# 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. Mar 1, 2016 at 8:21
• @MWijnand, would you like to be more explicit about that and post it as an answer? Mar 1, 2016 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. Mar 1, 2016 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. Mar 1, 2016 at 15:32
• So you want to take the results of an FEA and build a mass and stiffness matrix from it? Mar 1, 2016 at 18:19