A NEW FLOOR RESPONSE SPECTRUM METHOD FOR SEISMIC ANALYSIS OF MULTIPLY SUPPORTED SECONDARY SYSTEMS

The objective of this thesis is to present an improved floor-spectrum method for seismic analysis of linear, multi-degree-of-freedom secondary systems multiply supported on linear, multi-degree-of-freedom primary systems. The method defines and utilizes an extension of the conventional floor response spectrum denoted cross-oscillator, cross-floor response spectrum or, in short, cross-cross floor spectrum (CCFS). The CCFS is defined to be proportional to the covariance of the responses of two fictitious oscillators subjected to the motions of the primary system at two support points. Through this extended concept, important effects, which are not accounted for in the current floor-spectrum methods, are correctly included in the analysis. These effects include: cross-correlations between motions of the support points, cross-correlations between modal responses of the secondary system, interaction between primary and secondary systems, resonance or tuning between the frequencies of the two subsystems and the non-classical damping effect of the combined primary secondary system.;Several representative primary-secondary systems are numerically analyzed. Results obtained using the proposed method are compared with results obtained by considering the primary-secondary system as a single structure. Close agreement is found between the two results for all cases.;The proposed method consists of two basic steps: (1) Generation of CCFS in terms of the ground response spectrum and the modal properties of the primary system; and (2) determination of the mean peak response of the secondary system by modal combination in terms of the CCFS, the modal properties of the fixed-base secondary system, and the stiffnesses of the elements connecting the secondary to the primary system. The generation of the CCFS requires repeated evaluations of the modal properties of combined oscillator-primary systems. Recent results employing perturbation theory are used to make this evaluation efficient. The effects of interaction and non-classical damping are implicitly included in the derived CCFS in approximate manners. The effects of cross-correlation between the support motions and cross-correlation between the modal responses of the secondary system are included in the derived CCFS and in the modal combination rule for the response of the secondary system.