5. Final solution for u

Try these first

1. 1.

   Define Young's Modulus in your own words.

   Hint

   Think about the relationship between stress and strain.

2. 2.

   What are boundary conditions?

   Hint

   Consider them as the limits of a system.

3. 3.

   What symbol represents longitudinal displacement in a hollow cylinder?

   • u
   • σ
   • ε

   Hint

   Think about the variables we've been using for displacement.

4. 4.

   True or False: The boundary condition at the outer surface for a hollow cylinder under no external pressure is that radial stress is zero.

   • True
   • False

   Hint

   Reflect on our definitions for outer boundary conditions.

5. 5.

   A hollow cylinder with an internal radius of 2 cm and an external radius of 4 cm is subjected to an internal pressure of 10 MPa. Derive the expressions for longitudinal and radial displacement.

   Hint

   Ensure you apply the correct integration constants based on boundaries you've established.

6. 6.

   If the material of the hollow cylinder has a significant Poisson's ratio, how would the behavior differ under high internal pressures?

   Hint

   Consider how high Poisson's ratio affects both deformation types.