500 [kg-m]

M(x) = -500 300(x-1.5)2 [kg-m]

-500 kg-m

-1700 kg-m

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19.-

250 Kg 250 Kg

X

0.5 m 0.75 m 0.5 m

D.C.L.

250 Kg 250 Kg

1 2 3

Ax

Ay 1 2 3 By

0.5 m 0.75 0.5 m


V M

n

Ay =250 kg 1

x

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2. Anlisis por corte 2

250 kg

V M

n

Ay 0.5 m 2

x


250 kg 250 kg

V M

n

Ay 0.5 m 0.75 m 3

x

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61

Diagrama Cortante

V(x)

250 kg 0.5 m 1.25 m 1.75 m V(x) = 250 kg

V(x) = 0

-250 kg V(x) = -250 kg


M(x)

125 kg-m 0.5 m 1.25 m 1.75 m M(x) = 250*x [kg-m]

M(x) = 125 [kg-m]

M(x) = -250x + 437.5 [kg-m]

20.-

0.50 m 1 m 0.50m

200 Kg/m 200 Kg/m

X

D.C.L.

0.5 m 1 m 0.5 m

200 Kg/m 200 Kg/m

Ax

Ay 1 2 3 By

Captulo 6



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200x

V M

n

Ay 1

x


100 kg

x/2 V M

n

Ay =100 kg 0.5 m 2

x

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100 kg 200x

V M

n

Ay 0.5 m 1 m 3

x

Diagrama cortante

V(x)

100 kg 0.5 m 1.5 m 2 m V(x) = -200x+100 kg

V(x) = 0

V(x) = -200(x-1.5) kg


M(x)

25 kg-m 0.5 m 1.5 m 2 m M(x) = -250x2+100x [kg-m]

M(x) = 25 [kg-m]

M(x) = 25 100(x-1.5)2 [kg-m]

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21.-

2 m 2 m

100 Kg/m 200 kg/m

X

D.C.L.

2 m 2 m

100 Kg/m 1 2 200 kg/m

Ax

Ay 1 2 By


100x

V M

n

Ay =250 kg 1

x

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200 kg 200x

V M

n

Ay 2 m 2

x

kg

Diagrama Cortante

V(x)

250 kg 2 m 4 m V(x) = -100x+250 kg

50kg V(x) = -200x+450 kg

-350kg

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M(x)

300 kg-m 2 m 4 m M(x) = -50x2+250x [kg-m]

M(x) = -100(x-2)2 +50x+200[kg-m]

22.-

1000 kg/m

z

X

1 m 3 m 2 m

D.C.L.

1 2 3

1000 kg/m z

Ax 1 m 3 m 2 m

Ay 1 2 3 By

Captulo 6



67


V M

n

Ay =1750 kg 1

x


1000x

V M

n

Ay 1 m 2

x

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3000 kg

V M

n

Ay 1 m 3m 3

x

Diagrama Cortante

V(x)

1750 kg 1 m 4 m 6 m V(x) = 1750 kg

V(x) = 1750-1000(x-1) kg

-1250 kg V(x) = -1250 kg


M(x)

2500 kg-m 1 m 4 m 6 m M(x) = 1750x [kg-m]

1750 Kg-m M(x) = 1750x-500(x-1) [kg-m]

M(x) = 1750x + 3000(x-2.5) [kg-m]

Captulo 6



69

23.-

300 Kg-m 450 Kg-m

2.5 m

D.C.L.

300 Kg-m 1 450 Kg-m

Bx

Ay 1 2.5 m By

1. - Anlisis por Corte 1

300 kg-m V M

n

Ay =60 kg 1

x

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Diagrama Cortante

V(x)

60 kg 2.5 m V(x) = 60kg


M(x)

450 kg-m 2.5 m M(x) = 60x+300 [kg-m]

300 kg-m

24.-

600 Kg 1300 Kg

z

X

1 m 1.5 m 2.5 m

D.C.L.

600 Kg 1300 Kg

1 2 3

Ax

1 2 3

Ay 1 m 1.5 m 2.5 m By

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V M

n

Ay =1130kg 1

x


600 kg

V M

n

Ay 1 m 2

x


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600 kg 1300 kg

V M

n

Ay 1 m 1.5m 3

x

Diagrama Cortante

V(x)

1130 kg 1 m 2.5 m 5 m V(x) = 1130 kg

530 kg V(x) = 530 kg

-770 kg V(x) = -770 kg


M(x)

1925 kg-m 1 m 4 m 6 m M(x) = 1130x [kg-m]

1130 Kg-m M(x) = 1130x-600(x-1) [kg-m]

M(x) = -770x + 3850 [kg-m]

25.-

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1600 Kg/m 1800 Kg-m

1 m

X

3 m 0.5 m z

D.C.L.

1 1600 Kg/m 2 1800 Kg-m

3

Ax

Ay 1 3 m 2 0.5 m 3 1m By


1600x V M

n

Ay =2800kg 1

x


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1600 kg/m

V M

n

Ay 3 m 2

x


1600 kg/m

1800 kg-m V M

n

Ay 3 m 0.5m 3

x

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Diagrama Cortante

V(x)

2800 kg 3 m 3.5 m 4.5 m V(x) = -1600x+2800 kg

V(x) = -2000 kg

-2000 kg V(x) = -2000 kg


M(x)

1925 kg-m 3 m 3.5 m 4.5 m M(x) = 1130x [kg-m]

1130 Kg-m M(x) = 1130x-600(x-1) [kg-m]

M(x) = -770x + 3850 [kg-m]

26.-

10000 Kg

1200 Kg/m

X

1.5 m 3.5 m

D.C.L.

1 10000 Kg 2

1200 Kg/m

Ax

Ay 1 1.5 m 2 3.5 m By

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V M

n

Ay =8470kg 1

x


10000 kg 1200x

V M

n

Ay 1.5 m 2

x

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Diagrama Cortante

V(x)

8470 kg 1.5 m 5 m V(x) = 8470 kg

V(x) = -1530 -1200(x-1.5) kg

-1530 kg

-5730 kg

Diagrama Momento flector

M(x)

12705 kg-m 1.5 m 5m M(x) = 8470x [kg-m]

M(x) = -1530x -600(x-1.5)2 +15000[kg-m]

27.-

z 1200 Kg/m z

X

6 m

D.C.L.

z 1200 Kg/m z

Ax

Ay 6 m By

28.-

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600 Kg 400 Kg

X

2 m 2 m 1 m

D.C.L.

1 600 Kg 2 3 400 Kg

Ax

Ay 1 2 By 3

2 m 2 m 1 m


V M

n

Ay =200kg 1

x

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600 kg

V M

n

Ay 2 m 2

x


600 kg

V M

n

Ay 2 m 2 m By 3

x

Diagrama Cortante

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V(x)

400 kg 2 m 4 m 5 m V(x) = 200 kg

200 kg V(x) = -400 kg

-400 kg V(x) = 400 kg


M(x)

400 kg-m 2 m 4 m 5 m M(x) = 200x [kg-m]

M(x) = 200x-600(x-2) [kg-m]

-400 Kg-m M(x) = 400x - 2000 [kg-m]

29.-

2000 Kg 800 Kg-m

X

2 m 1.5 m 1.5 m

0.5 m

D.C.L.

1 2000 Kg 2 3 4

800 Kg-m

Ax By

Ay 2 m 1.5 m 1.5 m

1 2 3 0.5 m 4

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V M

n

Ay =800kg 1

x


2000 kg

V M

n

Ay 2 m 2

x


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2000 kg 800x

V M

n

Ay 2 m 1.5m 3

x


2000 kg 800x

0.5m V M

n

Ay 2 m 1.5m By 4

x

Diagrama Cortante

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V(x)

1200 kg 2 m 3.5 m 4 m 5.5 m V(x) = 800 kg

800kg V(x) = -1200 kg

-1200 kg V(x) = -1200-800(x-3.5) kg

-1600 kg V(x) = 1600-800(x-3.5) kg


M(x)

1600 kg-m 2 m 3.5 m 4 m 5.5m M(x) = 800x [kg-m]

-200 kg-m M(x) = 800x-2000(x-2) [kg-m]

-900 Kg-m M(x) = -1200x-400(x-3.5)2+4000 [kg-m]

M(x) = 400x - 2000 [kg-m]

Problemas Propuestos Capitulo 6

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