Effects of strength hardening, stiffness degradation, strength deterioration and pinching on the seismic response of SDoF systems

Abstract

One of the most commonly used seismic analysis methods, over the last few decades is the equivalent lateral force method. This procedure, which was initially intended for elastic design of structures, has been extended to inelastic design, with the incorporation of the behaviour factor q or with the integration of response spectrum procedures with non-linear static pushover analysis. The behaviour factor, which is meant to reduce the elastic forces, depends on the ductility capacity of each structure. However, the connection between the ductility ratio and the behaviour factor has been approximated by employing an elastic-perfectly plastic hysteretic system, which is a very simplistic form of inelastic behaviour. Meanwhile, the last decades, a number of non-linear effects, that develop during the cyclic loading of an earthquake on different types of structures have been identified. The influence of those effects on the response of single degree of freedom (SDoF) systems subjected to seismic load has been recognized by various authors. The purpose of this work is to enhance the understanding of the impact of various typically observed effects on the seismic response of structures. Models that incorporate the effects of strength hardening, stiffness degradation, strength deterioration and pinching are examined and their response is compared to the response of the elastic-perfectly plastic system. The non-linear models are subjected to an ensemble of 167 earthquake ground motions, which is divided into eight different groups according to the magnitude of the earthquake, the significant duration, the soil conditions while one more group consists of signals similar to the ground motions of the area of Groningen. The response measures that are examined have been selected through an extensive investigation of various damage indices and measures proposed in the literature. Through this investigation, it is concluded that the measures of the maximum displacement response, the residual displacement, the total hysteretic energy, the total dissipated by viscous damping energy and the total input energy are sufficient to describe the response of a structure subjected to seismic load. The results of this investigation showed that these non-linear effects influence more the response of the systems with short eigen-period. The effect that seems to affect the most the response is the pinching effect. Additionally, it is shown that there is high dependency between the frequency content of the input signal and the deviations of the response calculated by the models that incorporate this non-linear effects and the response calculated by elastoplastic model.