Third-order statistical linearization-based approach to derive equivalent linear properties of bilinear hysteretic systems for seismic response spectrum analysis

• Derivation of effective damping and stiffness from bilinear hysteretic oscillators.
• Third-order statistical linearization for design spectrum compatible random processes.
• New statistical criterion to reduce a third-order linear system to a SDOF oscillator.
• Inelastic peak response estimation of bilinear systems without numerical integration.
• Inelastic response spectra for bilinear systems without numerical integration.

A novel statistical linearization based approach is proposed to derive effective linear properties (ELPs), namely damping ratio and natural frequency, for bilinear hysteretic SDOF systems subject to seismic excitation specified by an elastic response/design spectrum. First, an efficient numerical scheme is used to derive a power spectrum satisfying a certain statistical compatibility criterion with the given response spectrum. Next, the thus derived power spectrum is used in conjunction with a frequency domain higher-order statistical linearization formulation to replace the bilinear hysteretic system by a third order linear system by minimizing an appropriate error function in the least square sense. Then, this third-order linear system is used to derive a second order linear oscillator possessing a set of ELPs by enforcing equality of certain response statistics of the two linear systems. The thus derived ELPs, are utilized to estimate the peak response of the considered nonlinear system 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 uniform hazard elastic response spectrum are presented to demonstrate the applicability and the usefulness of the proposed approach. These are further supported by Monte Carlo analyses involving an ensemble of 250 non-stationary artificial EC8 spectrum compatible accelerograms. It is believed that the proposed approach can be an effective tool in the preliminary aseismic design stages of yielding structures following either a force-based or a displacement-based methodology.