Hi,

I am studying the response spectrum analysis with CAESARII. I found some strange description about summation method of response. The grouing method and ten percent method show different equation and description. For example, grouping method said "the response of any modes which have frequencies within 10% of each other first be added together absoultely, with the results of each of these groups then combined with the remaining individual modal results using the SRSS method". The equation said different meaning.

The equation said that results of all mode are summed using square. The group modes are summed absoultley with each other mode.

My questions are

1. The square sum should be used to sum the other mode that are not included in the grouping?

2. The absoultely sum should be sum with one by one not multiply with each other?

Please give me a piece of advice.

Both the Grouping method and 10% method are similar. They differ in how they define the closely spaced mode band. The Grouping method presumes that modes that fall within a group are within a 10% band, while the 10% method considers modes within 10% of a mode of interest, that is, taking 10% above and below the mode of interest; an effective mode band of 20%.
In both cases, these closely spaced modes are absolutely summed within their group, based on the assumption that they will likely see their maximum response at the same time during the dynamic response. In both cases, modes that are outside of the prescribed closely spaced mode band are presumed to see their maximum at a different time, so are added to other modes and grouped mode summations using the SRSS method.

Thank you for your kind response. I know the methodlogy of 10% and grouping method. The point that I'd like to know is the difference between description and equation.

I think that the equation for grouping should be as follows to meet the descriptoin.

R= sqrt(sum(Rx^2) + sum(sum(Ri))^2 )
First part Rx : x means the mode that wide spaced exclude close space

Second
Ri : i mean close spaced mode of q th group

There is an error in the equation in the Technical Reference Manual. The correct equation should be


This equation then does match the words as shown by this simple example. Let's assume we have 5 modes a through e, where b,c, and d are grouped. The words say that R = [a^2+|b+c+d|^2+e^2]^.5 which can also be written
R = [a^2+b^2+c^2+d^2+e^2+2bc+2bd+2cd]^.5

This is exactly what you will get by expanding the equation given above.

Thank you for your kind response.

I understand the equation and description.

Jaewan,

For more details, see REG GUIDE 1.92 "Combining Modal Responses and Spatial Components in Seismic Response Analysis". Also following materials will be useful for your study.
-WRC Bulletin 352 Independent Support Motion Method of Modal Spectra Seismic Analysis
-REG GUIDE 1.60 Design Response Spectra for Seismic Design
-REG GUIDE 1.61 Damping Values for Seismic Design

You can get copies for all of them from Changyu or Samin.

Sun Wee
from Calgary