4. Solution for σ and σ

Try these first

1. 1.

   What is radial stress, and how does it act in a hollow cylinder?

   Hint

   Consider how forces act along the radius.

2. 2.

   Define hoop stress in the context of hollow cylinders.

   Hint

   Think about how a cylinder would resist pressure from the inside.

3. 3.

   What is the relationship between the radial and hoop stresses in a hollow cylinder?

   • They are always equal.
   • Hoop stress is always greater than radial stress.
   • Radial stress does not depend on hoop stress.
   • None of the above.

   Hint

   Refer back to the definitions of both stresses.

4. 4.

   True or False? Boundary conditions only affect the outer surface of a hollow cylinder.

   • True
   • False

   Hint

   Think about where pressure is applied and how it transmits through the material.

5. 5.

   A hollow cylinder is subjected to internal pressure P. Given that you know the dimensions and are able to express σ_rr and σ_θ derived from equilibrium equations, calculate the stress variation through the thickness of the cylinder.

   Hint

   Ensure proper integration based on radial distance relations.

6. 6.

   Discuss the impact of increasing internal pressure on the shear stress distribution in a hollow cylinder. What assumptions might you need, and how would these vary in practical applications?

   Hint

   Remember the material properties and how they interact with increasing forces.