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Prepared by: 1STRESSES & MACHINE ELEMENTSPROBLEM SET 1INSTRUCTION: Encircle the letter that corresponds to the correct answer of your choice. MULTIPLE CHOICE: Two cylinders rolling in the opposite direction has a speed ratio of 3. If the diameter of driver is 10 inches, find the center distance ...

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STRESSES & MACHINE ELEMENTS PROBLEM SET 1 INSTRUCTION:

Encircle the letter that corresponds to the correct answer of your choice.

MULTIPLE CHOICE:

1. Two cylinders rolling in the opposite direction has a speed ratio of 3. If the diameter of driver is 10 inches, find the center distance between cylinders.

speed ratio of 2.5 and center distance of 50 cm. n

D.

66.67 in

a speed ratio of A:B:C:D = 5:3:1:4. If center d the diameter of cylinder D. D.

16 .37 in

pulley diameter is 10 inches, find the speed of 22 rpm

D.

32.34 rpm

at 250 rpm is connected to shaft B by means of t B 16 inches diameter is connected to 10 of shaft C. 173.45 rpm

D.

197.44 rpm

ull of 6200 lbs. Find the diameter of the rod of 66,000 psi. D.

0.734 in

5,000 psi, what force is necessary to punch a actor of safety of 3.5. 378 lbs

D.

69,345 lbs

is to carry 5000 lb load at 320 rpm using SAE Compute the bearing pressure. 123.34 psi D. 197.34 psi h to diameter ratio of 3. Find the projected 18,058 D. 17,017 h to 5 cm when the load is applied at both ends. city of the steel. 110,000 psi

D.

130,000 psi

0 in-lb. It has a diameter of 1.25 inches and onent stress. 5475.95 psi

D.

7834.56 psi

punch in one motion of a 1/8 inch thick plate s is 52 ksi and factor of safety of 3. A. 7

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13. Determine the minimum diameter of a taper pin for use to fix a lever to a shaft, if it is to transmit a maximum torque of 750 in-lb. The shaft diameter is 1.5 inches and has a stress of 20,000 psi. A. 0.252 in B. 0.452 in C. 0.642 in D. 0.826 in 14. A 19mm stud bolts is used to fastened on a 250 mm diameter cylinder head of diesel engine. If there are 10 stud bolts, determine the pressure inside the cylinder if bolt stress is 50 Mpa. A. 288.8 KPa B. 2888 KPa C. 3426 KPa D. 4828 Kpa 15. A column supports a compressive load of 250 KN. Determine the outside diameter of column if inside diameter is 185 mm and compressive stress of 50 Mpa. A.

200.62 mm

B.

201.47 mm

C.

216.42 mm

D.

208.41 mm

16. A steel hollow tube is used to carry a tensile load of 500 KN at a stress of 140 Mpa. outside diameter is 10 times the tube thickness of the tube. A.

11.24 mm B.

107 mm C.

20.64 mm

D.

22.61 mm

17. A 20 mm diameter rivet is used to fastened two 25 mm thick plate. rivet is 80 Mpa, what tensile force applied each plate to shear the bolt? A.

26.35 KN B.

28.42 KN C.

30.41 KN D.

33333.33 KPa B.

4444.44 KPa C.

If the shearing stress of

25.13 KN

18. Two 30 mm thick plate is fastened by two bolts, 25 mm in diameter. to 50 KN tension, find the bearing stress in bolts. A.

If

5555.55 KPa D.

If the plate is subjected

555555 Kpa

19. What force is necessary to punch a 30 mm hole in 12.5 mm thick plate if ultimate shear stress is 410 Mpa? A. 480 KN

B. 481 KN

C. 482 KN

D. 483 KN

20. A 2.5 inches shaft is subjected to 3 KN.m torque. Find the stress developed. A.

48.62 MPa B.

52.75 MPa

C.

59.67 MPa

D.

38.64 Mpa

21. A shaft when subjected to pure torsion developed a stress of 50 Mpa. If polar moment of inertia is 6.1359 x 10-7 m4, determine the maximum torque the shaft could handle. A. 1.23 KN.m B. 1.68 KN.m

C. 1.84 KN.m

D. 2.48 KN.m

22. A lever, secured to a 50 mm round shaft by a steel tapered pin (d = 10 mm), has a pull of 200 N at a radius of 800 mm. Find S, the working stress on the pin, in Mpa. Consider double shear on the pin. A. 41 B. 43 C. 46 D. 48 23. In a 2.0 m cantilevered I-beam, 2 Mton weight is applied at free end. If the allowable stress in beam is 110 Mpa, determine the section modulus. A. 18.54 in3 B.

21.77 in3 C. 26.83 in3 D. 24.28 in3

24. A 6 mm steel wire is 5 m long and stretches 8 mm under a given load. If modulus of elasticity is 200 Gpa, find the load applied. A. 7 KN B. 8 KN C. 9 KN D. 10 KN 25. A steel wire 10 m long, hanging vertically supports a tensile load of 2 KN. Neglecting the weight of wire, determine the required diameter if the stress is not to exceed 140 Mpa and the total elongation is not to exceed 5 mm. Assume E = 200 Gpa. A. 2 mm B.

3 mm

C. 4 mm

D. 5 mm

26. An iron rod 4 m long and 0.5 cm2 in cross section stretches 1 mm when a mass of 225 kg is hang on it. Compute the modulus of elasticity of the iron. A. 176.58 GPa

B.

169.81 Gpa

C. 160.41 GPa

D. 180.26 Gpa

27. A 20 m rod is stretches to a strain of 0.001. Determine the deflection of the rod. A.

20 mm

B.

25 mm

C.

30 mm

D.

35 mm

28. A rail having a coefficient of linear expansion of 11.6 x 10-6 m/mC increases its length when heated from 70F to 133F. Determine the strain. Prepared by:

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A. 2.04 x 10-4 B.

6.05 x 10-4

C. 4.06 x 10-4

D.

2.77 x 10-4

29. What temperature will the rails just touched if steel railroad is 10 m long are laid with clearance of 3 mm at initial temperature of 15C. Use k = 11.7 x 10-6 m/mC. A.

35.64C

B.

40.56C C. 45.64C D. 50.64C

30. A hollow shaft has an inner diameter of 0.035 m and outer diameter of 0.086 m. Determine the polar moment of inertia of the hollow shaft. A. 1.512 x 10-6 m4

B. 1.215 x 10-6 m4

C.

1.52 x 10-6 m4 D. 1.125 x 10-6 m4

31. It is a problem of expansion and shrinkage of steel material so that the slightly smaller hole of a steel bushing of 1.999 diameter with the following process/materials/data to apply: Coefficient of expansion of carbon steel = 0.0000068 in/in-F. Temperature raised by gas heating = 24.5oF Cooling media to use dry ice with boiling point of -109.3oF (-78.5oC). Shrinkage rate below boiling point is 0.00073 in/in. Determine the final clearance between the expanded steel bushing hole against the shrinkage of the steel shaft. A.

0.000793 B.

0.000693 in

C.

0.000750 in

D.

0.000800 in

32. What modulus of elasticity in tension is required to obtain a unit deformation of 0.00105 m/m from a load producing a unit tensile stress of 44,000 psi? A. 42,300 x 106 psi

B. 41,202 x 106 psi

C. 43,101 x 106 psi

D. 41,905 x 106 psi

33. If the weight of 6” diameter by 48” long SAE 1030 shafting is 174.5 kg, then what will be the weight of chromium SAE 51416 of same size? A.

305.5 lbs B.

426.4 lbs C.

384.6 lbs D.

465.1 lbs

34. Compute the maximum unit shear in a 3 inches diameter steel shafting that transmits 2400 in-lb of torque at 99 rpm. A. 4530 psi B. 4250 psi C. 3860 psi D. 4930 psi 35. If the ultimate shear stress of a 1/8 inch thick drawn steel plates is 35 ksi what force is required to punch a 1 1½ inch diameter hole? A.

10,011 lbs

B.

22,322 lbs

C.

11 Mtons D.

20620 lbs

36. The shaft whose torque varies from 2000 to 6000 in-lbs has 1 ½ inch in diameter and 60,000 psi yield strength. Compute for the shaft mean average stress. A. 6036 psi B. 6810 psi C.

5162 psi D.

5550 psi

37. A link has a load factor of 0.80 the surface factor of 0.80. The surface factor is 0.92 and the endurance strength is 28000 psi. Compute the alternating stress of the link if it is subjected to a reversing load. Assume a factor of safety of 3. A.

8150 B.

10920

C.

9,333

D.

7260

38. The shaft is subjected to a steady load of 36,000 in-lb at a shear stress of 10,000 psi. Compute the diameter of the said shaft in inches. A.

1 7/8B.

2¼

C.

3

D.

2¾

39. A shear pin is to be shear at 15 hp and 1000 rpm. The pin attaches a hub to a shaft 1.5 inches in diameter and ultimate shearing stress of 50,000 psi. Find the diameter of the pin. A.

1/8 in

B.

¼ in

C.

¾ in

D.

1 in

40. A steel 0.5 inch x 1 inch steel 200 ft long is subjected to a 5000 lbs tensile load. deformation along its width if poison’s ratio is 0.25. A. 0.000007 in

B. 0.0000417 in

C. 0.000015 in

Find the

D. 0.000067 in

41. A steel rod is stretched between two rigid walls and carries a tensile load of 5000 N at 20oC. If the allowable stress is not to exceed 130 MN/m2 at -20oC, what is the minimum diameter of the rod? Assume k = 11.7 µm/(m-oC); E = 200 Gpa A.

10.22 mm

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B.

11.22 mm

C.

12.22 mm

D.

13.22 mm 3

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SHAFTING PROBLEM SET 2 INSTRUCTION:

Encircle the letter that corresponds to the correct answer of your choice.

MULTIPLE CHOICE:

1. A shaft is used to transmit 200 KW at 300 rpm by means of a 200 mm diameter sprocket. Determine the force tangent to the sprocket. A.

60.44 KN B.

60.33 KN C.

60.88 KN D.

63.66 KN

2. Find the diameter of a steel shaft which will be used to operate a 110 KW motor rotating at 5 rps if torsional stress is 90 Mpa. A.

60.20 mm B.

58.30 mm

C.

38.30 mm

D.

46.20 mm

3. A shaft has an ultimate stress of 350 Mpa and has a factor of safety of 5. The torque developed by the shaft is 3 KN-m and the diameter outside diameter is 80 mm. Find the inside diameter of the shaft. A.

83.45 mm B.

76.45 mm

C.

69.62 mm

D.

66.34 mm

4. What is the speed of 63.42 mm shaft transmitted 75 KW if stress is not to exceed 26 Mpa. A. 550 rpm

B. 600 rpm C. 650 rpm D.

700 rpm

5. A steel shaft transmit 50 hp at 1400 rpm. If allowable stress is 500 psi, find the shaft diameter. A. 3.58 in. B. 2.84 in. C. 1.65 in. D. 2.54 in. 6. The shaft of a motor has a length of 20 times its diameter and has a maximum twist of 1 degrees when twisted at 2 KN-m torque. If the modulus of rigidity of the shaft is 80 Gpa, find the shaft diameter.

A.

69.23 mm

B.

73.23 mm C.

64.23 mm D.

66.33 mm

7. A hollow shaft developed a torque of 5 KN and shaft stress is 40 Mpa. If outside diameter of shaft is 100 mm, determine the shaft inner diameter. A.

68.43 mm B.

63.28 mm

C.

58.38 mm

D.

77.64 mm

8. A hollow shaft that has 100 mm outside diameter and 80 mm inside diameter is used to transmit 100 KW at 600 rpm. Determine the shaft stress. A.

13.73 MPa B.

16.82 MPa

C.

19.86 MPa

D.

17.21 Mpa

9. What is the polar moment of inertia of a solid shaft that has a torque of 1.5 KN and a stress of 25 Mpa? A. 2.46 x 10-6m4 B. 2.02 x 10-6m4 C. 3.46 x 10-6m4 D. 1.24 x 10-6m4 10. A force tangent to 1 foot diameter pulley is 5 KN and is mounted on a 2 inches shaft. Determine the torsional deflection if G = 83 x 106 Kpa. A.

0.804/m B. 0.654/m C.

0.786/m D. 0.938/m

11. What is the minimum diameter of a steel shaft which will be used to operate a 14 KN.m torque and will not twist more than 3 in a length of 6 m? (G = 83 x 106 kPa) A.

100.64 mm

B.

96.80 mm

C.

118.45 mm

D.

120.72 mm

12. A solid shaft 5 m long is stressed to 60 Mpa when twisted through 4. Find the shaft diameter if G =6 83 Gpa. A. 95. 46 mm B. 90.42 mm C. 101.32 mm D. 103.54 mm

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13. Compute the maximum unit shear in a 2 inches diameter steel shafting that transmits 24,000 in-lb of torque at 120 rpm. A.

15,279 psi B.

17,456 psi

C.

14,233 psi

D.

16,344 psi

14. What is the diameter of line shaft that transmit 150 KW at 15 rps? A. 2.28 in.

B. 3.54 in.

C. 1.62 in.

D. 2.06 in.

15. A main shaft has 50 mm diameter is running at 300 rpm. What is the power that could be deliver by the shaft. A. 30.40 hp B. 28.60 hp C. 32.50 hp D. 16.42 hp 16. A 2 inches diameter main shaft running at 600 rpm is mounted by a 12 inches diameter pulley and is then connected to the shaft of driven machine mounted by a 40 inches diameter pulley by means of a belt. The belt efficiency is 90%. Find the diameter of the short shaft. A.

4.23 inches

B.

3.23 inches

C.

2.25 inches

D.

1.45 inches

17. A 1.5” diameter short shaft is used to transmit 44.4 hp. Determine the shaft speed. A.

500 rps

B.

8.33 rps C.

400 rpm D.

450 rpm

18. A 3” diameter solid shaft is desired to replace a hollow shaft having 4” outside diameter. Consider the strength to be the same, determine the inside diameter of hollow shaft. A.

2.5 in. B.

3.0 in.

C.

3.5 in.

D.

4.0 in.

19. A motor is used to drive a centrifugal pump that discharges 3000 li/min at a head of 10 m. The pump efficiency is 68% and running at 550 rpm. Find the torsional stress of shaft if shaft diameter is 35 mm. A. 13.85 MPa B. 11.85 MPa C. 12.85 MPa D. 14.87 Mpa 20. A circular saw blade has a circular speed of 25 m/sec and 500 mm diameter is driven by a belt that has a slip of 7%. Find the required speed of driven shaft if speed ratio is 3. A.

954.80 rpm

B.

2533.56 rpm C.

3542.45 rpm

D.

3015.57 rpm

21. An 800 mm diameter circular saw blade is driven by a 1800 rpm motor with gear speed ratio of 1.8. Find the peripheral speed of the blade. A.

137.43 ft/sec

B.

140.65 ft/sec C.

132.43 ft/sec D.

135.21 ft/sec

22. A machine shaft is supported on bearings 1 m apart is to transmit 190 KW at 300 rpm while subjected to bending load of 500 kg at the center. If shearing stresses 40 Mpa, determine the shaft diameter. A.

100 mm

B.

90 mm

C.

94 mm

D.

98 mm

23. A 100 mm diameter shaft is subjected to a torque f 6 KN.m and bending moment of 2.5 KN.m. Find the maximum bending stress developed. A.

45.84 MPa B.

60.25 MPa

C.

50.28 MPa

D.

55.46 Mpa

24. A shaft has a length of 10 ft. Find the diameter of the shaft that could safely deliver. A. 1.18 in

B. 7.55 in

C. 2.34 in

D. 1.64 in

25. A 12 ft shaft is running at 260 rpm. What that this shaft could safely deliver? A. 3.37 hp

B. 5.34 hp

C. 4.56 hp D. 2.34 hp

26. Two circular shafts, one hollow shaft and one solid shaft, are made of the same material and have diameters as follows: hollow shaft inside diameter is one-half of the external diameter. The external diameter is equal to the diameter of the solid shaft. What is the ratio of the twisting moment of the hollow shaft to that of the solid shaft? A.

¼

B.

1/3

C.

9/16

D.

15/16

27. Determine the thickness of a hollow shaft having an outside diameter of 100 mm if it is subjected to a maximum torque of 5,403.58 N-m without exceeding a shearing stress of 60 Mpa or a twist of 0.5 degree per meter length of shaft. G = 83,000 Mpa. A.

15 mm

Prepared by:

B.

86 mm

C.

16.8 mm D.

14.2 mm 5

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28. An engine of a motor vehicle with a wheel diameter of 712 mm develops 50 KW at 2,000 rpm. The combined efficiency of the differential and transmission is 75% with an overall speed reduction of 25 is to 1. Determine the torque to be delivered by the clutch in N-m. A.

239

B.

359

C.

432

D.

471

29. An engine of a motor vehicle with a wheel diameter of 712 mm develops 50 KW at 2,000 rpm. The combined efficiency of the differential and transmission is 75% with an overall speed reduction of 25 is to 1. Determine the draw bar pull developed in KN. A.

13.40 KN B.

15.45 KN C.

14.55 KN D.

12.57 KN

30. A 102 mm diameter solid shaft is to be replaced with a hollow shaft equally strong (torsion) and made of the same material. The outside diameter of the hollow shaft is to be 127 mm. What should be the inside diameter? The allowable shearing stress is 41.4 Mpa. A.

107.88 Mpa

B.

105.82 Mpa

C.

291.53 mm

D.

109.60 mm

31. A steel shaft operates at 188 rad/sec and must handle 2 KW of power. The shearing stress is not to exceed 40 MN/m2. Calculate the minimum shaft diameter based on pure torsion. A. 9 mm B. 11 mm C. 13 mm D. 15 mm 32. A round steel shaft transmits 373 watts at 1800 rpm. The torsional deflection is not to exceed 1 deg in a length equal to 20 diameters. Find the shaft diameter. A.

6.53 mm B.

8.72 mm C.

12.84 mm

D.

18.16 mm

33. A 25 mm diameter shaft is to be replaced with a hollow shaft of the same material, weighing half as much, but equally strong in torsion. The outside diameter of the hollow shaft is to be 38 mm. Find the inside diameter. A. 21.25 mm B. 33.64 mm C. 47.21 mm D. 50.28 mm 34. What factor of safety is needed for a 1.998 in diameter shaft with an ultimate strength of 50,000 psi to transmit 40,000 in-lb torque. A.

2.25

B.

1.95

C.

2.14

D.

1.55

35. A tubular shaft, having an inner diameter of 30 mm and an outer diameter of 42 mm, is to be used to transmit 90 KW of power. Determine the frequency of rotation of the shaft so that the shear stress cannot exceed 50 Mpa. A. 26.6 Hz B. 20.6 Hz C. 97.5 Hz D. 66.5 Hz 36. A solid transmission shaft is 3.5 inches in diameter. It is desired to replace it with a hollow shaft of the same material and same torsional strength but its weight should only be half as much as the solid shaft. Find the outside diameter and inside diameter of the hollow shaft in millimeters. A. 107.315 mm ; 86.97 mm

B. 112.231 mm ...