An algorithm for computing isoductile response spectra

M. Inel, M. A. Aschheim, D. P. Abrams

Research output: Contribution to journalArticlepeer-review


The computation of constant ductility (or isoductile) response spectra for single-degree- of-freedom systems can require numerous individual response history analyses. Recognising that the same ductility response may be obtained for different strength oscillators of a given period, greater computational effort is required to reduce the possibility that a desired solution is not overlooked. Even a single solution may not exist if a local discontinuity in the strength-ductility relationship coincides with the desired value of ductility. This paper describes a two-phase algorithm to identify the highest strength solution for which the corresponding ductility equals (or does not exceed) the desired ductility. The first phase adopts a “check-reject” approach to reject intervals of strength where the possibility of unidentified higher-strength solutions is considered to be remote, thereby narrowing the strength interval in which the solution will be found. The second phase identifies a solution within this interval as rapidly as possible using a bisection approach. The algorithm is implemented in the USEE software program. The efficiency and accuracy of the algorithm are demonstrated by comparison to results obtained with other software programs.

Original languageEnglish (US)
Pages (from-to)375-390
Number of pages16
JournalJournal of Earthquake Engineering
Issue number3
StatePublished - 2002
Externally publishedYes


  • Constant ductility spectra
  • Inelastic response spectra
  • Isoductile response spectra
  • Nonlinear response
  • SDOF oscillators
  • Seismic response

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality


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