1.2 - Diagonality of matrix for in principal coordinate system
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Practice Questions
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What is a principal coordinate system?
💡 Hint: Think about how matrices change in this special system.
What do off-diagonal components signify in a matrix?
💡 Hint: Recall the definition of diagonality.
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Interactive Quizzes
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What happens to the stress matrix in the principal coordinate system?
💡 Hint: Think about how off-diagonal elements relate to shear.
True or False: In principal strains, the angles between line elements change during deformation.
💡 Hint: Consider how the shape of a cuboid changes under stress.
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Challenge Problems
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Analyze a rectangular beam deformed under tensile load. Describe how to determine whether principal strain directions are diagonal in a transformation matrix.
💡 Hint: Consider eigenvalue calculations.
A cylindrical object undergoes torsion. Explain how diagonal matrices help in simplifying stress-strain relationships.
💡 Hint: Use the object’s geometry in your explanation.
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