The Effect of Low-Cycle Fatigue on Ductility Demand Factor

Ductility demands of structures are increased during strong ground motion as a consequence of the dissipation of hysteretic energy caused by cyclic load reversals. In other word, the cumulative damage of the structures due to cyclic loading reduces the ductility capacity of the structures. This phenomenon is called Low-cycle fatigue. If the real force-deflection model of members is used to nonlinear analysis; the effect of cumulative damage will be concluded in design automatically. But the monotonic ductility capacity could not take into account Low-cycle fatigue. Hence this ductility capacity should be reduced in design procedures (equivalent ductility factor) and should be used instead of the conventional monotonic ductility supply in design procedures. The equivalent ductility factor is applied for determination of force reduction factor.
In this study, the effect of low-cycle fatigue on ductility capacity factor is examined. For this reason the replies of a single degree of freedom system was evaluated using nonlinear dynamic analysis. Seven records related to soil type II from strong ground database are extracted. Also in order to assess the effect of low-cycle fatigue on ductility factor, various models of damage have been selected. Three models have been proposed to determine the equivalent ductility factor taking into account cumulative damage. The first two models based on the maximum displacement and maximum dissipation energy are the upper and lower values. The third one model is Park-Ang model. According to the Park-Ang model, the damage is related to hysteretic energy and concluded of maximum displacement and maximum dissipation energy. The parameter γ controls the hysteretic energy and depends on maximum displacement and natural frequency of the system. In order to obtain the quantity of the parameter γ, a parametric study of the inelastic response of SDOF systems was carried out. In the parametric study, input ground motion, as well as the initial stiffness (period), strength, ductility, hysteretic behavior and damping of SDOF systems, was varied.
In this paper the variation of this parameter was considered and the effect of the ductility factor, force reduction factor, time history acceleration and damping ratio was evaluated. The results show that the reduction of the ductility factor due to low-cycle fatigue (controlled by parameter γ) is significant. It is proved that the parameter is relatively stable during all length of periods. If approximate values for γ are used, the determination of equivalent ductility is very simple, and thus appropriate for design purpose.
The formulae for equivalent ductility factors include damage indices. In design procedures only life safety limit states are considered and the other purposes such as serviceability, immediate occupancy and collapse prevention limit states do not. A more rational design procedure should permit the designer to choose rational limit state. This idea has been realized by including damage indices into the formula for equivalent ductility factors.
The parameter γ varies from 0.6 to 1.2. For practice peruses it is assumed that the value of γ is 0.9. Using this assumption it is possible to determine equivalent ductility factor taking into account low cycle fatigue.