4. Stepped Shafts

Try these first

1. 1.

   What is a stepped shaft?

   Hint

   Think about how different sections can be used.

2. 2.

   What does the polar moment of inertia measure?

   Hint

   Consider its role in the torque equation.

3. 3.

   What is the formula for total twist in a stepped shaft?

   Hint

   Remember how each variable contributes to the twist.

4. 4.

   True or False: The internal torque remains constant for all sections of a stepped shaft.

   • True
   • False

   Hint

   Think about the effect of fixing or loading the ends.

5. 5.

   An engineer must design a shaft for a motor. If the shaft has three sections with respective torques of 200 Nm, 150 Nm, and 100 Nm, lengths of 0.5 m, 0.7 m, and 0.4 m, shear moduli of 80 GPa, 100 GPa, and 75 GPa, and polar moments of inertia of 0.0004 m^4, 0.0006 m^4, and 0.0002 m^4, calculate the total twist.

   Hint

   Ensure unit consistency when calculating.

6. 6.

   Discuss the design changes needed if the boundary conditions of one segment change from fixed to free.

   Hint

   Consider material fatigue and safety factors.