Chapter Five - Critical Excitation for Elastic-Plastic Response

Abstract

This chapter discusses a new probabilistic critical excitation method for single-degree-of-freedom elastic–plastic structures. More specifically, this chapter is aimed at presenting a new measure for describing the degree of criticality of recorded ground motions. The power and the intensity of the excitations are fixed, and the critical excitation is found under these restrictions. However, the analytical expressions cannot be utilized in elastic–plastic structures. This situation causes difficulties in finding a critical excitation for elastic–plastic structures. To overcome such difficulty, a statistical equivalent linearization technique is used. This chapter discusses the concept proposed by Drenick to utilize an equivalent linearization technique in finding a critical excitation for nonlinear systems. However, this concept is restricted to deterministic equivalent linearization. In view of the similarity to the theory for linear elastic systems, the shape of the critical power spectral density (PSD) function is restricted to a rectangular function attaining its upper bound in a certain frequency range. The central frequency of the rectangular PSD function is regarded as a principal parameter and varied in finding the critical PSD function. The critical excitations are obtained for two examples and their responses are compared with those to the corresponding recorded earthquake ground motions.