## effective modal mass

## effective modal mass

(OP)

Does anyone know if I can obtain the effective modal mass from RAM elements? I am trying to implement SCI P354 for vibration. In order to apply the formuals you need the effective modal mass or the kinetic energy per mode. Am I right in thinking RAM normalizes the mass of the system, or does it normalize the mode shape? The only reason I think it normalizes mass is the modal deflections for a simple beam do not have a 1 as a value.

If the modes are mass normalized I would think the effective modal mass is the mass participation factor squared, but that value doesnt make sense to me for a simple beam. Is the reported participation factor really for mass and not a modal participation factor? I guess I'm a little lost on which is which.

If the modes are mass normalized I would think the effective modal mass is the mass participation factor squared, but that value doesnt make sense to me for a simple beam. Is the reported participation factor really for mass and not a modal participation factor? I guess I'm a little lost on which is which.

## RE: effective modal mass

In the Ram Elements Dynamic analysis report it includes a section for normalized mode shaes with the following note:

MODAL SHAPES

** Normalized displacements to Phi*M*Phi=1 **

Modal shapes : 1

W = 16.39 [RAD/SEC] PERIOD = 0.38333 [SEC]

DISPLACEMENTS

Node Trans.X Trans.Y Trans.Z Rot.X Rot.Y Rot.Z

[phi] [phi] [phi] [phiRot] [phiRot] [phiRot]

19 -1.20E-03 0.00E+00 2.03E-01 0.00E+00 -7.25E-06 0.00E+00

If that's not clear, here is some text from an old email regarding the units for mode shapes:

"In vibration theory, what is really important is the shape of the Eigenvector, the magnitude of the Eigenvector is not important.

We use mass normalization. We could also use "unity" normalization in which mode shape terms are divided with the largest value. In fact, you can divide with any number you want, it does not change the results (I mean calculated displacements, member forces, etc...)

Let's say, you use "unity" normalization (and for the argument sake, you are dividing every term with the largest value which is typically one of the translational components).

Then, units for the mode shapes are "mm" and "rad/mm".

If you do not use any normalization (which also leads us to correct results), then you have "mm" and "rad".

If you use "mass" matrix normalization, then (if I am correct) we have "Sqrt(KN/mm)" and "Sqrt(KN*mm)". I know, this is confusing and does not say too much.

But what we can say that reported mode shapes are consistent with some units. These units reflects the units chosen for mass. In SI units, the program uses "KN" and "mm". If you switch to another units, these mode shape values change. Hence, it is very important that if someone wants to use these mode shapes (other than visual purpose), then, their calculation has to be consistent with the units reported."

## RE: effective modal mass

The main reason I am doing this is so I can apply it to complicated floor systems. I notice a lot of limitation to hand calcs from design guide 11, and have seen some large discrepencies between DG 11 calcs and FE / real word results. Since i don't have a program that does dynamic loading, this is my only option.

From what you say, and from some sources I have, effective modal mass meff = (Li)^2/mii , and modal participation is GAMMAi = Li/mii, so with mass normalization meff = GAMMA^2 essentially. I guess some trial and error will give me a sense.

## RE: effective modal mass

## RE: effective modal mass

I'm still searching a way to obtain the modal mass for each respective mode from SAP 2000 output. The modal participation ratio does not directly reflect the modal mass (did a check from a simple beam model and the output is not as expected). Did you have any further research about this? I'm still trying to find ways around SAP 2000 output and will update if I find anything.