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SUMMARYA methodology for the optimal design of supplemental viscous dampers for regular as well as irregular yielding shear-frames is presented. It addresses the problem of minimizing the added damping subject to a constraint on an energy-based global damage index (GDI) for an ensemble of realistic ground motion records. The applicability of the methodology for irregular structures is achieved by choosing an appropriate GDI. For a particular choice of the parameters comprising the GDI, a design for the elastic behavior of the frame or equal damage for all stories is achieved. The use of a gradient-based optimization algorithm for the solution of the optimization problem is enabled by ÿrst deriving an expression for the gradient of the constraint. The optimization process is started for one 'active' ground motion record which is e ciently selected from the given ensemble. If the resulting optimal design fails to satisfy the constraints for other records from the original ensemble, additional ground motions (loading conditions) are added one by one to the 'active' set until the optimum is reached. Two examples for the optimal designs of supplemental dampers are given: a 2-story shear frame with varying strength distribution and a 10-story shear frame. The 2-story shear frame is designed for one given ground motion whereas the 10-story frame is designed for an ensemble of twenty ground motions.

Summary This paper presents an effective approach for achieving minimum‐cost designs for seismic retrofitting using nonlinear fluid viscous dampers. The damping coefficients of the dampers and the stiffness coefficients of the supporting braces are designed by an optimization algorithm. A realistic retrofitting cost function is minimized subject to constraints on inter‐story drifts at the peripheries of frame structures. The cost function accounts for costs related to both the topology and the sizes of the dampers. The behavior of each damper‐brace element is defined by the Maxwell model, where the force–velocity relation of the nonlinear dampers is formulated with a fractional power law. The optimization problem is first posed and solved as a mixed integer problem. For the reduction of the computational effort required in the optimization, the problem is then reformulated with continuous variables only and solved with a gradient‐based algorithm. Material interpolation techniques, which have been successfully applied in topology optimization and in multi‐material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3‐D irregular frames are presented and discussed. Copyright © 2017 John Wiley & Sons, Ltd.

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SUMMARYA 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 e ort is appreciably reduced by ÿrst 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 e cient 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.