The maximum seismic response of torsionally coupled plan asymmetric structures can be rationally visualized and computed through a Mohr Circle Response Spectrum Analysis (MCRSA). This is done combining the graphic modal properties of the torsional dynamic equations of motion with the structural earthquake demand in terms of a displacement spectrum as a function of the modal eigenvalues SD(ω2). A compact representation of the modal properties and of the response envelope is built and visualized in the Mohr plane. The maximum modal responses are then combined using a graphic adaptation of the SRSS and CCQ combination rules based on the elastic response spectrum. This Graphic Dynamic rule proves to be an effective response prediction tool, and is particularly suited to estimate the response of seismic base isolation systems

The assessment of maximum displacement demand is a crucial point in the design of seismic isolating systems, in particular when the non linear behaviour of devices is modeled through visco-elastic equivalent schemes, as common in the design practice. Several phenomena influence the maximum demand assessment, among which the torsional and earthquake directionality effects can be of great impact. International codes use some formulations which allow to consider torsional effects, while the impact of the other phenomena is commonly assessed through time-history analyses. In this paper an innovative design method is developed based on an exact linear elastic formulation with response spectrum, which keeps in count both torsional and directivity effects considering natural and accidental eccentricity and by using the CQC3 (Menun and Der Kiureghian, 1998) as directional combination rule. The method models the seismic action through the response spectra of a set of natural recorded ground motions, properly oriented along their principal axes to assess the correct ratio between the horizontal components of spectral accelerations; thus accounting for the site-specific earthquake source, without the need to perform timehistory analyses. A specific formalization of the dynamic problem is presented to emphasize the parameters which more affects the response (e.g. torsional factor, eccentricity, geometrical aspect ratio) and simplify its interpretation. Results obtained on two case studies are compared with time-history analyses to show the effectiveness of the procedure.