Estimation of maximum damper forces in shear-type buildings subjected to seismic input

In the last decades, the use of added viscous dampers for the mitigation of the effects due to the seismic action upon the structural elements has been worldwide spread. On the same time, a large research effort has been devoted to the study of the behaviour and performances of building structure equipped with added dampers with special attention to the development of procedures for the optimization of dampers performances through the use of complex algorithms and iterative procedures whose application requires, in most cases, a significant expertise beyond that of the average practitioner and its use is therefore essentially limited to researchers or to large firms specialized in the field of structural control. Nonetheless, less attention has been devoted to the development of practical design procedures. In this regard, on the knowledge of the authors, few practical procedures have been proposed. Among others, the authors recently proposed a five-step procedure for the dimensioning of inter-storey viscous dampers to be added in frame structures (Silvestri et al., 2010). The procedure aims at guiding the practical design from the choice of a target reduction in the seismic response of the structural system (with respect to the response of a structure without any additional damping devices), to the identification of the corresponding damping ratio and the mechanical characteristics (i.e., damping coefficient values for chosen damping exponent, stiffness of the oil) of the commercially available viscous dampers. The application of the procedure requires the use of a computer program to perform linear and non-linear time-history analysis in order to evaluate the damping force in the added dampers. In the present paper a simplified version of the 5-step procedure leading to a 3-step procedure which does not require any numerical analyses for the sizing of the viscous dampers is proposed. In detail, simple analytical expressions for the damping forces (leading to a specific target damping ratio) are derived starting from appropriate drift profiles representative of different stiffness distribution along the height