Effect of hysteretic smoothness on inelastic response spectra with constant-ductility
This paper presents an efficient methodology for computing constant-ductility inelastic response spectra. The computation of constant-ductility spectra involves numerical root-finding algorithms to find the strongest structure providing a desired ductility response. Smooth inelastic structural behavior is modeled using a first-order nonlinear differential equation and the transient structural response is solved using an implicit algorithm requiring Newton iterations at each time step. For structural models with smooth hysteretic behavior (not piece-wise linear), a simple root-finding method involving a combination of hyperbolic fits, linear interpolation, and Newton's method converges upon the highest strength (conservative) solution with a small number of iterations. The effect of the hysteretic smoothness on the occurrence of multiple roots is examined for two near-fault and two far-fault earthquake records, and for two measures of ductility and for normalized hysteretic energy. The results indicate how the smoothness of the hysteretic behavior affects ductility demand and constant-ductility response spectra. © 2010 John Wiley & Sons, Ltd.
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