This paper presents a consistent approach for the optimal seismic design of added viscous damping in framed structures. The approach presented is appropriate for use in elastic as well as yielding frames. The sum of added damping is chosen as the objective function and the performance of the structure, under the excitation of an ensemble of deterministic ground motion records, is constrained. The performance of the structure is measured by the maximal inter-story drifts in both the linear and nonlinear cases. The nonlinear case however, uses an additional performance measure of the normalized hysteretic energy of the plastic hinges
Gradients of the performance measures are first derived to enable the use of an appropriate first order optimization scheme. Moreover, an efficient selection scheme enables the consideration of only a few records rather than the whole ensemble, hence making the optimization process efficient in terms of the computational effort.