11.11. Lumped Mass Matrix and Shear Building Model

Try these first

1. 1.

   What is a lumped mass matrix?

   Hint

   Think about how mass can be distributed in a building.

2. 2.

   What does a shear building model help analyze?

   Hint

   Consider environmental forces affecting structures.

3. 3.

   What does a lumped mass matrix represent?

   • Concentration of mass on structural beams
   • Concentration of mass at discrete points
   • Uniform mass distribution

   Hint

   Consider how mass is distributed in real structures.

4. 4.

   True or False: A shear building model cannot be used for seismic analysis.

   • True
   • False

   Hint

   Think about the purpose of the model.

5. 5.

   Consider a six-storey building represented by a lumped mass matrix. If the mass at each floor is 1000 kg and the inter-storey springs have a stiffness of 200 kN/m, derive the tridiagonal stiffness matrix for the building.

   Hint

   Use the pattern of stiffness between each floor.

6. 6.

   Discuss how neglecting mass concentration in the lumped mass matrix affects the predicted responses of a multi-storey building under seismic loading.

   Hint

   Consider the impact of mass distribution on structural response.