The energy factor of systems considering multiple yielding stages during ground motions

• We derive the energy factor considering multiple yielding stages of systems during ground motions.
• The influence of the multiple yielding stages is significant.
• The multiple yielding stages should be considered for innovative systems with significant post-yielding stiffness.
• The proposed energy factor can be used to improve the current procedures motivated by energy-balance concept.

This communication focuses on the energy factors of systems considering multiple yielding stages during ground motions. Based on an improved energy-balance model, the energy balance of systems is re-established and the energy factor is derived, considering the multiple yielding stages. To comprehensively investigate the influence of yielding stages and critical parameters on the energy factor, nonlinear dynamic analyses of single-degree-of-freedom systems are performed based on the validated numerical tool. Representative numerical evaluations are presented for different combinations of parameters denoting the yielding stages. The results indicate that the energy factor is significantly influenced by the yielding stages of systems. The results of this study are instructive for the calculation of the energy factor of systems showing multiple yielding stages during ground motions, and can be helpful to improve the current procedures based on the energy-balance concept.