18.3.1. Modal Decomposition

Try these first

1. 1.

   What does modal decomposition allow us to represent in structural analysis?

   Hint

   Think about how different modes contribute together.

2. 2.

   Define orthogonality in the context of mode shapes.

   Hint

   Consider how two perpendicular lines do not influence each other.

3. 3.

   What does modal decomposition allow us to analyze?

   • Only single-degree-of-freedom responses
   • Total dynamic response as a combination of modes
   • Static loads only

   Hint

   Focus on the term 'dynamic response'.

4. 4.

   True or False: Orthogonality of modes is not necessary for effective modal decomposition.

   • True
   • False

   Hint

   Think about independent contributions.

5. 5.

   Consider a 5-story building modeled as an MDOF system. Describe how you would approach modal decomposition to analyze its seismic response, focusing on the number of modes to consider.

   Hint

   Think about how the height of the building affects the number of modes considered.

6. 6.

   Suppose you have a structure where higher modes significantly contribute to the response. Discuss the implications of truncating these higher modes during modal analysis.

   Hint

   Consider the balance between computational efficiency and analysis accuracy.