建築構造物の確率論的地震応答解析について

Abstract

A method of probabilistic seismic response analysis is described for determining the stochastic res-ponses and predicting the seismic reliability of hysteretic structures. The bilinear hysteretic character-istics are expressed in the form of first-order quasi-linear differential equation. The seismic safety mea-sures, such as the maximum ductility ratio, cumulative plastic deformation ratio, cumulative hystereticenergy and low-cycle fatigue damage, are also expressed in the non-linear differential forms. The bi-linear hysteretic characteristics and the safety measures are considered as extended state variables.The Fokker-Planck equation for the hysteretic structures subjected to non-stationary random exci-tations is derived by using the differential forms of state variables, and is solved approximately by assu-ming an appropriate non-Gaussian joint probability density function. The statistics and probability den-sity functions of structural responses and safety measures are obtained. The reliability functions for thewhole structure and those for the structural components are determined directly from the joint proba-bility density function of the safety measures and its marginal probability density functions. The mainadvantage of the present method is to obtain the reliability functions for various failure criteria of hys-teretic structures without treatment of the so-called first-passage problem. The accuracy of the presentmethod is verified against digital simulation for single-degree-of-freedom bi-linear hysteretic systems.Comparison of the present method with the stochastic linearization techniques for quasi-linear dynamicsystems is made, and the simplification of analytical procedures is discussed in applying the presentmethod to multi-degree-of-freedom hysteretic systems.