## 1 Introduction  
During an earthquake, the seismic energy introduced into a building leads to the creation of plastic deformations, hinges, and cracks [1]. Passive energy dissipation dampers have widely been used in recent years to reduce the dynamic response of civil engineering structures subjected to seismic loads. One of their advantages is easy replacement and repair, and they are effective because they minimize structural damage by absorbing structural vibrational energy and dissipating energy through their hysteresis behavior. More generally, they can be categorized into dampers that depend on displacement, dampers that depend on speed, and dampers with a combination of the two. The types of dampers that dissipate energy in construction include metallic dampers, friction dampers, viscous or viscoelastic dampers, self-centering dampers, and tuned mass dampers [2; 3; 4; 5; 6]. Other researchers focused their study in seismic-resistant steel framing system capable of providing stiffness and ductility to new or existing structures [7; 8], or the use of buckling-restrained braces [9; 10]. The pall damper is one type of friction damper presented in the literature, and it works based on the mechanism of solid friction for dissipating vibration energy [11]. As the joints slip, the cantilevered walls provide the elastic restraint required to create the centering action that ensures negligible residual displacement after an earthquake. Pall friction dampers have been used in both existing and new buildings in the USA and in Canada. According to [PERSON] [12], by 1996, several types of Pall friction dampers had been incorporated into six existing buildings and seven new ones, with more important applications in the Concordia University Library in Montreal and the Montreal Casino in Canada. The Concordia University Library in Montreal was designed so that the required stiffness was provided by 143 Pall-type dampers. The conventional solution was not used for the walls because, even though it would provide the required stiffness, it would limit the number of parking spaces in the basement of the building and would lead to greater foundational needs. Finally, the solution involving Pall dampers reduced the total construction costs by 1.5%, which corresponded to USD 65,000,000 [13]. The Montreal Casino, an eight-story metal building constructed in 1966 by the French government for the Expo 67 exhibition in Montreal, Canada, needed to be retrofitted, as the building no longer met the requirements of current anti-seismic regulations. The solution that was chosen after nonlinear dynamic analyses was to strengthen the structure with 32 Pall-type friction dampers, as they were less expensive and time-consuming than other conventional reinforcement solutions [14; 15]. The most popular friction-yielding damper is the ADAS (Added Damping and Stiffness) damper studied by [PERSON] [16; 17]. The layout consists of flat steel plates in a row, in which their bottoms are connected to the top of the diagonal braces and their upper parts are connected at the ceiling level. These dampers have been applied to the seismic reinforcements of the Wells Fargo Bank in San Francisco [18] but have also been applied to many other buildings in the USA, Mexico, and Japan. One of such buildings reinforced with ADAS-type metal dampers is the Izzaga building in Mexico. The building suffered moderate damage in 1985 during an earthquake, and further damage occurred during another earthquake in 1986. It was finally reinforced with 250 ADAS dampers, which were incorporated into metal diagonal bars on the perimeter of the building [19]. [PERSON] et al. [20; 21] proposed an innovative energy dissipation system known as CAR1, consisting of very simple materials and which does not need to be accomplished in heavy industry so enables its use in both developing and undeveloped countries.