Consistent inelastic design spectra: Hysteretic and input energy

Abstract This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo‐acceleration spectrum and the time integral of the square of the ground acceleration ∫ a 2 d t. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio E H E I ) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low‐cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio E H / E I is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R , proposed in the companion paper, and the proposed values for γ and E H / E I