Strength reduction factor spectra based on adaptive damping of SDOF systems

The strength reduction factor spectrum is traditionally obtained from a single-degree-of-freedom (SDOF) system with a constant damping coefficient. However, according to the principle of Rayleigh damping, the damping coefficient matrix of a system changes with the stiffness matrix, and the damping coefficient of an equivalent SDOF system changes with the tangent stiffness coefficient. In view of that, this study proposes an equivalent SDOF system with an adaptive damping coefficient and derives a standardized reaction balance equation. By iteratively adjusting the strength reduction factor, the corresponding spectrum with an equivalent ductility factor is obtained. In addition, the ratio between the strength reduction factor that considers adaptive damping and the traditional strength reduction factor, denoted by n, is determined, and the n-u-T relationship is obtained. Seismic records of Classes C, D, and E sites are selected as excitations. Moreover, a nonlinear response time-history analysis is performed to establish the relationship between the n and T values for the equivalent ductility factor u. Further, by exploring the effects of the site class, ductility factor, second-order stiffness coefficient, and period T on the mean value of n, a simplified calculation equation of mean n is derived, and n is used as a modified value for the traditional strength reduction factor R spectrum.