Probabilistic Approach to the Effects of Earthquakes on Structures

This second chapter of applications deals with the response of certain structures subjected to earthquakes. Only some aspects of this wide area of investigation will be treated. Sections VII. 1 and VII.2 present briefly the notions necessary for stating the problems. Concerning applications to calculation of structures three types of methods may be envisaged: a) linear filtering methods, which presume that the system of differential equations governing the mechanical system is linear; b) methods using the Fokker-Planck equation, which are rigorously applicable when the behaviour of the mechanical system is governed by a linear or nonlinear system of differential equations; c) methods using generalized Fokker-Planck equations, which take into consideration the imperfect elasto-plastic behaviour of materials. d) Numerical simulation methods which allow calculations for arbitrary nonlinear systems.

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