Experience, acquired with the studies on structural response during severe earthquakes, has shown great vulnerability of the bridge structures. Currently, employment of isolation and/or damping systems, as passive control devices, is the strategy of seismic design that allows limiting the damages. Recently, numerous scientific papers, codes of practice and design documents, have been published to the topic. Principal objective is the definition of simple criterions for structural design and their validation through experimental studies. Method followed in these works is primarily based on a deterministic approach, without taking into account the stochastic characteristics of the seismic excitation. In this paper a method of analysis that has its foundation on stochastic dynamic is introduced. This paper focuses on the analysis of bridge isolation/damping system; in particular, the tools for the analysis of non-classically damped systems, like the structures with passive control devices, are provided. Preliminarily, the bridge is represented, in real way, by the assemblage of two substructures: a) the piers, represented by means of continuous models; b) the girder, by means of FEM model, the connections piers-girder and abutments-girder are pictured as some equivalent linear devices characterized by suitable stiffness and dissipation parameters. The component-mode synthesis method for coupled substructure is used. A simple method for the evaluation of the cross-correlation coefficients is proposed, useful to combine the modal responses in the response spectrum method for seismic analysis. The proposed method allows avoiding the standard complex eigenproblem of a nonclassically damped system.
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