Periodic Response vs Rigid Response 1

[BAGW]

Hi,

In Response Spectrum Analysis, what is the difference between periodic response and rigid response?

 

[JoshPlumSE]

That's a very general question..... I'll answer it in terms of how the modes are combined together.

As a means of combining the response of modes together statistically, you generally start with the assumptions that the modal responses have no interaction effects. This would be an SRSS (square root sum of the squares). However, this isn't true for closely spaced modes. Hence the requirements to use methods like CQC (complete quadratic combination) to combine modes. Because this method considers the interaction effects of closely spaced modes.

There's a method of modal combination called the "Gupta Method", which is probably more likely to be used for nuclear projects. Ajaya Kumar Gupta wrote a nice little book about the Response Spectra Method that you might want to check out at some point. In it he points out that the CQC method is very conservative for closely spaced RIGID modes. Therefore, he created the Gupta combination method which suggests transitioning from the CQC method for periodic modes to a direct summation for Rigid modes.

 

[JoshPlumSE]

Another comment about Rigid response. Often there is a "Residual Rigid Response" in response spectra analysis. Meaning that you may have been about to get 94% mass participation with however many modes you were able to solve for. But, there is a residual rigid response of 6%.

There are methods (Residual Mass Vectors and such) for adding this response into the response spectra solution as well.

I hope this has helped....