Structures often become nonlinear and inelastic under severe lateral force produced by natural hazards such as earthquakes, severe winds and waves. The restoring force of the structures under such load may become hysteretic and deteriorate in strength or stiffness, or both. This paper gives an overview of the major developments in the modeling and response analysis of inelastic structures under random excitation. It includes: (1) modeling of the hereditary behavior of inelastic system; (2) methods of solution based on semi-empirical approaches, Fokker–Planck equation, and equivalent linearization; and (3) applications to performance and safety evaluation of real structural systems. Limitations of current methods are mentioned and suggestions of areas for further research are given.

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