Problem Formulation

This paper addresses the optimization problem of minimizing the added damping subject to con­straints on local performance indices for framed structures excited by an ensemble of realistic ground motion records. The local performance indices are interstory performance indices for 2D frames, and interstory performance indices of the peripheral frames for 3D structures. Dampers are initially located at each story of the 2D frames or at each story of each peripheral frame in the 3D structures. As the optimization process progresses towards the optimum, however, some of the dampers will attain zero values.

The formulation of the optimization problem is comprised of the total added damping as an objective function, and an inequality constraint on the upper bound of each of the local performance indices which are computed based on the behavior of the structure, i. e., satisfying the equations of motion of the damped structure. The damping coefficients which are the design variables are required to be nonnegative.

The local performance indices are normalized by their allowable values such that a value of unity indicates that the local performance index is “fully stressed”. Useful local performance indices are the maximal interstory drift, maximal interstory ductility, interstory hysteretic energy, combination of interstory ductility and interstory hysteretic energy such as the damage index of Park and Ang (1985), etc. or the maximal values of all of the above.