2.3. Hollow Circular Shaft Formula

Try these first

1. 1.

   What is the formula for calculating shear stress in a circular shaft?

   Hint

   Remember the relationship between torque, radius, and polar moment of inertia.

2. 2.

   Define polar moment of inertia.

   Hint

   Think about what it means in terms of geometry.

3. 3.

   What does the polar moment of inertia (J) measure?

   • Resistance to bending
   • Resistance to twisting
   • Resistance to compression

   Hint

   Think about the implications of twisting on structure.

4. 4.

   True or False: The angle of twist increases with the length of the shaft.

   • True
   • False

   Hint

   Consider the factors that influence twisting.

5. 5.

   You have a hollow shaft with outer diameter 90 mm, inner diameter 70 mm, and it’s 3 m long. If a torque of 500 N·m is applied, find the angle of twist and shear stress.

   Hint

   Make sure to consider the dimensions while calculating.

6. 6.

   Given a hollow shaft designed for rigidity, how would you optimize the outer diameter for a specified shear stress if the inner diameter is fixed? Present calculations.

   Hint

   Discuss material selection and dimensions effectively.