1.1. Solution

Try these first

1. 1.

   Define torsion and explain its significance in mechanics.

   Hint

   Think about real-world applications like twisting a doorknob.

2. 2.

   What is the relationship between shear modulus, radius, and torsion?

   Hint

   Recall the formula for maximum stress under torsion.

3. 3.

   What is the formula for maximum shear stress in torsion?

   • τ_max = T/J
   • τ_max = Gκr
   • τ_max = MV/L

   Hint

   Remember the components involved in shear stress.

4. 4.

   True or False: The torque is constant across cross-sections of a variable radius shaft.

   • True
   • False

   Hint

   Consider the principles of torque balance.

5. 5.

   A cylindrical shaft made of varying radius is subjected to an external torque of 200 Nm. Calculate the twist and maximum shear stress if the radius varies from 10 mm to 20 mm.

   Hint

   Focus on the J calculation using the variable radius.

6. 6.

   Design a beam from three different materials (steel, aluminum, and titanium) under the same torque. Determine the optimal material configuration to achieve the minimum twist.

   Hint

   Consider how varying the cross-section and material choice affects overall stiffness.