Optimal design of dampers in seismic excited structures by the Expected value of the stochastic Dissipated Power

• A novel design criterium based on the Expected value of stochastic Dissipated Power (EDP) is adopted.
• In stationary state the EDP is equal to the expected value of Input Power.
• Through the EDP a novel optimal design for optimal damper placement is presented.
• The EDP gives also an optimal value of the total damping capacity and to the capacity of each damper.
• The application to a ten-story building shows the effectiveness of the procedure.

The usefulness of passive energy dissipation devices to reduce seismic response of structures is now well established. In this paper, a method is presented to obtain the amount and the placement of viscous or visco-elastic damping necessary for having a suitable reduction of the response quantities. It is based on the minimization of the Expected value of the stochastic Dissipated Power (EDP) by the structure. The optimal placement of the dampers is obtained through the solution of a simple optimization problem. The method gives also values of the total capacity damping and the upper bound values of damping to each story. At first, the theory of the EDP is illustrated through simple applications to SDOF and 2DOF systems; then, the effectiveness of the method is shown through its application to a ten-story shear-type building, subjected to stochastic ground motion model, with different values of soil profile.