Damage-Based Design Earthquake Loads for Single-Degree-Of-Freedom Inelastic Structures

This paper develops a new framework for modeling design earthquake loads for inelastic structures. Limited information on strong ground motions is assumed to be available only at the given site. The design earthquake acceleration is expressed as a Fourier series, with unknown amplitude and phase angle, modulated by an envelope function. The design ground acceleration is estimated by solving an inverse dynamic problem, using nonlinear programming techniques, so that the structure performance is minimized. At the same time, the design earthquake is constrained to the available information on past recorded ground motions. New measures of the structure performance based on energy concepts and damage indexes are introduced in this paper. Specifically, the structural performance is quantified in terms of Park and Ang damage indexes. Damage indexes imply that the structure is damaged by a combination of repeated stress reversals and high-stress excursions. Furthermore, the use of damage indexes provides a measure on the structure damage level, and making a decision on necessary repair possible. The material stress-strain relationship is modeled as either bilinear or elastic-plastic. The formulation is demonstrated by deriving the design earthquake loads for inelastic frame structures at a firm soil site. The damage spectra for the site are also established, to provide upper bounds of damage under possible future earthquakes.