The strategies commonly adopted for the seismic design of building structures may be substantially traced back to two ways: (1) the maximization of the structural ductility capacity (traditional approach) based upon the hysteretic dissipation which occurs when structural elements develop non-linear behavior, and (2) the minimization of the energy transmitted by the earthquake to the structural system (innovative approach) based upon innovative technologies for the seismic protection of building structures aimed at guaranteeing the capacity of the structure of facing strong earthquake ground motions without recourse to structural ductility as main resource.

An example of such seismic protection systems is added dampers which maximize of the part of energy dissipated in dampers minimize the part of elastic energy absorbed by the structural elements. Although its high performance, this second strategy is characterized by elevate cost; so, for this reason, it is used above all for structures for particular destination use.

It is thus clear that the first approach is characterised by low cost but also low efficiency, whilst, on the contrary, the second one is characterised by high cost but also high efficiency. So we can couple the best aspects of both strategies (the inexpensiveness due to the ductility capacities of the structure and the efficiency due to the added viscous dampers); this is the focus of the present paper.

The main purpose of this research work is the development of a simplified methodology for the seismic design of structures equipped with viscous dampers which allows to consider, at the same time, the non-linear behaviour of both the structural elements and the damper system, with the use of a properly calibrated force reduction factor.

In particular, it is important to know the limits due to the joint use of viscous dissipation due to the presence of added dampers and of the hysteretic dissipation associated to the ductility capacity and to the excursion in plastic field. Thus, the highest problem to solve in this context is to determinate how much ductility is possible to assign to the structure when viscous dampers are located inside it. Such limits (in terms of use of the ductility characteristics of the structures) have broadly been studied in the past for structures not endowed with systems of additional dampers, and represent the heart of the usual methodologies of seismic design of the structures founded on the force reduction factor (or behavior factor). The final objective becomes therefore from economic to scientific, and it consists in investigating how the relationship between the force reduction factor and the request of ductility in the structure is influenced (i) by the presence of additional viscous dampers and (ii) by values of elevated damping ratio.