This paper is concerned with the analytical estimation of probabilistic properties of the stationary random response for a single-degree-of-freedom system with the bilinear hysteresis, when subjected to the Gaussian white excitation. This has been successfully achieved under the consideration that the response of a bilinear hysteretic system, which corresponds to one of the typical restoring force characteristics of building structures, could be evaluated by the comparison of this system with the equivalent Coulomb damping one, the approximate solution of which is obtained referring to one of the exact solutions of the associated Fokker-Planck equation.

The important expressions thus obtained have been examined by the Monte-Carlo simulation. As the results, it has been found that the analytical solution of the R.M.S. response of the displacement coincides with the corresponding experimental one with sufficient accuracy, and that the theoretical R.M.S. plastic deformation gives the good information about its general tendency at least, although it does not always bring about the satisfactory quantative prediction in a strict sense. In addition, it has been concluded that the theoretical values of the expected accumulated plastic deformation agree quite well with the simulated ones over the wide ranges of related parameters.