Practice Principal Axes And Eigenvectors (30.14) - Eigenvectors

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is an eigenvector?
Show hintHide hint
Think of vectors in a direction that does not change.
Question 2.
What does an eigenvalue indicate?
Show hintHide hint
It is a scalar associated with an eigenvector.
3Question 3.
What is the primary purpose of eigenvectors in materials?
- To measure temperature
- To determine principal stresses and directions
- To calculate the volume of materials
Show hintHide hint
Consider how forces behave in different directions within structures.
4Question 4.
True or False: Principal stresses are eigenvalues derived from stress tensors.
- True
- False
Show hintHide hint
Reflect on how stress tensors relate to these concepts.
Question 5.
Given a 2x2 stress tensor, compute the principal stresses and directions analytically.
Show hintHide hint
Start by calculating the determinant for the characteristic polynomial.
Question 6.
Explain how you would approach designing a beam based on its principal stresses.
Show hintHide hint
Consider real-world applications in construction materials.

4 more questions in this section. Enroll free to practise them all.