The T-shaped friction damper (TFD) is a damping system that appropriately absorbs and dissipates input energy during seismic excitations. In this paper, a practical method for determining optimum slip load of TFDs in multi-storey steel frames is proposed. The seismic performance index (SPI) is used as a measure to quantify the effectiveness of TFDs in improving the seismic behaviour of prototype structures. The optimum slip load of TFDs is acquired based on this index. The endurance time (ET) method is a seismic analysis in which structures are subjected to gradually increasing dynamic excitation. It is shown that using the ET method, instead of the large number of time-history analyses, to obtain the SPI of the system, results in a considerable reduction in computational effort. An approximate relation to obtain the optimum slip load of the TFD is also proposed according to the design base shear of the frames. The performance of the TFDs in the steel frames is investigated by examining a prototype weak steel structure before and after rehabilitation using TFDs. The rehabilitated structure, by considering the optimum slip load of TFDs, satisfies the collapse prevention and life safety levels in BSE-2 and BSE-1 hazard levels, respectively.
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