# How can we derived the equivalent Lumped Mass Model for irregular building and how to calculate the errors?

Intuitively, building can be represented as a lumped mass model ( the taller the merrier!):

Assuming a building is a lumped mass cantilever column also makes the global stability checks easier because building codes often assume building structure as a cantilever column.

But if my building structure is discretized and response analyzed in terms of FEM ( with column/beam as line element, and slab/wall as area element), then is it possible that, from the stiffness matrix and everything I have in FEM, I can still approximate the structure as a lumped mass model? If yes, how to do it? How to calculate the errors involved?

A practical application of doing this is in this question. But for the purpose of this question, let's assume that I do it for academic purpose and don't really want to care about the application.

• An idea would be to consider each element of the FEM grid as a lumped mass. – Karlo Mar 1 '16 at 8:21
• @MWijnand, would you like to be more explicit about that and post it as an answer? – Graviton Mar 1 '16 at 8:50
• I am not an expert in FEM, though. I think that I cannot (yet) contribute enough of information for a full answer. – Karlo Mar 1 '16 at 8:52
• Your question here is fairly broad. It might help if you elaborated on what your objective is? What are you trying g to use this lumped mass model for? If you're after the OTM, my answer on your other question explains how you can do that with your existing FE model. – William S. Godfrey- S.E. Mar 1 '16 at 15:32
• So you want to take the results of an FEA and build a mass and stiffness matrix from it? – John Alexiou Mar 1 '16 at 18:19