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

enter image description here

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.

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Graviton
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  • An idea would be to consider each element of the FEM grid as a lumped mass. – Karlo Mar 01 '16 at 08:21
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    @MWijnand, would you like to be more explicit about that and post it as an answer? – Graviton Mar 01 '16 at 08:50
  • I am not an expert in FEM, though. I think that I cannot (yet) contribute enough of information for a full answer. – Karlo Mar 01 '16 at 08:52
  • 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 01 '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 01 '16 at 18:19
  • @WilliamS.Godfrey , yes, I want to get the OTM and also the P delta effect checking – Graviton Mar 02 '16 at 00:17
  • @ja72 , yes I want to take the FEA result and try to derive a effective lumped mass model-- with appropriate mass and stiffness at each effective floor – Graviton Mar 02 '16 at 00:18
  • @ja72 , besides calculating OTM, I just want to know how a n irregular structure can be represented as a lumped mass cantilever column – Graviton Mar 02 '16 at 00:19
  • For the OTM calculation, I suggest you use a method discussed on your previous question. You don't need to created a lumped mass model. In fact, you'd be working backwards if you did that since you already have an FE model. For the P-Delta, your FE software may already/be able to perform that analysis. What software are you using? – William S. Godfrey- S.E. Mar 02 '16 at 01:04
  • @WilliamS.Godfrey, I'm learning how to do the P-Delta from the first principle,, so I will be grateful if you have any finite element formulation for P-delta effects – Graviton Mar 02 '16 at 05:23
  • @WilliamS.Godfrey, question edited: so now I just want to get the lumped mass at each floor as a kind of theoretical exercise. – Graviton Mar 03 '16 at 06:09
  • After reading the comments, I'm still not sure I understand what the question is. If you have your structure modeled in an FEM package, you already have access to the more rigorous solution (and inclusion of second-order effects is usually an option in FEM software). You could easily create a second 'lumped mass' lollipop model and run that for comparison. As I understand FEM, you're usually dealing with a 'lumped mass' model --- it's just a question of how fine a resolution you get on the structure discretization. – CableStay Oct 23 '16 at 00:46

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I perform this kind of analysis all the time when running pressure vessels and other scrubbers, using LISA:enter image description here

As you can see, I have the option to add lump mass onto individual nodes (for my "live loads", or other non structural dead weight), and my material has a density option available:

enter image description here

Typically, I set a 1g gravity load downwards, and then plan my seismic loading based upon code. ASCE for scrubbers and vessels has a few variations, depending on the designers discretion. I use the most conservative one with this method however, and go with a horizontal gravity in one of the main directions, equal to SDS * I / R. Since LISA is not a non-linear FEA, this does not get P-Delta effects, but still gets displacements and stresses:

enter image description here

As you can see, the scrubber has shifted slightly to the left under the seismic loading (the internal vacuum is doing most of the displacement though). The software has automatically lumped the mass of the individual structural elements (as given in the "density" dialog for material) to the middle of the individual elements. I place the live load mass directly on top of the applicable elements. This way, the gravity load will affect them completely. Then, it spits out the displacements and stresses.

Since I don't have P-delta effects from my linear FEA, I will typically go back to the drawing board, and make a lumped mass model for buckling analysis. While the FEA is done in fine strokes and small elements, this is done by hand instead.

Mark
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  • I am not talking about using a software package to do it; I am talking about writing a software package to model this – Graviton Jun 25 '16 at 02:36