A stochastic approach for deriving effective linear properties of bilinear hysteretic systems subject to design spectrum compatible strong ground motions

A novel statistical linearization based approach is proposed to derive effective linear properties (ELPs), namely damping ratio and natural frequency, for bilinear hysteretic oscillators subject to seismic excitations specified by an elastic response/ design spectrum. First, an efficient numerical scheme is adopted to derive a power spectrum, satisfying a certain statistical criterion, which is compatible with the considered seismic spectrum. Next, the thus derived power spectrum is used in conjunction with a frequency domain higher-order statistical linearization formulation to substitute a bilinear hysteretic oscillator by a third order linear system. This is done by minimizing an appropriate error function in the least square sense. Then, this third-order linear system is reduced to a second order linear oscillator characterized by a set of ELPs by enforcing equality of certain response statistics of the two linear systems. The ELPs are utilized to estimate the peak response of the considered hysteretic oscillator in the context of linear response spectrum-based dynamic analysis. In this manner, the need for numerical integration of the nonlinear equation of motion is circumvented. Numerical results pertaining to the European EC8 elastic response spectrum are presented to demonstrate the applicability and usefulness of the proposed approach. These results are supported by Monte Carlo analyses involving an ensemble of 250 non-stationary artificial EC8 spectrum compatible accelerograms. The proposed approach can hopefully be an effective tool in the preliminary aseismic design stages of yielding structures following either a force-based or a displacement-based methodology.