Noniterative Equivalent Linear Method for Evaluation of Existing Structures

The equivalent linear system is one of the approximate methods for estimating the maximum inelastic displacement response of structures in performance-based seismic design and evaluation. Traditionally, the equivalent period and damping of such a system are defined by the ductility ratio ( $\mu =\text{maximum}$ displacement/yield displacement). However, for existing structures, the strength ratio ( $R=\text{elastic}$ lateral strength/yield lateral strength) is generally known rather than the ductility ratio. If the ductility ratio is used for defining the equivalent period and damping, the maximum inelastic displacement demand of existing structures has to be determined through an iterative procedure until the computed displacement is within an allowable tolerance to the assumed displacement. In addition, it was reported that the existing equivalent linear system may overestimate the maximum inelastic deformation of short-period structures because it is independent of periods of vibration $\left(T\right)$ . To avoid iteration and improve accuracy, this paper presents results of a comprehensive statistical investigation on the equivalent linearization in which both the equivalent period and damping are defined by strength ratios and periods of vibration. The accuracy of the developed equivalent linear system is also discussed based on a set of 72 recorded earthquake ground motions. In addition to the advantage of noniteration, the recommended equivalent linear system gives good predictions of the mean maximum inelastic displacement of structures for systems with all period ranges.