17.11. Numerical Example (Optional for Students)

Try these first

1. 1.

   What does the mass matrix [M] represent?

   Hint

   Think about how weight is distributed across the building.

2. 2.

   What is the purpose of solving the eigenvalue problem?

   Hint

   Recall how these relate to vibration.

3. 3.

   What does the mass matrix [M] indicate?

   • It indicates structural stiffness
   • It indicates mass distribution
   • It indicates damping

   Hint

   Think about the building's weight.

4. 4.

   True or False: The eigenvalue problem must be solved to find mode shapes.

   • True
   • False

   Hint

   Remember the connection between modes and eigenvalues.

5. 5.

   Given a 4-storey building with evenly distributed masses of 1500 kg each and a stiffness of 100 kN/m per storey, calculate the mass and stiffness matrices.

   Hint

   Consider each storey as a separate mass-spring system.

6. 6.

   In a practical seismic analysis, how would you use modal superposition to evaluate the total displacement of your structure under a given input ground motion?

   Hint

   How does each mode respond to the initial ground motion?