The study proposes a retrofitting method with an optimum design of viscous dampers in order to improve the structural resistant capacity to earthquakes. The retrofitting method firstly uses a 2D frame model and places the viscous dampers in the structure to satisfy the performance requirements under code-specific design earthquake intensities and then performs an optimum design to increase the structural collapse-resistant capacity. The failure pattern analysis and fragility analysis show that the optimum design leads to better performance than the original frame structure. For regular structures, it is demonstrated that the optimum pattern of viscous damper placement obtained from a 2D frame model can be directly used in the retrofitting of the 3D frame model. The economic loss and repair time analyses are conducted for the retrofitted frame structure under different earthquake intensities, including the frequent earthquake, the occasional earthquake, and the rare earthquake. Although the proposed method is based on time-history analyses, it seems that the computational cost is acceptable because the 2D frame model is adopted to determine the optimum pattern of viscous damper placement; meanwhile, the owner can clearly know the economic benefits of the retrofitting under different earthquake intensities. The retrofitting also causes the frame to have reduced environmental problems (such as carbon emission) compared to the original frame in the repair process after a rare earthquake happens.
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