A solid circular shaft will be 2 m long, and its diameter is to be determined. It is made of steel with a shear modulus of 75 GPa, When the shaft is subjected to a torque of 100 Nm, the maximum shear stress is to remain below 10 MPa and the angle of twist is to remain below 3 degrees. What is the minimum diameter of the shaft which meets the above requirements? Where is the minimum shear stress in the shaft and what is its value?

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A solid circular shaft will be 2 m long, and its diameter is to be determined. It is made of steel
with a shear modulus of 75 GPa, When the shaft is subjected to a torque of 100 Nm, the
maximum shear stress is to remain below 10 MPa and the angle of twist is to remain below 3
degrees.
i.
What is the minimum diameter of the shaft which meets the above requirements?
ii.
Where is the minimum shear stress in the shaft and what is its value?
b)
Another shaft is a compound circular shaft formed by two circular shafts which are rigidly
attached along their cross-sections at B, as shown in figure Q3(b). The first section of the shaft,
from A to B, is a solid cylinder which has a length of 50 cm and a diameter of 3cm. The second
section of the shaft, from B to C, is a hollow cylinder with a length of 100 cm, an outer diameter
of 3cm and an internal diameter of 2cm. This whole shaft is subjected to a torque of 200 Nm.
The material in both sections of the shaft has a shear modulus of 85 GPa.
Determine the total angle of twist in degrees in the shaft from A to C.
ii. If instead the entire 150 cm shaft length was hollow with the same internal and external diameters
as the section from B to C, would the total angle of twist increase or decrease? Briefly justify your
answer.
Transcribed Image Text:A solid circular shaft will be 2 m long, and its diameter is to be determined. It is made of steel with a shear modulus of 75 GPa, When the shaft is subjected to a torque of 100 Nm, the maximum shear stress is to remain below 10 MPa and the angle of twist is to remain below 3 degrees. i. What is the minimum diameter of the shaft which meets the above requirements? ii. Where is the minimum shear stress in the shaft and what is its value? b) Another shaft is a compound circular shaft formed by two circular shafts which are rigidly attached along their cross-sections at B, as shown in figure Q3(b). The first section of the shaft, from A to B, is a solid cylinder which has a length of 50 cm and a diameter of 3cm. The second section of the shaft, from B to C, is a hollow cylinder with a length of 100 cm, an outer diameter of 3cm and an internal diameter of 2cm. This whole shaft is subjected to a torque of 200 Nm. The material in both sections of the shaft has a shear modulus of 85 GPa. Determine the total angle of twist in degrees in the shaft from A to C. ii. If instead the entire 150 cm shaft length was hollow with the same internal and external diameters as the section from B to C, would the total angle of twist increase or decrease? Briefly justify your answer.
B
200 Nm
3 cm
2 cm
Not to scale
50 cm
100 cm
Transcribed Image Text:B 200 Nm 3 cm 2 cm Not to scale 50 cm 100 cm
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