Modal Analysis - Hand Calculations Request for Assistance

[dmj2015]

Good evening, I am looking for assistance (paid) in performing a very simple modal analysis of a 4-story steel moment frame using hand/spreadsheet calculations. It is not for a school project, I am a practicing engineer (not trained in dynamic analysis) and am curious how the procedure actually works (outside the blackboxes of RISA, ETABS, etc. My limit of understanding is that it really is a mathematical problem (solving multiple differential equations) I know the soliciting of work on this site is generally prohibited, but I think my request is an expansion of the ideas presented on the site. Thanks you.

 

[EDub24]

This book from SK Ghosh goes over modal analysis with an example.

http://shop.skghoshassociates.com/c...dynamics-2015-ibc-asce-7-10-aci-318-14-4.html

 

[JoshPlumSE]

Attached is a zipped file of a couple of problems I put together awhile back.

One of them uses the Rayleigh method to determine the natural frequency of a structure. The 2nd is a hand calc of response spectra analysis. Including only two modes. However, it's assumed that you already have the normalized mode shapes.

This was done using RISA, so I have included the RISA model as well.

 

[JoshPlumSE]

I left out one file, the write up on doing the Rayleigh Method.....

Note that it is not necessary to use seismic loads to come up with the natural period. In this case, I believe, I used wind loads. The key is that the deflected shape should approximately represent the mode shape, which is almost always the case for the first mode.

My belief is that the Rayleigh method could theoretically be used to solve for the 2nd natural frequency as well. But, you'd have to come up with a load condition that created a deflected shape that is a reasonable approximation of the 2nd mode shape.

Obviously, there are matrix methods that you can / should use to solve for the full mode shapes and natural frequencies. But, that wasn't the purpose of developing the particular problem. Rather, this was meant to be a simplified way to verify the "black box" solution of a structural program.

 

[WARose]

There are a variety of texts out there that can be useful. Mario Paz's book on Structural Dynamics is one of the best.