# Hysteretic Behavior of Steel Reinforced Concrete Columns Based on Damage Analysis
## 3 Analysis of Hysteretic Behavior  
The loading-displacement (\(P-\Delta\)) hysteresis curves of the members under cyclic loading are the basis of the hysteretic performance for the structural members. Based on the test results, the loading-displacement hysteretic curves and skeleton curves for the SRC frame columns, which can be obtained by connecting the peak points of the hysteretic loops, are shown in Figure 5. It can be seen that:  
1. All of the test members have a similar failure process under repeat cyclic loading that experiences three failure stages, namely, the elastic stage, the inelastic stage with cracks, and the failure stage. At the initial stage of loading, several horizontal cracks appear first at the root of the column. The stress and strain of the rebars are small, and the action of the steel has not yet occurred. The specimen is mainly in the elastic stage. At this time, the hysteresis behavior of the SRC frame columns is similar to the reinforced concrete frame columns. Therefore, the hysteresis loops have different degrees of pinching phenomenon. With the increase of the displacement amplitude and the number of cycles, the cracks continually expand and develop. Meanwhile, the concrete cover appears severely cracked with partial spalling. At this point, because of the effect of the steel and core concrete, the pinching phenomenon of the hysteresis loops is gradually improved. When the displacement ductility \(\mu\) reaches 3, some of the horizontal cracks develop into shear diagonal cracks, but the development speed of the diagonal cracks is relatively slow. The pinching phenomenon of the hysteresis loops disappears basically. At this time, the hysteresis loop becomes a plump fusiform shape. With continuous increase in load, the longitudinal rebars, steel flange, and most of the steel web yield at the crack section. Meanwhile, due to the action of the repeated load, the horizontal crack gradually runs through. The whole process is in the inelastic stage with cracks. Finally, with the increase of load further, the specimen comes into the failure stage. The concrete cover of the compression zone at the root of the column is a large spalling area. The stirrups and longitudinal rebars are exposed, and some of the longitudinal rebars buck. However, since the core concrete is constrained by a steel flange frame, the ability of compression deformation of the SRC frame column is obviously enhanced. Meanwhile, the strength and stiffness degradation of the members are slow, due to the constraint of the transverse stirrups on the concrete, there is a lateral bracing on the outside of the steel, which can prevent the global and local buckling of the steel. The whole process of the hysteresis cycle shows that there is a good ductility and an ability of energy consumption of the SRC frame column. 2. Compared to the reinforced concrete members, the initial stiffness of the skeleton curve of the SRC frame column is larger due to the steel, and the declining part of the skeleton curve is relatively flat. At the same time, the peak load of the positive loading skeleton curve is slightly higher than the one of the reverse loading skeleton curve, since the specimen has a certain residual  
Figure 4: Loading history of specimens. deformation after positive loading. Under reverse loading, it is necessary to offset the influence of residual deformation in the members. In addition, positive loading generates a certain damage to the members, which reduces the bearing capacity of the members under repeated loading. 3. With the increase of the axial compression ratio, the initial stiffness and peak load of the specimen gradually increase. However, after reaching the peak load, the larger the axial compression ratio, the faster the specimen strength and stiffness degrade. The energy dissipation capacity of the specimens significantly reduces, and the ductility becomes poor. With the increase of steel ratios, the peak load of the specimen gradually increases.