Mode Shape Amplitude

[n.88]

Hi everyone,

New user here so hopefully not a dumb question to start me off.

I'm trying to understand how to conduct building vibration analyses using finite element analysis and I've been primarily referencing AISC Design Guide 11 to help guide me in my process. I've also reviewed some of the reference material that DG11 is based on. I am stuck on a particular part of analyzing a structure for vibration effects on sensitive equipment.

I have run an eigenvalue modal analysis and a steady-state analysis on my model, so I have mode shapes and have an FRF to identify the dominant frequencies at which my equipment can get excited by footfall. I am now trying to calculate the one-third octave spectral velocity to compare with my limiting value for my equipment type. For each mode I need the mode shape amplitude at the location of the sensitive equipment and the location of footfall. According to DG11 this has the units of sqrt(1/mass). DG11 alludes to the fact that these amplitudes can be outputted natively by a program like SAP (which is what I am using), however I cannot figure out how to get this number for each mode. For a particular joint in my model I can output the joint mass, acceleration, etc. Can anyone help me understand how I can calculate/output these amplitudes? I've uploaded the screenshot of the equation I am trying to solve for each mode.

Nick

 

[JoshPlumSE]

Actually, mode shapes are dimensionless.

However, they are specifying that you use a mass normalized mode shape in your equation. That's how SAP reports their mode shapes (I'm pretty sure). So, you just have to know the values for the mode shape at those two locations.

 

[WARose]

Can anyone help me understand how I can calculate/output these amplitudes?

SAP can't output them?

 

[JoshPlumSE]

He said he had the mode shapes.... I just don't think he realized that this is what those equations were referencing.

 

[n.88]

Thanks, that makes sense that you would use those units when normalizing to mass. I guess the problem I am having is that I cannot determine which output table (or combination of tables) would be correct. I can get the modal participation ratios but those are generic for the entire structure. I feel like I am missing the connection between the modal response of the structure, the location of a specific joint on a structure, and how to relate those two.

 

[WARose]

Even with simple structures it's hard to relate modal values to a actual (displacement) value with hand clacs. (I've seen a few techniques to obtain a maximum response....but these are not entirely accurate.) The fact is, a lot of modal values are not occurring simultaneously.

Seems to me that if you have a FEA model, you could get the dominant frequency and/or acceleration from the time-history output and compare it to the allowable values in DG 11. In most guides like that you have you have charts for acceleration vs. frequency (for acceptable vibration) and so on.