Inelastic Deformation Ratios for Design and Evaluation of Structures: Single-Degree-of-Freedom Bilinear Systems

The relationship between the peak deformations of inelastic and corresponding linear single-degree-of-freedom (SDF) systems is investigated. Presented are the median of the inelastic deformation ratio for 214 ground motions organized into 11 ensembles of ground motions, representing large or small earthquake magnitude and distance, and National Earthquake Hazards Reduction Program (NEHRP) site classes B, C, and D; near-fault ground motions are also included. Two sets of results are presented for bilinear nondegrading systems over the complete range of elastic vibration period, $T_n:$ $C_{\mu }$ for systems with known ductility factor, μ, and $C_R$ for systems with known yield-strength reduction factor, $R_y\text{.}$ The influence of postyield stiffness on the inelastic deformation ratios $C_{\mu }$ and $C_R$ is investigated comprehensively. All data are interpreted in the context of acceleration-sensitive, velocity-sensitive, and displacement-sensitive regions of the spectrum for broad applications. The median $C_{\mu }$ versus $T_n$ and $C_R$ versus $T_n$ plots are demonstrated to be essentially independent of the earthquake magnitude and distance (over their ranges considered), and of site class. In the acceleration-sensitive spectral region, the median inelastic deformation ratio for near-fault ground motions is systematically different when plotted against $T_n;$ however, when plotted against normalized period $T_n/T_c$ (where $T_c$ is the period separating the acceleration- and velocity-sensitive regions) they become very similar in all spectral regions. Determined by regression analysis of the data, two equations—one for $C_{\mu }$ and the other for $C_R$—have been developed as a function of $T_n/T_c\text{,}$ and μ or $R_y\text{,}$ respectively, and are valid for all ground motion ensembles considered. These equations for $C_{\mu }$ and $C_R$ should be useful in estimating the inelastic deformation of new or rehabilitated structures—where the global ductility capacity can be estimated—and existing structures with known lateral strength.