# Hysteretic Behavior of Steel Reinforced Concrete Columns Based on Damage Analysis
## 1 Introduction  
Due to their high bearing capacity and good seismic performance such as energy dissipation and ductility, steel reinforcement concrete (SRC) members, especially frame columns, are widely used in high-rise and super high-rise hybrid structures [1; 2; 3; 4]. To ensure that the seismic performance of the structure meets the design requirements, the engineering designer must apply a strict elastoplastic calculation analysis of the structures. As the basis of elastoplastic calculation analysis, the hysteresis model that can accurately reflect the strength and stiffness degradation, deformation performance, and energy dissipation capacity of structures and members under cyclic repeated loading has been studied [5; 6]. Generally, the existing hysteresis model includes two parts, namely, the skeleton curve and the hysteresis rule. The former is determined by all the hysteresis feature points and the latter reflects the highly nonlinear character of the structures [7]. For the structural seismic analysis, the existing hysteresis model can be divided into two categories: the polyline hysteresis (PH) model and the smooth hysteresis (SH) model. The PH model consists of piecewise lines obtained by simplifying the hysteresis behavior of the structure members, and is relatively easy to express and apply [8; 9; 10; 11]. The SH model needs more computational burden to obtain more accurate results and is consequentlyrelatively difficult to implement [12; 13]. Therefore, in this paper, the polyline hysteresis model was adopted for seismic analysis of SRC members. Meanwhile, in most of the existing PH models, the strength and stiffness degradation rule of structure members under an earthquake is described by inducing the cyclic degradation index that only considers energy dissipation [14; 15; 16; 17]. However, an earthquake is a random load, and the loading path has a significant effect on the ability of seismic energy consumption of the members. Therefore, it is difficult to obtain a uniform expression of the energy dissipation capacity of the members. Compared to methods mentioned above for establishing the hysteresis model, the hysteretic model of structural members is established by introducing a damage index (DI) that can better describe the stiffness and strength degradation rule [18; 19]. At present, there are several damage analysis models for structure members. There are two main approaches to establish the damage index: one is sensor based and the other one is hysteresis based. The sensor-based DI often employs distributed sensors that are embedded or surface bonded to the structure to capture the change of certain physical parameters, which can reflect the severity of damages to the structure [20; 21; 22; 23; 24]. A commonly employed sensor is the Lead Zirconate Titanate (PZT) transducer in structural damage detection. PZT is a type of piezoceramic material with very strong piezoelectric effect that enables the PZT transducer to have dual actuation and sensing capacity. In addition, PZT transducers have wide bandwidth and high sensitivity, and are widely used to generate and detect stress waves [25; 26; 27; 28]. With the active sensing approach, a pair of PZT sensors and an actuator located along a stress wave path can monitor the damage on the path and a damage index can be established to reflect the severity of the damage. The active-sensing based DI has been used in concrete structures [29; 30; 31], SRC structures [32; 33; 34], and concrete filled tubular structures [35; 36; 37]. Damage indices based on impedance have also been reported [38; 39; 40]. The advantage of the sensor-based DI is that it is suitable for real time monitoring of the structure via sensors integrated with the structure [41; 42; 43], however, this index does not directly relate to an inherent structural parameter. The other approach to establish a damage index is based on hysteresis.