16.3.1. Lumped Mass Idealization

Try these first

1. 1.

   What is the main purpose of lumped mass idealization?

   Hint

   Think about how mass is treated in structural models.

2. 2.

   What type of matrix represents mass in lumped mass idealization?

   Hint

   Consider how mass values are arranged in a matrix form.

3. 3.

   What does the lumped mass model simplify in structural analysis?

   • Structural damping
   • Mass distribution
   • Dynamic loading

   Hint

   Focus on where mass is allocated in the model.

4. 4.

   True or False: The mass matrix in a lumped mass model is off-diagonal.

   • True
   • False

   Hint

   Recall the structure of a diagonal matrix.

5. 5.

   Given a 5-storey building, with masses 500 kg, 600 kg, 700 kg, 800 kg, and 900 kg at each floor respectively, calculate the mass matrix [M] and the resulting forces if the uppermost mass displaces 0.2m during an earthquake.

   Hint

   Consider how forces are based on displacement and mass.

6. 6.

   Create a detailed lumped mass model for a 3-storey frame structure with stiffness values of 12000 N/m between levels. If each level has a mass of 1000 kg, derive the equations of motion for this system.

   Hint

   Focus on how stiffness affects dynamic response equations.