Optimal Softening and damping design for buildings

Retrofit strategies based on softening techniques with supplemental damping have shown promise in reducing dynamic response of civil infrastructures as compared with other optimal retrofit techniques. This technique involves the determination of optimal locations and corresponding capacities of dampers and softened stories. The three optimal design methodologies presented in this paper are capable of determining optimal locations and optimal stiffnesses and capacities of softened stories and dampers placed in a building. Initially, a preliminary design procedure based on a spectral approach is used to estimate global stiffness modification and total damping which should be Lidded to the original building. This procedure allows for reducing the maximum expected spectral demands to acceptable levels. The first method presented for the structural performance optimization is based on a procedure for finding optimal storey stiffnesses and damper placements that minimize the sum of amplitudes of the transfer functions of inter-storey drifts. The second approach is based on concepts of optimal control theory through an adaptation of a gain matrix obtained from using the linear quadratic regulator (LQR) algorithm. The third method is a modification of the simplified sequential search algorithm that uses a performance index, which considers inter-storey drifts and absolute floor velocities and accelerations to find the optimum placement of damping devices and storey stiffnesses. Two examples of shear-type buildings with uniform and non-uniform initial stiffness distributions are presented to show effectiveness of the proposed design methodologies. The optimum distributions obtained using these optimization methods are compared using response time history analysis.