## 4 Results and Discussions
### Analysis of Bending Behavior of RC Beams with Different Number of SMA Bars
The camber predicted by the FE simulation matches the RC beam prestressed by 5 Fe-SMA bars very well, and the predicted values become slightly larger than those observed in the experiments with decreasing the number of the Fe-SMA bars. This again indicates that the FE simulation models used in this study slightly overestimate the prestress introduced by the activation of the Fe-SMA bars, due to the highly idealized assumptions of the perfectly bonded interfaces. However, the predicted RC beam cambers are in overall very good agreement with the experimental data with errors less than 0.052 mm. Figure 13 shows the normal \(x\)-axis stress distributions along each Fe-SMA bar after activations, calculated by the FE simulations for the RC beams prestressed by different numbers of Fe-SMA bars. It can be clearly seen that the prestress induced by the Fe-SMA bars tends to increase slightly with decreasing the number of Fe-SMA bars. Especially, in the case of the RC beam with 2 Fe-SMA bars, the stress distributions in the Fe-SMA bars are very close to the ideal value of 335 MPa (i.e., prestress that can be obtained by activating the Fe-SMA bar in the fully constrained condition) over nearly the entire length of the bars, as shown in Figure 13c. This confirms the idea that the loss of prestress in the studied RC beam systems is due to the combined effects of degradation of the concrete and the elastic shortening during the activation, as the number of Fe-SMA bars is reduced, the cracking as well as the elastic shortening of the concrete during the activation are both reduced. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Number of SMA Bars**} \\ \cline{3-6}  & & **5** & **4** & **3** & **2** \\ \hline \multirow{2}{*}{RC Beam camber (mm)} & FE simulations & 0.423 & 0.340 & 0.258 & 0.171 \\ \cline{2-6}  & Experiments & 0.420 & 0.297 & 0.206 & 0.140 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: RC beam cambers due to activation of Fe-SMA measured by experiments [31] and calculated by FE simulations. Figure 13: Normal \(x\)-axis stress distributions along Fe-SMA bars after activation, calculated by FE simulations with various numbers of Fe-SMA bars. (**a**) With 4 Fe-SMA bars, (**b**) with 3 Fe-SMA bars, and (**c**) with 2 Fe-SMA bars. Evolutions of equivalent stress fields of the concretes with bending deformations, predicted by the FE simulations of the RC beams prestressed with different numbers of the Fe-SMA bars, are shown in Figure 14. It can be seen that the overall stress fields in the RC beams with different numbers of the Fe-SMA bars are very similar, indicating that the stress in the concrete during bending is controlled mainly by the applied bending strain. When the applied bending deflection was higher than 2 mm, a high compressive stress region appears at the upper part of the RC beam near the center due to the bending of the RC beam. At a relatively large bending deflection of 10 mm, heterogeneously distributed localized high stress regions appear near the center of the RC beams, which are indicative of local bending due to the cracking of the concrete. These cracked regions are widely formed in the RC beam prestressed by 4 Fe-SMA bars, and it becomes narrower with decreasing the number of activated Fe-SMA bars. This means that the smaller number of activated Fe-SMA bars causes more concentrated distribution of serious cracking and crushing of the concrete, due to the less prestressing effect. Figure 15 shows the concrete cracking and crashing patterns predicted by the FE simulations, for the RC beams prestressed with different numbers of the Fe-SMA bars. The regions where the concrete is seriously damaged becomes narrower and narrower with a decreasing number of Fe-SMA bars at the same bending deflection, indicating once again that increasing the number of activated Fe-SMA bars can result in more distributed cracking pattern due to the prestressing effect.