include the effect of bracing in the eigenvalue analysis of a single bay MDOF system

[Zouatine]

Hello all,

hope you are doing well,

How to include the effect of bracings in the eigenvalue analysis of a single bay MDOF system?

My project is dynamic response control using shake table and I have attached bracings to the MDOF model and now I want to perform analytical calculations so I wanted to know how to incorporate the effect of those bracings.

As far as I know when I include the bracing their effect will Ultimately increase its stiffness than its inertia but I don't know how can include its effect in the stiffness matrix as well as the mass matrix.

thank you all

 

[JoshPlumSE]

I'm not sure I understand the point of the question. You're talking about vertical braces in the lateral force resisting system, right? Like and X braced bay, a V brace or a Chevron or something. Right?

Alternatively, you could be talking about the effect of beam bracing on a moment frame or something along those line.

 

[Zouatine]

Dear JoshPlumSE

Thank you for your reply, I'm talking about V invert bracing system ( as it is described in the picture), I want to include the effect of the bracing in the stiffness matrix for the eigenvalue problem K-w^2*M=0 where M is the mass matrix of the system.

 

[JoshPlumSE]

Are you doing a hand calculation? Or, are you modeling this with a structural analysis program?

If you're using a structural analysis program, then you should go through the manual or program documentation for instructions on how to do this properly. If you're doing this by hand, then I would suggest something other than a true eigenvalue solution.

Instead, I'd use the Rayleigh Method. Which is based on applying your static seismic loads to the structure, looking the deflection that is produced at each level. Then you can turn this into a natural period or natural frequency. Below is an excerpt from a write-up I put together on using the Rayleigh Method for this purpose. It really ends up being pretty accurate, and the method is code approved (it's in ASCE-7). To me, this is much easier than assembling a full stiffness matrix, mass matrix and such.

https://files.engineering.com/downl...e1-94ec-9fe711d5937c&file=Rayleigh_Method.pdf

 

[Zouatine]

Dear JoshPlumSE,

thank you for your kind reply, after reading your file which I do appreciate that you shared with me, I strengthened my knowledge about how to do the hand-calculation to get the time period of the structure, Moreover, I'm using Etabs software to design my structure.

I got the same result when I compared it with the above file method approximately, however, my main task is the mode shape I'm not able to get the value of the eigenvector even from the software that's why I asked the question how can I include the stiffness or as I said the effect of the bracing in the stiffness matrix,

I'm extremely excited about your coming answer,

 

[Zouatine]

While I am looking at the result I found the option where it shows the modal participation factors is it the same as to mode shapes vector or is there any possibility to determine the modes shapes vector from it,