15.4. Computation of Mode Shapes

Try these first

1. 1.

   What is a mode shape?

   Hint

   Think about how a structure moves when there is no external force.

2. 2.

   Name one analytical method for computing mode shapes.

   Hint

   Consider easier methods for smaller structures.

3. 3.

   What does a mode shape represent?

   • A method of analyzing forces
   • The deformation pattern during vibration
   • The weight distribution in structures

   Hint

   Think about how buildings react when they sway.

4. 4.

   True or False: Numerical methods are unnecessary for large and complex structures.

   • True
   • False

   Hint

   Consider the challenges large buildings present.

5. 5.

   Consider a cantilever beam subjected to a dynamic load. Explain how you would compute its first three mode shapes using both analytical and numerical methods.

   Hint

   Think about the different approaches to get to the solution!

6. 6.

   A structural engineer reads that the mode shapes show localized deflections in a complex frame structure. What implications does this have for design and safety against seismic loading?

   Hint

   What does localized mean in terms of design safety?