# Damage Analysis of Reinforced Concrete Columns Based on Fiber Beam-Column Element
## 3 Damage Simulation of Reinforced Concrete Columns
### Cyclic Loading Test  
[PERSON] and [PERSON] [30] completed a series of quasi-static tests of reinforced concrete columns. In this paper, the specimen TP-29 was selected for simulation analysis. The effective height of the specimen was 1350 mm. The section size was 400 mm \(\times\) 400 mm. The axial force was 150 kN. In the analysis model, specimen TP-29 was divided into ten fiber beam-column elements along with the height. Element division and section fiber discretization of specimen TP-29 are shown in Figure 7. The mechanical properties of the concrete material and the steel material are given in Tables 1 and 2, respectively. Figure 6: The damage index of the steel bar. Figure 7: The element division and the fiber separation of the specimen TP-29. Figure 8 shows a comparison between the analytical and experimental force-displacement hysteretic curves of the specimen TP-29. The result showed that numerical simulation can predict the force-displacement hysteretic curves of the specimen TP-29 with good accuracy. The RSAPS platform can provide a precise prediction of the stiffness and strength degradation of the specimen TP-29 under cyclic loading. However, the unloading stiffness of the specimen in the simulation is larger than that in the experiment. The main reason may be that the bond-slip between concrete and steel bars reduced the overall stiffness of the specimen, which was not considered in the simulation model. In the analysis, the steel bar was severely damaged and fractured. The stress-strain relationship of the steel bar is shown in Figure 9.  
Figure 10 shows the final damage distribution of the specimen TP-29. The ordinate represents the height of the specimen. The simulated tensile cracks on each surface (tensile damage index reached 1) were mainly within 30 cm at the bottom of the specimen. Surface E and surface W were more seriously damaged. Surface N and surface S showed large damage for the edge and relatively small damage for the central region. The simulated compression failure of each surface (compression damage index reached 1) was mainly within 20 cm at the bottom of the specimen. Surface E and surface W were damaged more seriously. The compression failure of surface N and surface S was mainly concentrated at the bottom edge, showing a triangular distribution inside. Through comparison, it was found that the simulated damage distribution of the specimen was consistent with the test result, which verified the validity of the damage analysis model. Figure 8: Force–displacement hysteretic curves of specimen TP-29. Figure 9: The stress–strain relationship of the steel bar. Figure 11: The element division and the fiber separation of the specimen. Figure 10: Final damage distribution of specimen TP-29. (**a**) Tensile damage; (**b**) Compression damage; (**c**) Test result [30]. Figure 14 shows the final damage distribution of the specimen. The ordinate represents the height of the specimen. The simulated tensile cracks (tensile damage index reached 1) were found to be mainly within 700 mm at the bottom of the specimen, and the crack distribution was consistent with the experimental results. The simulated compressive failure (compressive damage index reached 1) was mainly within 250 mm at the bottom of the specimen. The compressive damage at the bottom edge was relatively small, which was consistent with the experimental results. The simulation results can show the failure parts of the specimen and the damage of the incomplete failure parts (damage index less than 1). The damage of the steel bars was found to be very small and no separate analysis was performed. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Concete** & \(f_{\mathbf{c}}\) (**MPa**) & \(\epsilon_{\mathbf{0}}\) & \(\epsilon_{\mathbf{20}}\) & \(f_{\mathbf{t}}\) (**MPa**) \\ \hline Cover & \(-33.7\) & \(-0.002\) & \(-0.005\) & \(3.37\) \\ Core & \(-37.9\) & \(-0.0031\) & \(-0.012\) & \(3.37\) \\ \hline \end{tabular}
\end{table} 
Table 3: Parameters of the concrete material. Figure 12: Takatori station record.