Document: NUREG-0800
Document ID: 1f106a50-722f-45fa-952a-2e7ab7d836c1
Document Type: srp
Title: DYNAMIC TESTING AND ANALYSIS OF SYSTEMS, COMPONENTS, AND EQUIPMENT
Source: NUREG-0800
Source URL: https://www.nrc.gov/docs/ML0523/ML052360453.pdf
Revision Date: 2023-06
Chapter: 3
Section ID: 3.9.2
CFR Part: 
CFR Title: 

Content:
e calculated using the time history method instead of the spectrum method. (b) To obtain time history responses from each of the three components of the earthquake motion and combine them at each time step algebraically: the maximum response in this case can be obtained from the combined time solution. When this method is used, to be acceptable, the earthquake motions specified in the three different directions should be statistically independent. e. Combination of Modal Responses When the response spectrum method of analysis is used to deter- mine the dynamic response of damped linear systems, the most probable response is obtained as. the square root of the sum of the squares of the responses from individual modes. Thus, the most probable system response, R, is given by R =(N Rk) 2 (1) k = 1 where Rk is the response for the kth mode and N is the number of significant modes considered in the modal response combination. When modes with closely spaced modal frequencies exist, an acceptable method for obtaining the system response is to take the absolute sum of the responses of the closely spaced modes and combine this sum with other remaining modal responses using 3.9.2-8 Rev. 2 - July 1981 the square root of the sum of the squares rule. Two modes having frequencies within 10% of each other are considered as modes with closely spaced frequencies. This approach is simple and straightforward in all those cases where the group of modes with closely spaced fre- quencies is tightly bundled, i.e., the lowest and the highest modes of the group are within 10% of each other. However, when the group of closely spaced modes is spaced widely over the frequency range of interest (while the frequencies of the adjacent modes are closely spaced), the absolute sum method of combining responses tends to yield over-conservative results. To obviate this problem, a general approach applicable to all modes is considered appropriate. The following equation is merely a math- ematical