Abstract : In structural engineering it is imperative to design each system to survive the inputs anticipated over the design life of the structure. Strong motion inputs cause systems to execute nonlinear responses, and during the strong motion responses, structures accumulate damage. Therefore, the capability to model nonlinear responses and to assess the damage level in a structure is essential for optimal design. Techniques for the diagnosis of damage in inelastic structures have been developed. The dissipated energy in mechanical systems is taken as a measure of damage accumulation. Two models for the simulation of damaged structural response have been developed. Both the single-degree-of-freedom and multi-degree-of-freedom systems were included in the analysis. The objective of this study is to use these models to estimate the amount of energy dissipated due to a strong motion input. The results show that structural damage can be predicted, even in the presence of measurement noise. (Author)