29.6.4. Principal Stresses and Strains

Try these first

1. 1.

   What are principal stresses?

   Hint

   Think about the stresses that occur without shear.

2. 2.

   What does a stress tensor represent?

   Hint

   Consider it as a matrix of stress values.

3. 3.

   What do principal stresses represent?

   • Only maximum stress
   • Only minimum stress
   • Maximum and minimum stresses

   Hint

   Consider both extremes of stress.

4. 4.

   True or False: Eigenvalues of a stress tensor can indicate shear stresses.

   • True
   • False

   Hint

   Recall the definition of eigenvalues.

5. 5.

   Given a stress tensor of [[50, 20], [20, 30]], find the principal stresses and explain their significance.

   Hint

   Use the characteristic equation to solve for eigenvalues.

6. 6.

   Analyze a failure scenario where miscalculating principal stresses led to a structural collapse and suggest measures to avoid such failures.

   Hint

   Consider historical cases where this occurred.