Equivalent ductility factors, taking into account low‐cycle fatigue

TLDR

Strong earthquakes reduce structural deformation capacity due to cumulative damage from cyclic load reversals, and these effects are modeled under various failure hypotheses. The study proposes equivalent (reduced) ductility factors that incorporate low‑cycle fatigue effects. Ductility reduction is governed by a dimensionless parameter γ—dependent on dissipated hysteretic energy, maximum displacement, and natural frequency—and the derived formulae include damage indices that let designers set acceptable damage levels. Using approximate γ values, the equivalent ductility factors enable simple design calculations, and when applied to the El Centro 1940 SOOE record, the resulting inelastic acceleration spectra closely match spectra from full nonlinear dynamic analysis.

Abstract

Abstract During strong earthquakes, the deformation capacity of structures is reduced due to the cumulative damage caused by cyclic load reversals. In the paper, equivalent (reduced) ductility factors have been proposed, which take into account this effect. They are based on different failure hypotheses. Ductility reduction due to low‐cycle fatigue is controlled by a dimensionless parameter γ, which is a function of dissipated hysteretic energy, maximum displacement and the natural frequency of the structural system, and which has been proved to be a relatively stable quantity in the whole period range. If approximate values for γ are used, the determination of equivalent ductility is very simple, and thus appropriate for design purposes. The formulae for equivalent ductility factors include damage indices, and permit the designer to choose acceptable level of structural damage explicitly. As an example, equivalent ductility factors have been used to construct inelastic acceleration spectra, which are proportional to strength demand, for the El Centro 1940 SOOE record. The results have been compared with the ‘exact’ spectra obtained by non‐linear dynamic analysis.