## 1 Introduction  
Passive energy dissipation and base isolation systems are increasingly adopted in the anti-seismic design of new frame structures as well as to retrofit existing ones. Remarkable innovations have been noticed in the last decade for both strategies. Concerning base isolation, single and multiple curved surface sliders [1; 2; 3; 4] and roller-type isolators [5; 6; 7] became a competitive alternative to the widely used class of high damping rubber bearings. At the same time, new technologies, or improved versions of existing ones, have been implemented in the field of energy dissipation, capable of supplying supplemental damping and horizontal stiffness in different proportions, depending on the mechanical characteristics of dampers and their installation layout. Among the latest achievements in this field, systems incorporating updated models of metallic yielding devices like ADAS (Added Damping and Stiffness) and TADAS (Triangular Added Damping and Stiffness) elements [8; 9; 10; 11; 12], shear panels [13; 14; 15; 16; 17; 18], shear panels with openings [19; 20; 21; 22; 23], or buckling-restrained braces [24; 25; 26; 27], have been proposed, which typically provide significant contributions in terms of both properties. Viscous dampers can offer stiffening effects too, in addition to supplemental damping [28; 29; 30]. At the same time, special types of viscous dampers, when mounted at the tip of supporting braces in parallel with the overlying beam axis [31; 32], slightly increase the horizontal stiffness of the structural system, while supplying high additional damping. Differently from the base isolation systems, whose preliminary design is straightforward, a further spreading of dissipative bracing technologies in the professional community strongly depends on the availability of intuitive procedures, especially concerning the sizing of dampers. The first methods offered in literature start from setting the desired damping ratio (i.e., the ratio of the damping coefficient to the critical damping coefficient) in the fundamental mode of vibration of the structure, in the hypothesis that the relevant effective modal mass (EMM) is a predominant portion of the total seismic mass [33; 34; 35]. In general, the practical application of these methods consists in examining the response spectra at various damping ratios and choosing the value that allows constraining the maximum \"global\" response parameters (base shear, top lateral displacements, etc.) within targeted acceptable limits. When the devices are characterized by nonlinear viscous properties, the same objectives can be reached by transforming relevant damping capacity into equivalent linear viscous coefficients [28; 33]. These studies have provided the basis for the design procedures of buildings incorporating passive energy dissipation systems included in ASCE 41-06 [36] and ASCE 7-10 [37] Standards. Along the same conceptual line, some procedures based on the use of normative response spectra scaled by reduction factors corresponding to the damping capacity of the devices have been proposed more recently [38; 39], where reference is made to damping ratio values no greater than 0.3. Other approaches use equivalent linear or non-linear static analyses to evaluate the design actions and reduce their effects through added damping [40]. All the above-mentioned procedures are conceived for substantially regular structures. Few solutions are found for problems characterized by significant irregularities in plan and/or in elevation. Among these, a method based on properly calibrated expressions of the damping ratio derived from the results of non-linear dynamic analyses is formulated in [41; 42]. Alternative approaches refer to the energy balance computed from time-history analyses [43; 44], or optimization procedures [45].