Equivalent linearization of a friction damper–brace system based on the probability distribution of the extremal displacement

A new equivalent linearization technique is proposed for a friction damper–brace system (FDBS) idealized as an elastoplastic system. The proposed equivalent linearization technique utilizes secant stiffness and dissipated energy based on the probability distribution of the extremal displacement of the FDBS. In addition, a conversion scheme to convert an elastically designed equivalent linear systems to a FDBS is given. For comparative study, an existing model update technique based on system identification is modified to constraint elements to be updated. For the purpose of verification, shaking table tests for a small scale three-story shear building model, in which a rotational FDBS is installed, are conducted and equivalent linear systems are obtained using the proposed technique and the model update technique. Natural frequencies, modal damping ratios and response quantities predicted by those equivalent linear systems are compared with experimentally obtained ones. Finally, effects of the maximum friction force on the proposed equivalent linearization technique are investigated through numerical analysis of SDOF systems with a FDBS.