As part of an innovation policy introduced within the company to research into newer design of swings, the R and D department is proposing that work should be carried out on motorized swings. The initial consideration is to use an electric motor to spin the central shaft. For this purpose a hollow shaft of diameter ratio 3:5 is required to transmit 600 kW at 110 rpm, the maximum torque being 12% greater than the mean. The shear stress is not to exceed 60MPa and the twist in a length of 3m is not to exceed 1 Degree (1º). Calculate the minimum outer diameter (D) to satisfy both these conditions. Take G = 80GN/m2 Complete using torsion equation and polar second moment of area equation.

As part of an innovation policy introduced within the company to research into newer design of swings, the R and D department is proposing that work should be carried out on motorized swings. The initial consideration is to use an electric motor to spin the central shaft. For this purpose a hollow shaft of diameter ratio 3:5 is required to transmit 600 kW at 110 rpm, the maximum torque being 12% greater than the mean. The shear stress is not to exceed 60MPa and the twist in a length of 3m is not to exceed 1 Degree (1º). Calculate the minimum outer diameter (D) to satisfy both these conditions. Take G = 80GN/m2 Complete using torsion equation and polar second moment of area equation.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.3.12P: A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable...

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A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable stress in shear is 48 MPa, and the allowable rate of twist is 2.0° in 3.5 meters. (a) Assuming that the shear modulus of elasticity is G = 80 GPa, determine the maximum torque that can be applied to the shaft. (b) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d18. Compare values to corresponding values from part (a).
What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?
The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1= 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter will this stress be reached? Is this diameter an upper or a lower limit on the value of D2?
A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?
A motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at B, The allowable shear stress in the steel is 6000 psi. Calculate the required speed of rotation (number of revolutions per minute) so that the shear stress in the shaft does not exceed the allowable limit.
As part of an innovation policy introduced within the company to research into newer design of swings, the R and D department is proposing that work should be carried out on motorized swings. The initial consideration is to use an electric motor to spin the central shaft. For this purpose a hollow shaft of diameter ratio 3:5 is required to transmit 600 kW at 110 rpm, the maximum torque being 12% greater than the mean. The shear stress is not to exceed 60MPa and the twist in a length of 3m is not to exceed 1 Degree (1º). Calculate the minimum outer diameter (D) to satisfy both these conditions. Take G = 80GN/m2
Two solid shafts, 50 mm in diameter, are connected by a flange coupling with six bolts and a pitch circle diameter of 95 mm. If the maximum shear stress in the shaft due to a torque is to be the same as the shear stress in the bolts, calculate a suitable bolt diameter. If the maximum working shear stress is limited to 55 MPa, what maximum power will be transmitted by the coupling at 700 r/min?
A hollow shaft has to be designed for a marine engine delivering 1200 kW when running at 120 r/min. The maximum allowable shear stress is 50 MPa and the maximum torque to be transmitted by the shaft is 30 % greater than the mean torque. The internal diameter of the shaft is 50 % that of the external diameter. Calculate the shaft dimensions and the angle of twist of the shaft over 3 m when transmitting the above torque (G = 80 GPa).
A hollow shaft for marine applications has outer and inner diameters of 400 mm and 200 mm respectively and transmits 8000 kW at 100 r/min. Calculate the maximum shear stress in the hollow shaft. Calculate the shear stress on the inner surface of the hollow shaft. Determine the maximum length of this shaft if the maximum shear stress as well as an angle of twist of 30 is not to be exceeded. (G = 80 GPa) If this shaft is connected to a similar shaft, 1 m long, through a 10-bolt rigid flange coupling, determine the minimum standard bolt diameter if the pitch circle diameter of the coupling is pcd = 450 mm and the allowable shear stress in the bolts should not exceed 55 MPa. Determine the equivalent torsional stiffness of the shaft assembly.
2. A hollow shaft and a solid shaft constructed of the same material have the same length and the same outer radius. The inner radius R of the hollow shaft is 0.6R. Assuming that both shafts are subjected to the same torque, compare their shear stresses, angle of twist and weights. 3. A hollow aluminium tube used in a roof structure has an outside diameter 104mm and an inside diameter 82mm. The tube is 2.75m long and the aluminium has shear modulus G=28GPa. a. If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is 48 MPa.b. What diameter d is required for a solid shaft to resist the same torque with the same maximum stress.c. What is the ratio of the weight of the hollow tube to the weight of the solid shaft?
Example 10.10 A hollow circular shaft with the ratio of internal and external diameters of 0.6 is required to transmit 870 kW at 120 rpm, the maximum torque being 20% greater than the mean. Determine the dimensions of the shaft if the maximum shearing stress and twist in a length of 3m are limited to 60Mpa and 1.4°respectively. The G= 80Gpa.
A hollow shaft for a rotary compressor is to be designed to transmit a maximum of torque of 4750 N-m. The shear stress in shaft, if the ratio of the inside to the outside diameter is 0.4