# Hysteretic Behavior of Steel Reinforced Concrete Columns Based on Damage Analysis
## 1 Introduction
The hysteretic curves of structure members reflect the changes of strength, stiffness, energy dissipation capacity, and displacement ductility with the loading displacement and the number of cycles. Therefore, the rule of strength and stiffness degradation of the members can be described by the change of the hysteresis loop under an earthquake. Early on, researchers proposed non-cumulative damage indexes based on a single parameter, such as stiffness, strength, and hysteretic energy dissipation [44; 45; 46; 47]. Since an earthquake is a repeated loading process, the damage caused by an earthquake is cumulative. To better describe the damage of structures under cycle load, the cumulative seismic damage indexes, which consist of the combination of plastic deformation and cumulative hysteretic energy dissipation, were developed and are widely used to analyze structural damage [48; 49; 50]. Though the hysteresis-based DI involves a destructive test and cannot be used for real time monitoring of in-service structure, this damage index is directly link to inherent structural parameters, such as stiffness. In this research, we use the hysteresis-based DI to analyze the hysteresis rule of SRC columns. The existing research results show that the cyclic loading history and the number of cycles are the main influencing factors for the damage analysis of structure members. However, the damage index selected in the existing hysteresis model cannot well consider the influence of the number of loading cycles and loading path on the ultimate energy dissipation and deformation capacity of the members. Meanwhile, to the best of knowledge of the authors, this method has been applied only to the analysis of RC structures and steel structures. Few researches on the hysteretic behavior of SRC members have been reported. Since the SRC composite members consist of steel and RC, their damage process is more complex than pure steel or reinforced concrete structures [51; 52]. Therefore, the current method of establishing hysteresis model based DI cannot accurately reflect the seismic performance of the SRC members. In this paper, a new PH hysteretic model by considering the accumulated damage is proposed for the seismic analysis of SRC structures. Firstly, the experimental studies on SRC frame columnswere conducted to study the hysteresis behavior under low cycle repeated loading. Based on the test results, the hysteresis behavior was analyzed, and the skeleton curve and hysteresis loops were further simplified. The simplified trilinear skeleton curve model was obtained through the corresponding feature points determined by regression analysis. Secondly, the nonlinear combination seismic damage index, which was developed by the lots test results and can well reflect the effect of the loading path and the number of loading cycles of SRC frame columns, was used to establish the cyclic degradation index. The strength and stiffness degradation rule of the SRC frame columns was analyzed further by considering the effect of accumulated damage caused by an earthquake. Finally, a hysteretic model of SRC frame columns was established and the specific hysteresis rules given. The proposed hysteretic model was validated by comparing the experimental and the numerical results on SRC frame columns.