4.1. Mathematical form

Try these first

1. 1.

   Define longitudinal strain and give its symbol.

   Hint

   Think of how length changes under stress.

2. 2.

   What are the stress components discussed in this section?

   Hint

   Remember the cylindrical coordinate system.

3. 3.

   What does the longitudinal strain (ε) signify in the context of material deformation?

   Hint

   Consider the dimensions of the object.

4. 4.

   True or False: The stress components σrr and σθθ are both dependent on the radial position r only.

   • True
   • False

   Hint

   Think about the cylindrical symmetry.

5. 5.

   A hollow cylinder is subjected to an internal pressure P and an external tensile load. Derive the overall relationship between σrr and σθθ through integration.

   Hint

   Ensure to consider the boundary value at both surfaces.

6. 6.

   Analyze a scenario where a hollow cylinder is twisted without any internal pressure. Explain the stresses present and derive conditions leading to a zero stress state.

   Hint

   Visualize the cross-section before and after applying the torque.