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# Super-structure discretization for modal analysis

## Super-structure discretization for modal analysis

(OP)
Hi community members,

I would like to know what is the common procedure of super structure discretization for modal analysis with FEM?

Can I simply assume the whole structure as rod element where the storey masses have been lumped at storey height levels?

Regards,

### RE: Super-structure discretization for modal analysis

No, if every member is a single element then you're not getting the correct dynamic analysis as you limit the response by limiting the number of degrees of freedom (DOF).  If you're just looking at a inverted pendulum perhaps this is not a big concern as the primary response is that of a cantilever.  It is not the only response and those other responses can only be found with more nodes (DOF).

Typically a column should have 3 DOF at a minimum.  Beams may have more depending on the level of changes or loading.

Regards,
Qshake

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### RE: Super-structure discretization for modal analysis

(OP)
I agree with you that the exact solution should be as you depicted but If I'm not supposed to make any discretization/idealisation on structure then the solution domain can be enermous in size.

For example, assume that I have a model with 10000 structural elements(4-node quad shell) each node with 6 DOFs that will yield the 240000 linear algebraic equtions, which is not easy to solve, even the some products of this matrix will be zero.

In order to eliminate this, IMHO there should be employed some kind of discretization/idealisation process. IRC it's been mentioned somewhere in the codes that structures having the rigid diaphragm should introduce 3DOFs (2 displacement in principal horizontal axes and 1 rotation around vertical axis).

So I really wonder where this comes into play, since I may have plenty of FEM elements with diferent flavours(3 -node DKT,DST, 27 node hexa, etcc..)  which doesn't conform with required criteria by codes.

Regards,

### RE: Super-structure discretization for modal analysis

Are you doing modal analysis for a Response Spectrum Analysis? If that's the case then I agree with lumping the masses at each story level and limiting your DOF's to x, y, and rotation for most cases. I am assuming that you are using software to do this, not by hand, and most likely the software will do this for you.

### RE: Super-structure discretization for modal analysis

The most important mode is typically the first flagpole mode, and your lumped mass/beam element should catch that. As a rule of thumb I try and include sufficient DoF to predict 100 times the number of modes of interest. So if you are interetsed in all modes below 10 Hz, and there are 7 modes, you need to include at least 700 /meaningful/ DOF.

250000 DOF doesn't seem very many to me in a linear analysis, given that many of them won't be participating in the modes of interest. Sizewise that should solve in RAM on a 2GB computer, and solve in an hour or so, if the solver is competently written.

Subsystem lumping is a hard thing to do in continuous systems such as buildings, in which case the temptation is to model everything and hope that the errors in detail average out into a meaningful blur.

Mind you, here's the sig I use at work "All models are wrong. Some models are useful"

Cheers

Greg Locock

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### RE: Super-structure discretization for modal analysis

(OP)
Thanks for commenting,

#### Quote (Dave):

Are you doing modal analysis for a Response Spectrum Analysis? If that's the case then I agree with lumping the masses at each story level and limiting your DOF's to x, y, and rotation for most cases. I am assuming that you are using software to do this, not by hand, and most likely the software will do this for you.
No I don't do the RSA.
Actually I'm trying to program the modal analysis for structures comprised from column-beam (frame elements) and slabs (shell elements).

#### Quote (GregLocock):

As a rule of thumb I try and include sufficient DoF to predict 100 times the number of modes of interest. So if you are interetsed in all modes below 10 Hz, and there are 7 modes, you need to include at least 700 /meaningful/ DOF.
The problem is here I couldn't reconcile or find any kind of relation with what the theory provides and what the code requires.  It seems that there is no relation with both of them .
The so-called DOFs should be of element DOF's (e.g. triangle element 6 DOFs per node etc..) or code refered DOFs (2 displacement one vertical rotation) ?

#### Quote (GregLocock):

250000 DOF doesn't seem very many to me in a linear analysis, given that many of them won't be participating in the modes of interest
How do you decide that any specific mode is participating or not?

### RE: Super-structure discretization for modal analysis

(OP)

#### Quote:

strain energy plot.
Could you elababorate that a bit further?
What causes the current mode to be taken as not participating and participating related with strain-plot energy.

Do you have any comments on other issues, especially on how to reconcile the DOF of code and theory for structures.

Regards,

### RE: Super-structure discretization for modal analysis

(OP)
I see,

Your point of interest is a bit different than mine, I should have guessed that from your nick (automotive).

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