# Modal Analysis



## McEngr (May 30, 2014)

I got on eng-tips.com and asked this question with little success so far:

Do I use rho if the dynamic analysis

 falls between the elf and elfxrho?

ie:
Vmodal = 137 kips
Velfxrho = 167.4 kips (rho=1.3)
velf = 128.8 kips

I've not encountered a dynamic analysis in this scenario with section 12.9.6 of ASCE 7-10, so any corrections/comments are welcome. I'm using RISA for the scaling factor on a 5 story structure with several vertical and horizontal irregularities.


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## kevo_55 (May 30, 2014)

McEngr,

Like time no see!

Well, unfortunately you are to use the rho factor no matter what analysis procedure that you are using for strength purposes. For deflection rho is 1.

I think this answers the main question you have but let me play a little devil's advocate on this issue.

If you are using a dynamic and/or non-linear procedure shouldn't this take into account your irregularities and basically give you what you expect the forces should be under the design event? I suppose that the answer is both a yes as well as a no. We might be smart enough to predict what the forces should be but we don't have the experience with the theory to change what we already have been doing.

I hope this helps. I also hope this isn't too much for a Friday!


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## Andy Lin (May 30, 2014)

Kkevo_55 is correct. Rho needs to be applied for seismic no matter what.

Note that rho doesn't increase your base shear per se, it increases the design forces for the elements you are designing.

For some elements and design criteria, rho is equal to 1 per section 12.3.4.1. You also don't need to apply rho if you are using omega for the element you are designing.


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## McEngr (May 30, 2014)

You guys supported my original thought. I wanted to make sure that my analysis wasn't too conservative. And, yes Kevo, that's a little much for a Friday. 

If you guys want to have a little more fun, you might want to try to solve for the determinate of k-w2M.  That was frustrating my brain last night for a 5x5 matrix as I was trying to compare hand calcs to RISA numbers (I like pain?). Anyhow, I got it to work on one of my coworker's TI-89, which I sold after taking linear algebra and electrical engineering back in '99.


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## civilized_naah (May 31, 2014)

MATLAB does the eigenvalue analysis very simply:

[A,B]=eig(K,M) yields the eigenvalues in a diagonal marix B and a matrix A whose columns are the eigenvectors


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