The usefulness of energy dissipation devices to reduce seismic response of structures is now well established. For a given installation of such devices in a structure, one can easily compute the level of response reduction achieved. However, the solution of an inverse problem of how many devices one would need to achieve a desired level of response reduction in a structure, or to achieve an expected level of performance from a structural system, is not quite as straightforward and well formulated. In this paper, a method is presented to obtain the amount of viscous and visco-elastic damping one would need to obtain a desired level of response reduction. The needed supplemental devices are also optimally distributed in the structure to achieve the best performance. To solve the optimal problem, a gradient-based optimization approach is used. To illustrate the application, numerical results for a 24-storey building structure are presented where the objective is to achieve the maximum reduction in the performance functions expressed in terms of the inter-storey drifts, base shear, or oor accelerations. Other forms of performance functions can also be treated similarly.

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SUMMARYThis paper deals with the optimal design of yielding metallic dampers and friction dampers together as they both have similar design characteristics and parameters. Ample tests and analytical studies have conÿrmed the e ectiveness of these energy dissipation devices for seismic response control and protection of building structures. Since these devices are strongly non-linear with several parameters controlling their behaviour, their current design procedures are usually cumbersome and not optimal. In this paper, a methodology is presented to determine the optimal design parameters for the devices installed at di erent locations in a building for a desired performance objective. For a yielding metallic damper, the design parameters of interest are the device yield level, device sti ness, and brace sti ness. For a friction device, the parameters are the slip load level and brace sti ness. Since the devices and the structures installed with these devices behave in a highly non-linearly manner, and thus must be evaluated by a step-by-step time history approach, the genetic algorithm is used to obtain the globally optimal solution. This optimal search approach allows an unusual exibility in the choice of performance objectives. For demonstration purposes, several sets of numerical examples of optimal damper designs with di erent performance objectives are presented.

SUMMARYThe e ectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake-induced ground excitations. Frequency-dependent and -independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is deÿned in terms of several di erent forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for di erent building structures are presented showing the distribution and size of di erent dampers required to achieve a desired level of reduction in the response or a performance index.