1.1. Principal directions and principal components

Try these first

1. 1.

   What are principal stress planes?

   Hint

   Think of where stress might be concentrated the most.

2. 2.

   Define eigenvectors in the context of strain tensors.

   Hint

   They are connected to the directions of maximum or minimum strain.

3. 3.

   What determines the principal stress planes?

   • They have minimum traction
   • They maximize normal traction
   • They are random planes

   Hint

   Think about where stress is most concentrated.

4. 4.

   True or False: Mohr's Circle can only be constructed for stress, not strain.

   • True
   • False

   Hint

   Think about its versatility in analyses.

5. 5.

   Given a strain tensor, compute the eigenvalues and corresponding principal strain directions.

   Hint

   Break it down step by step.

6. 6.

   Construct Mohr’s Circle for a specific strain field and identify principal strains.

   Hint

   Ensure you verify the scales on your graph!