30.14 - Principal Axes and Eigenvectors
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Practice Questions
Test your understanding with targeted questions
What is an eigenvector?
💡 Hint: Think of vectors in a direction that does not change.
What does an eigenvalue indicate?
💡 Hint: It is a scalar associated with an eigenvector.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary purpose of eigenvectors in materials?
💡 Hint: Consider how forces behave in different directions within structures.
True or False: Principal stresses are eigenvalues derived from stress tensors.
💡 Hint: Reflect on how stress tensors relate to these concepts.
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Challenge Problems
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Given a 2x2 stress tensor, compute the principal stresses and directions analytically.
💡 Hint: Start by calculating the determinant for the characteristic polynomial.
Explain how you would approach designing a beam based on its principal stresses.
💡 Hint: Consider real-world applications in construction materials.
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