# Effect of Bond-Slip on Dynamic Response of FRP-Confined RC Columns with Non-Linear Damping
## 4 Effect of Bond-Slip on the Dynamic Response of the FRP-C RC Columns
### Seismic Simulation Results and Discussion  
Based on the OpenSees platform, the dynamic responses of the FRP-C RC circular and square columns considering bond-slip of steel bars are calculated by applying unidirectional and bidirectional harmonic loads. The specific algorithm refers to the literature [43] is as follows: The cross-section is evenly divided into 5 integral control points along the column height, the initial damping ratio of the first two modes is set as 0.02. The peak values of harmonic load acceleration are both selected as 0.1g in horizontal and vertical directions. The period of simple harmonic wave is 0.35 s, the duration is 1.35 s, the calculation time is set as 20 s, and the sampling period is 0.01 s.  
It should be noted that in the following figures: The nonlinear damping model proposed by this paper considered the bond slippage (i.e., Proposed model; the [PERSON]'s nonlinear damping model does not consider the bond slippage (i.e., [PERSON]'s model); the constant damping model does not account for the bond slippage (i.e., Constant damping model). Figures 7-10 show that under the uniaxial and biaxial harmonic loads, for two different nonlinear damping models (e.g., the proposed model and [PERSON]'s model [43]), the trend of  
Figure 10: The column head displacement response of FRP-C RC columns with rectangular section under biaxial harmonic load (C40, \(n=0.3\), \(\gamma=0.0032\), \(\rho=0.015\)). Figure 9: The column head displacement response of FRP-C RC columns with circular section under biaxial harmonic load (C50, \(n=0.3\), \(\gamma=0.0045\), \(\rho=0.0384\)). displacements with time is almost consistent. The displacement responses of the proposed model by this paper considering the bond slip-page are slightly larger than those of [PERSON]'s model. More importantly, the calculated results of the column top displacements with two time-varying damping ratios are both greater than that with constant damping. In addition, the displacement response calculated by the constant damping model decays obviously faster with time increasing. In addition, the displacement responses of biaxial harmonic loads are smaller than that of uniaxial harmonic loads. To illustrate this further, the comparison results of the maximum of column top displacement in the above three models are shown in Table 3.  
For the circular columns, the column top maximum displacement of the proposed damping model is almost 5% larger than that of the Li's model, and 15% larger than that of the constant damping model. Similarly, for the square columns, the column top maximum displacement of the proposed damping model is almost 7% larger than that of the Li's model, and 21% larger than that of the constant damping model. According to the above analysis results, the main reasons are as follows:  
1. Firstly, because the nonlinear damping model considering the stress/displacement and amplitude of change on the influence of damping values change, even in the elastic stage of material, the damping ratio will be increased with the increase of amplitude, which conform to the material when the forced vibration energy dissipation and reflect the damping performance of materials in vibration process [43];
2. secondly, once FRP-C RC columns are considered the bond slip of longitudinal reinforcement, the component of energy dissipation and stiffness are all in a certain degree of lower. Hence, in the time history analysis, the displacement response of the proposed model by this paper compared to the other two model results is larger. That means that if the influence of longitudinal reinforcement bond-slip is taken into account, it can improve the component's safety in the structural design;
3. thirdly, the displacement response calculated by the constant damping model attenuates faster, causing the analysis results may be too small in the seismic analysis of the structure.