## 3 Numerical Modeling of Concrete Beams Reinforced with SFCB
### Verification of Numerical Modeling with Experimental Results  
#### 3.3.1 Comparison of Monotonic Pushover Test  
For S12B43 beam, the predicted load firstly increases linearly with corresponding displacement before yield strength of 28.45 kN. After that, the curve has a turning point and keeps an approximate  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Concrete** & \(f_{y}\)**/MPa** & \(\varepsilon_{co}\) & \(f_{ca}\)**/MPa** & \(\varepsilon_{cu}\) & \(\lambda\) & \(f_{t}\)**/MPa** \\ \hline unconfined & 26.20 & 0.0020 & 5.24 & 0.0044 & 0.1 & 2.01 \\ confined & 34.06 & 0.0026 & 6.81 & 0.0277 & 0.1 & 2.01 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Constitutive control parameters of Concrete02 material.  
Figure 13: Mechanical properties of steel bar in OpenSees.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fiber Types** & \begin{tabular}{c} **Original Fiber** \\ **Strength (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Fiber Ultimate Strength** \\ **in SFCBs (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Original Fiber** \\ **Elongation (\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Elongation** \\ **in SFCBs (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Area** \\ **(mm2/bundle)** \\ \end{tabular} \\ \hline \hline BFRP(2400 tex) & 2250 & 1540 & 2.5 & 2.2 & 0.833 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mechanical and physical properties of BFRP fibers in OpenSees.  
line at a lower slope until ultimate capacity is reached at 55.08 kN. At this stage, the load increases obviously and the displacement also increases to 56 mm. When the beam deformation and load continue to increase, concrete crushing occurs in the compression zone. Finally, the outer fiber begins to break and the components reach ultimate capacity. When most of the fiber breaks, the load drops sharply and the components fail. The simulated curves of monotonic loading beam can be divided into three stages. The predicted load firstly increases linearly with corresponding displacement before yielding of composite bar occurs. After that, the beam enters the stage of post-yield, both the load and displacement increase greatly at this stage, which ends with the fiber breaking and the member reaching the ultimate capacity.  
The comparison of the monotonic load-lateral displacement curves between the experimental and simulation results are shown in Figure 14a. By comparison, it is found that the pushover analysis results agree well with the test results in terms of yield displacement, yield load, ultimate load and corresponding displacement. It is worth noting that the simulated yield displacement is slightly less than the test value. It shows that the numerical stiffness before yielding is larger than the test value. The simulation results are good for the ultimate capacity of concrete beam at the FRP fracture point and after fracture. The experimental and simulation curves show that the S12B43 beam has a stable post-yield stiffness. When the horizontal displacement is about 57 mm, the corresponding drift ratio is 4.75%, showing the specimen has good ductility. The moment that the load drops sharply indicates that the component is damaged. After the component is damaged, it still has a certain residual bearing capacity because the inner steel of the composite reinforcement is still at the yielding state.