Optimal design of supplemental viscous dampers for linear framed structures

A methodology for the optimal design of supplemental viscous dampers for framed structures is presented. It addresses the problem of minimizing the added damping subject to a constraint on the maximal interstorey angular drift for an ensemble of realistic ground motion records while assuming linear behaviour of the damped structure. The solution is achieved by actually solving an equivalent optimization problem of minimizing the added damping subject to a constraint on a maximal weighted integral on the squared angular drift. The computational effort is appreciably reduced by first using one 'active' ground motion record. If the resulting optimal design fails to satisfy the constraints for other ground motions from the original ensemble, additional ground motions (loading conditions) are added one by one to the 'active' set until the optimum is reached. An efficient selecting process which is presented herein will usually require one or two records to attain an optimum design. Examples of optimal designs of supplemental dampers are presented for a 2-storey shear frame and a 10-storey industrial frame. The 2-storey shear frame is required to withstand one given ground motion whereas the 10-storey frame is required to withstand an ensemble of twenty ground motions. The resulting viscously damped structures have envelope values of interstorey drifts equal or less than the target drifts.