Influence of Stiffness and Damping Parameters of Passive Seismic Control Devices in One-Sided Rocking of Masonry Walls

This paper analyzes the influence of horizontal damped and undamped restraints in terms of the amplification of the response of rocking masonry walls subjected to seismic excitations. It also makes a practical contribution to the design of antiseismic devices conceived to control rocking motion, avoiding or at least limiting undesirable response amplifications that would lead to local or global failure. A horizontal restraint, simulating an elastoplastic steel tie-rod, was coupled with a damper, whose action is included in a proposed equation of motion. Parametric analyses were performed for three typical façades of masonry buildings, showing that, if the stiffness of tie-rod increases, the seismic vulnerability of a rocking façade is not necessarily reduced. Therefore, the calculation of rocking spectra is recommended in order to identify stiffness ranges in which amplification could occur. A simple method for calculating the design damping coefficient of a shock absorber is proposed and the consequent mitigation of vulnerability is demonstrated in various analysis configurations. Graphs plotting time-dependent ratios between the energy dissipated by the shock absorber and the seismic input energy are shown to be a useful tool for quantifying the effectiveness of the shock absorber itself in dissipating energy. The reduction of these time-dependent ratios occasionally observed for specific earthquake time ranges reveals that adverse frequencies are occasionally present in seismic excitation and allows for the identification of the optimal damping coefficient.