MECHANICAL DESIGN LAB PROBLEMS
1. In a thick walled walled cylinder, cylinder, the inside diameter is 50 mm and the wall wall thickness thickness is 60 mm. IfIf the pressure inside the cylinder is 15 MPa and the material used has 70 GPa elastic modulus and 0.3 Poisson’s ratio, find the strain reading from a tangential strain gage at the outer surface. 2. A thick-walled cylinder cylinder has has an inside inside diameter diameter of 30 mm mm and a wall thickness thickness of 70 mm .The inner pressure is 10 MPa. The cylinder is made of steel having an elastic modulus of 200 GPa and a Poisson’s ratio of 0. 3. Find the strains in the radial and tangential directions at the following points: i. Point a at the inner surface. ii. Point b at 65 mm from center. center. iii. Point c at the outer surface. 3. In a thick walled walled cylinder, cylinder, the inside diameter is is 50 mm mm and the wall wall thickness thickness is 60 mm. If If the pressure inside the cylinder is 15 MPa and the material used has 70 GPa elastic modulus and 0.31 Poisson’s ratio , find the stresses at points a, b, and c in the radial and tangential directions where point “a” is at the inner surface, point “c” is at the outer surface and point “b” is at 75 mm from center. 4. In a thick walled cylinder, the inside diameter is 60 mm and the wall thickness thicknes s is 90 mm. Find the strain at points “a” at the inner surface and “b” at 65 mm from center in the radial and tangential directions, if the strain in the tangential direction at the outer s urface is 80μ strain. The steel used has 201GPa elastic modulus and 0.28 Poisson’s ratio (neglect the axial stress). 5. A cylinder is 150 mm ID and 450 mm OD. OD. The internal pressure is 160 MPa MPa and the external pressure is 80 MPa. Find the maximum radial and tangential stresses and the maximum shear stress. The ends are closed. 6. A steel cylinder is 160 mm ID ID and 320 mm OD. If it is subjected to an internal pressure of 150 MPa, determine the radial and tangential stress distributions and show the results on a plot. Determine the maximum shear stress in the cylinder. Assume that it has closed ends. 7. A cylinder with with closed ends has outer diameter D and a wall thickness t = 0.1D. Determine the percentage error involved in using thin wall cylinder theory to calculate the maximum value of tangential stress and the maximum shear stress in the cylinder. 8. A cylinder has an ID of 100 mm mm and an internal pressure of 50MPa. Find Find the needed wall thickness if the factor of safety n is 2 and the yield strength is 250 MPa. Use the maximum shear stress theory, i.e. maximum shear stress = yield strength/2n. 9. A thin cylindrical cylindrical shell has an internal diameter of 200 mm, and is 50 mm thick. It is subjected to an internal pressure of 3 .5 MPa. Estimate the circumferential and longitudinal stresses if the ends of the cylinder are closed. If the ends of the cylinder are closed by pistons sliding in the cylinder, estimate the circumferential and longitudinal stresses. 10. A long steel tube, 75mm internal diameter and 1.5 mm thick, has closed ends, and is 10. subjected to an internal fluid pressure of 3 MPa. If E = 200 GN/ m 2 , and = 0.3, estimate the percentage increase in internal volume of the tube. 11. An air vessel, which is made of steel, is 2 m long; it has an external diameter of 450 11. mm and is 10 mm thick. Find the increase of external diamet er and the increa se of length when charged to an internal air pressure of 10 MPa. 12. A pipe of internal diameter 100 mm, and 3 mm thick is made of steel having tensile tensile yield strength of 375 MPa. What is the maximum permissible internal pressure if the factor of safety n is to be 4? Use the maximum shear stress theory, i.e. maximum shear stress = yield strength/2n.
13. A thin cylindrical shell is subjected to internal fluid pressure, the ends being closed by: (a) Two watertight pistons attached to a common piston rod. (b) Flanged ends. Find the increase in internal diamet er in each case, given tha t the internal diameter is 200 mm, thickness is 5mm.Poison's ratio is 0.3, Young's modulus is 200G N/m 2 , and t he internal pressure is 3.5 MN/m 2 . 14. A thin cylindrical shell has an internal diameter of 200mm, and is 50mm thick. It is subjected to an internal pressure of 3 .5 MN/m2. Estimate the circumferential and longitudinal stresses if t he ends of the cylinder are closed. If the ends of the cylinder are closed by pistons sliding in the cylinder, estimate the circumferential and longitudinal stresses. 15. A 5-mm- diameter shaft rotates at a variable speed. Two self- aligned ball bearings are supporting the shaft. If the first critical speed was 300 rpm, sketch the shape of the shaft at the first, second and third critical speeds, if the shaft was shorter will the critical speed increase or decrease? 16. A 5-mm diameter shaft rotates at a variable speed. Two self- aligned ball bearings are supporting the shaft. If the first critical speed was 400 rpm, how do you know that this is a critical speed? Sketch the shape of the shaft at the first, second and the third critical speeds. If the shaft is longer will the critical speed increase or decrease? 17. A steel column was axially loaded and the critical load for buckling was found to be 50 N when the two ends were hinged (free to rotate). Find the critical load if: (a) the two ends are fixed, (b) one end is fixed and the other is hinged. If the column was shorter, will the critical loads increase or decrease? 18. A steel column was axially loaded and the critical load for buckling was found to be 60 N when the two ends were hinged (free to rotate). Find the critical load if one end is fixed and the other is free. If the column was longer, will the critical loads increase or decrease? a
19. Locate the position of the center of gravity of the machine part shown in the figure if the periods of small oscillations when suspended from holes a and b are Ta=0.8 s and Tb=0.5 s respectively. The distance between the two points of suspension = 120 mm.
m m 0 2 1
b
20. Locate the position of the center of gravity of the machine part shown in the figure, and calculate the mass moment of inertia about the center of gravity. The periods of small oscillations when suspended from a and b holes are T a=1s and Tb=1.5s respectively, and the distance between the two points of suspension is 150 mm and its weight is 100N.
a
m m 0 5 1
b
21. Locate the position of the center of gravity of the machine part shown in the figure if the periods of small oscillations when suspended from holes a and b are T a=0.5 s and Tb=0.65 s respectively. The distance between the two points of suspension is 120mm.
a m m 0 2 1
b
22. A steel thin cylinder shown in Figure 1 where the end of the cylinder is free. The screw was adjusted so that the cylinder takes the longitudinal stress (and not the frame). The steel used has a 200 GPa elastic modulus and 0.28 Poisson’s ratio. The cylinder has an inside diameter 100 mm and a wall thickness 4 mm. Three C strain gages are fixed on the wall surface as shown. The B strain measurements at the sta in gage A, is 500μ strain. A Find the pressure inside the cylinder then find the strains at B and C. Figure 1
23. A steel thin cylinder shown in Figure 1 where the end of the cylinder is free, and the screw was adjusted to transfer the longitudinal stress to the frame (and not the cylinder). The steel used has 200 GPa elastic modulus and 0.28 Poisson’s ratio. The cyl inder has an inside diameter 100 mm and a wall thickness 4 mm. Three strain gages are fixed on the wall surface. If the strain at C was 150μ strain, find the pressure and the strain at A and B. 24. For a steel rectangular bar of 12-mm width, 5-mm thickness and 800-mm length, the relation between load and deflection, was recorded as shown in the table below. Calculate the modulus of elasticity and find the missing numbers in the table. Load (Newton) 0 5 7 10 11.5 ?? Deflection (mm) 0 2.1 3.1 4.2 ?? 6
25. A bar of 5-mm diameter and 800-mm length is used in a deflection bar experiment. The dial gauge to measure the deflection gives the following readings with the corresponding loads: Load (Newton) 0 2.5 4 7.5 Deflection (mm) .06 4.4 7 13.1 Calculate the modulus of elasticity of the bar material.
26. For a steel cylindrical bar of 6-mm diameter and 750-mm length, the relation between torque and deflection was recorded as shown in the table below. Calculate the modulus of rigidity and find the missing numbers in the table. Torque (Newton mm) 0 500 700 1000 1150 ?? Deflection (degree) 0 2.2 3 4.3 ?? 6
27. For a steel cylindrical bar of 6-mm diameter and 750-mm length, the relation between torque and deflection was recorded as shown in the table below. Calculate the modulus of rigidity.
Torque (Newton mm) 0 Deflection (degree) 0
500 2.2
700 3
1000 4.3
28. A hollow shaft transmits 100 kW at 15 rps. The outer and inner diameters are 40 mm and 20 mm respectively. Determine the angular deformation of the shaft in degrees for a length of 1.2 mm 29. The angular deformation of a steel shaft should not exceed 1 deg in a length of 1.8 m. The permissible shearing stress is 80 MPa. Find the shaft diameter. 30. A solid circular shaft of 250 mm diameter is to be replaced by a hollow shaft, the ratio of the external to internal diameters being 2 to 1. Find the size of the hollow shaft if the maximum shearing stress is to be the same as for the solid shaft. What percentage economy in mass will this change effect? 31. A shaft has external and internal diameters of 250mm and 150mm. What power can be transmitted at 110 rpm with a maximum shearing stress of 75 MPa, and what will then be the twist in degrees of a 10 m length of the shaft? G = 80 GN/m 2 . 32. A shaft transmits 7.5 MW at 240 rpm. The shaft has an internal diameter of 150 mm. Calculate the minimum permissible external diameter if the shearing stress in the shaft is to be limited to 150 MPa. 33. Find the maximum shearing stress in a shaft 400-mm external, and 200-mm internal diameter, when subjected to a torque of 450 kJ. If G =80 GPa, what is the angle of twist in a length of 20 diameters? What diameter would be required for a solid shaft with the same maximum stress and torque? 34. A propeller shaft, 45 m long, transmits an average of 10 MW at 80 rev/min. The external diameter of the shaft is 570 mm, and the internal diameter 240 mm. Assuming that the maximum torque is 1.2 times the mean torque, find the maximum shearing stress produced. Find also the relative angular movement of the ends of the shaft when transmitting the average torque. Take G =80GN/m2. 35. A steel tube 3 m long, 37.5 mm diameter, 0.6 mm thick, is twisted by a couple of 50N m. Find the maximum shearing stress, and the angle through which the tube twists. Take G =80 GN/m2. 36. Compare the mass of a solid shaft with that of a hollow one to transmit a given power at a given speed with a given maximum shearing stress, the inside diameter of the hollow shaft being two-thirds of the outside diameter.
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