Damage-based optimal control of steel moment-resisting frames equipped with tuned mass dampers

The efficacy of a tuned mass damper (TMD) in dissipating the seismic energy transmitted to a structure depends on the TMD's and structure's characteristics and the structural response(s) that the TMD is intended to control. This study presents an approach to designing TMDs considering seismic damage as a representative of structural response. Damage is quantified by the Park-Ang damage index, which integrates deformation-induced damages with the cumulative hysteretic energy dissipated by structural members. The design problem is formulated into an optimization framework. The objective function is assumed to be the maximum value of story damage averaged over an ensemble of independently applied, scaled historical ground motions, and constraints are defined such that an adjustably uniform distribution of the mean story damage along the height of the structure is achieved. The approach is demonstrated by finding the optimum design of a TMD for a 10-story inelastic steel moment-resisting frame (SMRF) using the passive congregation particle swarm and grey wolf optimization techniques and showing that the optimized TMD substantially mitigates local damage in beams and columns, achieves a more uniform damage distribution in stories, yields an improved balance of reduced drifts and accelerations in the structure, and reduces the seismic fragility of the SMRF at different performance levels.