###### Abstract
MRDs exploit the unique characteristics of magnetorheological fluids to provide multiple levels of damping when subjected to magnetic fields with different intensities [5]. A magnetic field is generated by a continuous current that has a tunable intensity and that runs along coils that are wrapped around the chamber that hosts the fluid; the current is provided by the electric grid and/or by high-performances batteries [6; 7]. In the case of an earthquake, a dedicated control system can be triggered to set the current intensity into the dampers on the basis of a predefined control algorithm. A semiactive control strategy of the dynamic response is implemented in this way since the control system does not directly apply force to the structure but, instead, is used to control the properties of the tunable passive damper [8]. Several control algorithms have been developed for the use of MRDs for the mitigation of the seismic responses of buildings [9]. [PERSON] et al. [10; 11] propose clipped-optimal control, which is the most popular algorithm in the literature thanks to its relative simplicity and effectiveness. More sophisticated approaches have also been adopted, which rely upon Lyapunov functions [12; 13], stochastic control [14], linear quadratic Gaussian with loop-transfer-recovery control [15], sliding mode control [16; 17], and intelligent control, such as neural-network-based control [18; 19] and fuzzy logic control [20; 21]. Even though all the algorithms have been proven to be successful on paper or in experiments conducted on simplified structural models, the intrinsic level of complexity makes their practical application to actual buildings difficult; thus, simpler and more robust strategies are needed in order to preserve the integrity of the structure and the safety of the occupants in cases of seismic events. This work proposes a practical approach to define a robust seismic protection system that is based on dissipative bracings that integrate magnetorheological fluid dampers (MRDs). The system is suitable for retrofitting civil constructions in areas with moderate and intense seismic activity, and it adopts commercially available dampers. The activation current of the MRDs is assumed to be constant during the seismic event, and its optimal intensity (\(\mathrm{i}_{\mathrm{opt}}\)) is set on the basis of the most probable seismic accelerogram and peak ground acceleration (PGA) that is expected in the geographical area of the structure. During the actual seismic event, the system is triggered by a sensor that measures the acceleration (a\({}_{\text{b}}\)) at the structure's base. The intensity of the current that is sent to all MRDs is kept equal to the i\({}_{\text{opt}}\) as long as the measured acceleration is lower than the PGA, and it is set to i\({}_{\text{opt}}\):a\({}_{\text{b}}/PGA\) in the (remote) case that the a\({}_{\text{b}}\) exceeds the expected PGA for the area of interest. This approach, therefore, combines the low level of sophistication of a passive system with the tuneability of the MRDs in order to implement a \"multi-level passive control\" of the seismic response, rather than a semiactive one. The low level of sophistication of the control law plays in favor of the higher safety and robustness of the protection system that is designed to work optimally with reference to the most probable seismic event(/intensity) for the area of interest, and conservatively in the remote case of more intense seismic activity. The key element for the design of such a system is the identification of the optimal MRDs and the activation current intensity in correspondence to a given seismic accelerogram(/PGA) for the area of interest and a mitigation target for the seismic response of the structure. To address this task, the dynamic response of a slender metallic structure to a typical seismic accelerogram at its base is first investigated to define the amount of modal damping to be introduced into the system to mitigate its vibrations, according to a predefined target.