## 1 Introduction  
The seismic resilience is defined as the capability of a structural system to maintain an appropriate level of functionality during and after a strong earthquake and the capability to restore its initial condition within a short time period. Passive energy dissipation systems are considered one of the most efficient and cost-effective solutions to mitigate the seismic risk for new and existing structures minimizing damage to the structural and non-structural elements. The installation of these systems allows to dissipate a large portion of earthquake input energy confining the eventual damage in structural replaceable anti-seismic devices, limiting cost and interruption of human occupancy and activities, with evident economic and social benefits. In the last decades the research and development of earthquake resilient performance of buildings equipped with dissipative systems achieved significant progress [1; 2; 3; 4; 5]. Energy dissipation dampers are classified in two main categories due to a velocity dependent or a displacement dependent mechanism. In displacement dependent damping devices, the force response is primarily a function of the relative displacement between each end of the device. The response is substantially independent by the relative velocity between each side of the device and the excitation frequency. Non-linear displacement dependent devices in which the hysteretic energy is dissipated through the yielding of steel material attracted more attention from civil engineers related to their cost-effectiveness and ease of fabrication, the symmetric and stable hysteretic behavior, better low-cycle fatigue property, long-term reliability, and resistance to the environmental actions. Aging is of least concern because corrosion may only slightly reduce the section geometrical properties and an inspection and maintenance program should eliminate the problem. The development and testing of hysteretic steel dampers for the seismic protection of structures started in 1970s on mild steel devices of solid cross section characterized by high stability at high levels of plastic strain. A flexural metallic damper initially proposed and experimentally tested by [PERSON] et al. [6] was designed to provide energy dissipation between structural walls and adjacent floors. Thereafter, several metallic dampers such as torsional or flexural beam [7], single-axis dampers [8], U-strip [9], buckling-restrained brace (BRB) [10], were developed and tested for implementation in structures [11; 12; 13; 14; 15; 16; 17; 18; 19]. Successful experimental and real applications widely demonstrated the effectiveness and reliability of hysteretic steel dampers installed in various structural systems, such as connecting element between walls and frames [15], in coupled walls [16; 17] and at beam-column and column-foundation connections of frames [18]. One of the fundamental parameters investigated to demonstrate the efficacy of metallic dampers is the number of cycles, which can be related to the capacity to dissipate energy for a given displacement and to the fatigue and eventual failure of the devices, leading to different level of damage to the structural system [19]. Several design procedures and various configurations of dissipative bracing systems incorporating replaceable metallic dampers have been developed for the seismic retrofitting of existing buildings and for the new buildings construction with different constitutive materials [20; 21; 22; 23; 24]. Traditional steel braces equipped with hysteretic dissipative devices were successfully used to reduce the seismic demand of existing reinforced concrete framed structures in [25]. Steel frames equipped with buckling-restrained axial dampers (BRAD) and externally connected to the facades of an existing building were considered in [26] in order to improve energy efficiency and earthquake-resistant performance.