2. Mathematical form of u

Try these first

1. 1.

   What is the definition of longitudinal strain (ϵ)?

   Hint

   Think of it as how much the length of the cylinder changes under load.

2. 2.

   What do we denote the displacement component in a hollow cylinder?

   Hint

   Remember it captures how the cylinder stretches.

3. 3.

   What does u represent in a hollow cylinder?

   • Radial displacement
   • Angular displacement
   • Longitudinal displacement

   Hint

   Think of how the cylinder stretches along its length.

4. 4.

   True or False: Longitudinal strain ϵ is dependent on radial distances.

   • True
   • False

   Hint

   It's constant for the analysis.

5. 5.

   A hollow cylinder experiences an internal pressure of 10 MPa. Derive the expressions for radial and hoop stresses, given that inner radius is 0.1 m and outer radius is 0.2 m. Assume linear elastic behavior.

   Hint

   Focus on how pressure influences the radial stress at different points.

6. 6.

   When a hollow cylinder undergoes an axial load, how does it affect the hoop stress? Explain the relationship mathematically and contextually.

   Hint

   Evaluate how axial and hoop stresses interact through the derived equations.