30.6.1. Structural Analysis

Try these first

1. 1.

   Define eigenvector in your own words.

   Hint

   Think about how it transforms.

2. 2.

   What does dynamic loading refer to?

   Hint

   Consider examples like storms or earthquakes.

3. 3.

   What do eigenvectors represent in structural analysis?

   • A method of calculation
   • Mode shapes of vibration
   • Load capacity

   Hint

   Think about the patterns of motion under loads.

4. 4.

   True or False: Eigenvectors are unique for every matrix.

   • True
   • False

   Hint

   Consider whether a vector can be scaled.

5. 5.

   Given a simplistic model of a triangular truss system, determine the mode shapes using certain eigenvalue calculations. Explain how you would use this information to reinforce unsafe areas of the truss.

   Hint

   Use the concept of eigenvectors to identify key areas for reinforcement.

6. 6.

   Evaluate how the absence of eigenvector analysis could lead to catastrophic failures in a building design aimed to withstand seismic activity.

   Hint

   Consider the importance of understanding movement in design.