ETSI Industriales: Ampliacion de Resistencia de Materiales …bigmac.mecaest.etsii.upm.es/.../Problemas/arm_tema1_problemas.pdf · ETSI Industriales: Ampliacion de Resistencia de

ETSI Industriales: Ampliacion de Resistencia de Materiales

Master en Ingenierıa Industrial, curso 2017/18. Prof. Ignacio Romero

1.1 Determinar el grado de indeterminacion estatica de los sistemas de la figura (lacelosıa NO).

1.2 ? La estructura de la figura estacompuesta de dos solidos prismaticos, unorecto y otro con forma de codo, unidos entresı con una rotula y sujetos en sus extremospor apoyos articulados fijos. Calcula elgrado de hiperestaticidad, las reacciones,los leyes de esfuerzos y las diagramas deesfuerzos cuando se aplica sobre el conjuntouna fuerza puntual P como se indica

P

` `

`

1

1.3 Sabiendo que rDrG

= 2, encontrar el valorde TF en funcion de TE.

157Problems 3.19 The solid rod AB has a diameter dAB 5 60 mm. The pipe CD has an outer diameter of 90 mm and a wall thickness of 6 mm. Know-ing that both the rod and the pipe are made of steel for which the allowable shearing stress is 75 MPa, determine the largest torque T that can be applied at A.

3.20 The solid rod AB has a diameter dAB 5 60 mm and is made of a steel for which the allowable shearing stress is 85 MPa. The pipe CD, which has an outer diameter of 90 mm and a wall thickness of 6 mm, is made of an aluminum for which the allowable shearing stress is 54 MPa. Determine the largest torque T that can be applied at A.

3.21 A torque of magnitude T 5 1000 N ? m is applied at D as shown. Knowing that the diameter of shaft AB is 56 mm and that the diameter of shaft CD is 42 mm, determine the maximum shearing stress in (a) shaft AB, (b) shaft CD.

D

A

B

90 mm

dABC

T

Fig. P3.19 and P3.20

A

100 mm

40 mmC

BD

T ! 1000 N · m


3.22 A torque of magnitude T 5 1000 N ? m is applied at D as shown. Knowing that the allowable shearing stress is 60 MPa in each shaft, determine the required diameter of (a) shaft AB, (b) shaft CD.

3.23 Under normal operating conditions a motor exerts a torque of mag-nitude TF 5 1200 lb ? in. at F. Knowing that rD 5 8 in., rG 5 3 in., and the allowable shearing stress is 10.5 ksi in each shaft, determine the required diameter of (a) shaft CDE, (b) shaft FGH.

F

TEH

E

A

BD

C

GrG

rDTF


3.24 Under normal operating conditions a motor exerts a torque of mag-nitude TF at F. The shafts are made of a steel for which the allow-able shearing stress is 12 ksi and have diameters dCDE 5 0.900 in. and dFGH 5 0.800 in. Knowing that rD 5 6.5 in. and rG 5 4.5 in., determine the largest allowable value of TF.

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1.4 Dibuja los diagramas de esfuerzos en elsolido de la figura.

R

P

1.5 Dibuja los diagramas de esfuerzos en elsolido de la figura.

1.6 Dibuja, sin necesidad de calcular las leyes de esfuerzo, los diagramas de esfuerzosde las siguientes estructuras:

J

P

L/2 L/2

J J

a a

2

P P

a a

P P

a a

P

a

b

3

P

a

b

P

a a a

M

a a a

4

1.7 Dibuja y acota los diagramasde esfuerzos cortantes y momentosflectores de la barra ACDB.

325Problems 5.9 and 5.10 Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum abso-lute value (a) of the shear, (b) of the bending moment.

BAC

12 kN/m 40 kN

1 m2 m

Fig. P5.9

BA

C D

4 ft 4 ft 4 ft

2 kips/ft 15 kips

Fig. P5.10

5.11 and 5.12 Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum abso-lute value (a) of the shear, (b) of the bending moment.

60 kips 60 kips

CA D

EF

B

8 in. 8 in. 8 in.

3 in.250 mm 250 mm 250 mm

50 mm 50 mm

75 N

AC D

B

75 N

Fig. P5.12Fig. P5.11

5.13 and 5.14 Assuming that the reaction of the ground is uniformly distributed, draw the shear and bending-moment diagrams for the beam AB and determine the maximum absolute value (a) of the shear, (b) of the bending moment.

BC D E

2 kips/ft24 kips

A

3 ft 3 ft 3 ft 3 ft

2 kips/ft

Fig. P5.13

BAC D

1.5 kN1.5 kN

0.9 m0.3 m0.3 m

Fig. P5.14

3 kN

BAC D

1.8 kN/m

3 kN

80 mm

300 mm

1.5 m1.5 m1.5 m

Fig. P5.15

BA

C

200 lb/ft

4 ft 4 ft 6 ft

4 in.

8 in.

2000 lb

Fig. P5.16

5.15 and 5.16 For the beam and loading shown, determine the maxi-mum normal stress due to bending on a transverse section at C.

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1.8 Dibuja y acota los diagramasde esfuerzos cortantes y momentosflectores de la barra ACDB.

325Problems 5.9 and 5.10 Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum abso-lute value (a) of the shear, (b) of the bending moment.

BAC

12 kN/m 40 kN

1 m2 m

Fig. P5.9

BA

C D

4 ft 4 ft 4 ft

2 kips/ft 15 kips

Fig. P5.10

5.11 and 5.12 Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum abso-lute value (a) of the shear, (b) of the bending moment.

60 kips 60 kips

CA D

EF

B

8 in. 8 in. 8 in.

3 in.250 mm 250 mm 250 mm

50 mm 50 mm

75 N

AC D

B

75 N

Fig. P5.12Fig. P5.11

5.13 and 5.14 Assuming that the reaction of the ground is uniformly distributed, draw the shear and bending-moment diagrams for the beam AB and determine the maximum absolute value (a) of the shear, (b) of the bending moment.

BC D E

2 kips/ft24 kips

A

3 ft 3 ft 3 ft 3 ft

2 kips/ft

Fig. P5.13

BAC D

1.5 kN1.5 kN

0.9 m0.3 m0.3 m

Fig. P5.14

3 kN

BAC D

1.8 kN/m

3 kN

80 mm

300 mm

1.5 m1.5 m1.5 m

Fig. P5.15

BA

C

200 lb/ft

4 ft 4 ft 6 ft

4 in.

8 in.

2000 lb

Fig. P5.16

5.15 and 5.16 For the beam and loading shown, determine the maxi-mum normal stress due to bending on a transverse section at C.

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1.9 La barra AB esta unida ala barra BCDE a traves de unarotula en B. Dibuja y acota losdiagramas de esfuerzos cortantesy momentos flectores de la barraABCDE.

327Problems 5.22 and 5.23 Draw the shear and bending-moment diagrams for the beam and loading shown and determine the maximum normal stress due to bending.

24 kN/m64 kN ? m

BAC D

2 m 2 m 2 mS250 ! 52

Fig. P5.22

Hinge

2.4 m

0.6 m

1.5 m 1.5 m

CBA E

D

80 kN/m 160 kN

W310 ! 60

Fig. P5.23

5.24 and 5.25 Draw the shear and bending-moment diagrams for the beam and loading shown and determine the maximum normal stress due to bending.

25 kN/m40 kN ? m

BAC

1.6 m 3.2 mW200 ! 31.3

Fig. P5.24

BAC D

5 ft 5 ft8 ft

W14 ! 22

10 kips5 kips

Fig. P5.25

5.26 Knowing that W 5 12 kN, draw the shear and bending-moment diagrams for beam AB and determine the maximum normal stress due to bending.

5.27 Determine (a) the magnitude of the counterweight W for which the maximum absolute value of the bending moment in the beam is as small as possible, (b) the corresponding maximum normal stress due to bending. (Hint: Draw the bending-moment diagram and equate the absolute values of the largest positive and negative bending moments obtained.)

5.28 Determine (a) the distance a for which the absolute value of the bending moment in the beam is as small as possible, (b) the cor-responding maximum normal stress due to bending. (See hint of Prob. 5.27.)

Figs. P5.26 and P5.27

BC D E

A

8 kN 8 kN

W310 ! 23.8

1 m 1 m 1 m 1 m

W

Hinge

18 ft

B

aC

4 kips/ft

W14 ! 68

A

Fig. P5.28

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5

1.10 Una viga biapoyada con una seccionde rigidez a flexion constante esta sometidaa dos fuerzas puntuales de valor 8 kN y tieneenganchado un cable como se indica en lafigura.

i) Calcular las reacciones para un valorcualquiera de W .

ii) Dibujar el diagrama de momentosflectores en la viga para un valorcualquiera de W .

iii) Calcular el valor del peso W queminimiza el maximo momento flector enla viga (en valor absoluto).

327Problems 5.22 and 5.23 Draw the shear and bending-moment diagrams for the beam and loading shown and determine the maximum normal stress due to bending.

24 kN/m64 kN ? m

BAC D

2 m 2 m 2 mS250 ! 52

Fig. P5.22

Hinge

2.4 m

0.6 m

1.5 m 1.5 m

CBA E

D

80 kN/m 160 kN

W310 ! 60

Fig. P5.23

5.24 and 5.25 Draw the shear and bending-moment diagrams for the beam and loading shown and determine the maximum normal stress due to bending.

25 kN/m40 kN ? m

BAC

1.6 m 3.2 mW200 ! 31.3

Fig. P5.24

BAC D

5 ft 5 ft8 ft

W14 ! 22

10 kips5 kips

Fig. P5.25

5.26 Knowing that W 5 12 kN, draw the shear and bending-moment diagrams for beam AB and determine the maximum normal stress due to bending.

5.27 Determine (a) the magnitude of the counterweight W for which the maximum absolute value of the bending moment in the beam is as small as possible, (b) the corresponding maximum normal stress due to bending. (Hint: Draw the bending-moment diagram and equate the absolute values of the largest positive and negative bending moments obtained.)

5.28 Determine (a) the distance a for which the absolute value of the bending moment in the beam is as small as possible, (b) the cor-responding maximum normal stress due to bending. (See hint of Prob. 5.27.)

Figs. P5.26 and P5.27

BC D E

A

8 kN 8 kN

W310 ! 23.8

1 m 1 m 1 m 1 m

W

Hinge

18 ft

B

aC

4 kips/ft

W14 ! 68

A

Fig. P5.28

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1.11 Encontrar el valor de losesfuerzos normales en todos loselementos de la grua de la figura

46 Introduction—Concept of Stress 1.62 In the marine crane shown, link CD is known to have a uniform cross section of 50 3 150 mm. For the loading shown, determine the normal stress in the central portion of that link.

AD

C

B

3 m25 m15 m

35 m

80 Mg

15 m

Fig. P1.62

1.63 Two wooden planks, each 12 in. thick and 9 in. wide, are joined by

the dry mortise joint shown. Knowing that the wood used shears off along its grain when the average shearing stress reaches 1.20 ksi, determine the magnitude P of the axial load that will cause the joint to fail.

P'

P

!

a

b

Fig. P1.64

1.64 Two wooden members of uniform rectangular cross section of sides a 5 100 mm and b 5 60 mm are joined by a simple glued joint as shown. Knowing that the ultimate stresses for the joint are sU 5 1.26 MPa in tension and tU 5 1.50 MPa in shear and that P 5 6 kN, determine the factor of safety for the joint when (a) a 5 208, (b) a 5 358, (c) a 5 458. For each of these values of a, also determine whether the joint will fail in tension or in shear if P is increased until rupture occurs.

2 in.1 in.P' 2 in.

1 in. 9 in.P

in.58

in.58

Fig. P1.63


1.12 Encontrar el valor de todoslos esfuerzos en la barra ABCD

cuando θ = 0.

21Problems 1.7 Each of the four vertical links has an 8 3 36-mm uniform rectan-gular cross section and each of the four pins has a 16-mm diameter. Determine the maximum value of the average normal stress in the links connecting (a) points B and D, (b) points C and E.

0.2 m0.25 m

0.4 m

20 kN

C

B

AD

E

Fig. P1.7

1.8 Knowing that link DE is 18 in. thick and 1 in. wide, determine the

normal stress in the central portion of that link when (a) u 5 0, (b) u 5 908.

1.9 Link AC has a uniform rectangular cross section 116 in. thick and

14 in. wide. Determine the normal stress in the central portion of the link.

60 lb

F

D

E

JC D

B

A

8 in.

2 in.

4 in. 12 in. 4 in.

6 in.

!

Fig. P1.8

B

C

A

3 in.

7 in.

30"

6 in.

240 lb

240 lb

Fig. P1.9

1.10 Three forces, each of magnitude P 5 4 kN, are applied to the mechanism shown. Determine the cross-sectional area of the uni-form portion of rod BE for which the normal stress in that portion is 1100 MPa.

0.100 m

0.150 m 0.300 m 0.250 m

P P P

E

A B C D

Fig. P1.10


6

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ETSI Industriales: Ampliacion de Resistencia de Materiales …bigmac.mecaest.etsii.upm.es/.../Problemas/arm_tema1_problemas.pdf · ETSI Industriales: Ampliacion de Resistencia de