2.2. Special Case II

Try these first

1. 1.

   What happens to the stress components when λ1 = λ2 = λ3?

   Hint

   Think about how pressure acts in a fluid.

2. 2.

   Define hydrostatic state of stress.

   Hint

   Focus on the equality aspect of the stresses.

3. 3.

   What does it mean when λ1 = λ2 = λ3?

   • All principal stresses are equal
   • There is only shear stress
   • The material fails

   Hint

   Think about what the equality implies.

4. 4.

   In a hydrostatic state of stress, what is τ?

   • True
   • False

   Hint

   Consider the definition of shear stress.

5. 5.

   Consider a cylindrical pressure vessel subjected to equal internal pressures on all surfaces. Analyze how this situation represents a hydrostatic state.

   Hint

   Assess pressure distribution and shear.

6. 6.

   If a fluid has equal pressures acting in all directions, derive the condition for equilibrium under hydrostatic stress.

   Hint

   Reflect on the equilibrium conditions for static fluids.