Practice Orthogonality Of Mode Shapes (15.3.1) - Mode Shapes - Earthquake Engineering

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6 sample questions

Question 1.
Define mode shape in your own words.
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Think about how structures move when disturbed.
Question 2.
What does it mean for two mode shapes to be orthogonal?
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Consider vectors that point in different directions.
3Question 3.
What does the orthogonality of mode shapes allow in structural analysis?
- Interference of modes
- Independent analysis of modes
- Increased complexity
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Think about how vectors can behave in an analysis.
4Question 4.
True or False: Mode shapes are orthogonal with respect to the mass matrix.
- True
- False
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Consider the definition of orthogonality.
Question 5.
Using a 2-DOF system as an example, demonstrate how to establish the orthogonality of two mode shapes mathematically.
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Coordinate the analysis using the properties of eigenvectors.
Question 6.
In designing a building, how would you illustrate the importance of stiffness orthogonality when faced with uneven mass distribution?
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Think about how sway patterns might be altered with irregular mass distributions.

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