“Correlation of Various Response Spectrum Methods with Time History Analysis for a Tuned Subsystem”

Developing appropriate methods for designing structures subject to seismic stress concerns all engineers, but none more so than nuclear engineers.  For the nuclear industry, the NRC has set strict guidelines on design criteria for primary systems (‘supporting” structures) and secondary systems (“supported” structures or equipment).

Often, estimates of the seismic response of coupled primary and secondary structures are actually calculated separately (decoupled).  There are two reasons for this: (1) the sheer number of possible interactions exceeds the limits of accuracy of standard computational methods, and (2) appropriate seismic response spectra at the connection between primary and secondary systems are not available.

However, when designing primary and secondary structures in nuclear power plants, it is necessary to analyze their response as coupled systems, often using complex analytical models.  In their paper “Correlation of Various Response Spectrum Methods with Time History Analysis for a Tuned Subsystem,” Bechtel engineers M. Dong and H. M. Lee explore refined methodologies for analyzing the seismic response of these systems.  They address the physical conditions appearing when the natural frequency of an appendage subsystem is close to one of the natural frequencies of the primary structure.  This is called a “tuned” branch system.

While analyzing minor changes to a subsystem design, Dong and Lee applied the closely spaced modal combination rules of NRC Regulatory Guide 1.92.  They found that Regulatory Guide 1.92 leads to gross overestimation of subsystem behavior when responses from two very closely spaced modes are added absolutely, but in reality they are out of phase and have a canceling effect.

Dong and Lee found that when using modal response spectra techniques, unrealistic modal coupling effects will most likely occur when the subsystem is either tuned or nearly tuned to the primary system.  The current revision of Regulatory Guide1.92’s rules yields results that are grossly conservative when compared with results of a time history analysis of the tuned subsystem.   More refined modal coupling methods in use in the industry provide good correlation with solutions from time history analysis with synthetic time history.

Dong and Lee’s study indicates that the subsystem decoupled according to NRC’s SRP 3.7.2 (NUREG-0800) rules yields reasonable results as compared with time history solutions.  They recommend the use of independent support motion analysis (ISM) with the absolute grouping method together with seismic anchor motion (SAM) analysis to evaluate systems and subsystems.  This decoupled approach is simple and has significant safety margins even when the subsystem is tuned to the primary system.  An NRC committee is evaluating their findings.