Seismic retrofit of two-way unsymmetric-plan buildings with added masses

Abstract

A new methodology for retrofitting unsymmetric-plan buildings against earthquakes is proposed. When such buildings are subjected to ground acceleration, the lateral inertial forces created at the floors’ center-of-mass (CM) induce torsional moments about the center-of-rigidity (CR). The retrofit approach introduces masses to the building floors and places them so that the CM is moved closer to the CR to decrease the lever-arm of the torsional moment. The mass placement is challenging since adding mass also increases the lateral inertial forces linearly and changes the natural mode-frequencies nonlinearly. In order to determine the optimal mass placement, the proposed methodology seeks to develop a new sequential search algorithm. A transfer-function matrix, relating the interstory drifts of the floor-plan edges to the ground acceleration components, is presented and used to obtain the magnitude of the peak gains. The search algorithm examines the performance index (PI) of the square-root of the sum of the squares (SRSS) of the magnitudes of the peak gains over a range of added mass quantities, starting from the top-floor and sequentially stepping towards the first-floor. Thanks to the proposed transfer-function matrix, the minimum PI is obtained very quickly, saving computation time. The developed methodology is examined for retrofitting a three-story building of shear-frames, a ten-story building of moment-resisting-frames and an inelastic ten-story building of yielding shear-frames. The results show that the maximum interstory drifts within the structure, the maximum story shear-forces applied to the lateral-load carrying frames, and the maximum absolute acceleration are reduced by moving the CM closer to the CR, which mitigates the threat of structural failure and demonstrates the effectiveness of the proposed retrofit approach. The developed methodology introduces a new sequential search algorithm that calculates optimal mass quantities, and their location in the horizontal-plane, to minimize the frequency-response of the new transfer-function matrix, while subjected to side-constraints. This is a novel approach to the utilization of systematic search algorithms.