Simplified relationships between inelastic and elastic spectral acceleration demands for seismic design in New Zealand

This paper investigates the suitability of the equal displacement approximation for short period structures, noting that historic definitions of what constitutes a “short period structure” are vague. The research identifies a new parameter, Tpeak, defined as the period ordinate for the peak elastic spectral acceleration, to provide a lower-bound period for which the equal displacement approximation may be appropriate. The use of this parameter is supported by the results of inelastic spectra and reduction ratios generated for SDOF systems, with bilinear and Takeda hysteresis rules, subject to a large suite of ground-motion records. New equations for strength reduction factors are provided as a function of Tpeak and agree well with strength reduction ratios obtained from inelastic spectra for the ground-motion set. It is found that a “short period structure” should be defined as those with periods greater than 0.2 s-0.3 s for most sites and locations in New Zealand, at a ground shaking intensity with annual probability of exceedance of 1 in 500. The study then goes on to conclude that use of the equal displacement approximation for all periods may be reasonable, at least for the immediate future, given that (i) many buildings in New Zealand are likely to have a period of vibration greater than the short period limit, particularly when foundation deformations are considered, and (ii) recent literature suggests that the design ductility currently adopted for ductile short period buildings may be conservative. Nevertheless, if future research prompts revisions to ductility and deformation capacity estimates for short period buildings, then the authors advocate for a return to period-based relationships between inelastic and elastic spectral demands.