## 4 Results of FEA
### Beam Controlled by Shear  
Figure 17 shows the test (SB-C0) vs. analysis (Case-1) results of the uncorroded shear beam specimen. Table 4 outlines the results of each analysis performed using a total of 12 variables from the reference value \(\beta\) = 1 down to \(\beta\) = 0.4. The ultimate load of the shear beam specimen was 186.8 kN in the analysis (Table 4) vs. 181.9 kN in the test (Table 2), approximately 3% greater in the analysis, and the deflection at the ultimate load was 12.03 mm in the analysis and 11.3 mm in the test, approximately 6% greater. Analysis using VecTor2 yielded results similar to the test results. These results demonstrate that the FEA model used to determine the impact of the decrease in bonding performance of shear beam due to corrosion of rebars on the reduction in structural performance based on strength-deformation capacity is an effective method to understand the correlation between bonding factor (\(\beta\)) and performance degradation factor (\(\phi\)).  
Figure 16: Relationship between bonding factor (\(\beta\)) and average potential difference in terms of voltage (mV) of flexural beam specimens.  
Figure 18 shows the correlation between \(\beta\) and \(\phi\) for each case presented in Table 4, and Figure 19 shows that between the average potential difference in voltage (mV) and performance degradation factor (\(\phi\)) of the shear beam specimens, as conducted in our prior research [1]. The FEA-derived bonding factor (\(\beta\)) and performance degradation factor (\(\phi\)) can be approximated by Equation (13), obtained using regression analysis, and its R\({}^{2}\) = 0.98, which indicates a very high correlation. The mV and \(\phi\) of each specimen tested in the aforementioned prior research can be approximated by Equation (14).  
\[\phi=37.3\beta+63\,\left(Analysis\,:\,\text{R}^{2}=0.98\right) \tag{13}\]  
\[\phi=0.04(\text{mV})+106\,\left(Test\,:\,\text{R}^{2}=0.91\right) \tag{14}\]  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & \multirow{2}{*}{**Bonding Factor (\(\beta\))**} & \multicolumn{2}{c}{**Ultimate**} & \multirow{2}{*}{**Dissipation Energy**} & \multirow{2}{*}{**Performance Degradation**} \\  & & **Load** & & & (kN-mm) & Factor \(\phi\) (\%) \\ \hline Case-1 & 1.00 & 186.8 & 12.03 & 1728.21 & 100.0 \\ \hline Case-2 & 0.95 & 186.2 & 12.03 & 1674.6  
\(\phi\) in Equations (13) and (14) is a coefficient representing the rebar corrosion-induced structural performance reduction (test) and bonding performance (analysis) of shear beams. Because it represents the same physical value, Equations (13) and (14) can be combined to yield Equation (15) to express the relationship between the bonding factor (\(\beta\)) and the average potential difference in voltage (mV). Figure 20 is a schematic representation of the \(\beta\)-mV correlation of shear beams.  
\[\text{mV}=932.5\beta-1075 \tag{15}\]  
Figure 19: Relationship between average potential difference in terms of voltage (mV) and performance reduction factor (\(\phi\)) of shear beam specimens (Test).  
Figure 18: Relationship between bonding factor (\(\beta\)) and performance reduction factor (\(\phi\)) of shear beam specimens (FEM analysis).  
By interrelating the correlation between \(\beta\) and \(\phi\) derived from FEA, as expressed by Equation (13), and that between average potential difference in voltage (mV) and \(\phi\), as expressed by Equation (14), a \(\phi\)-\(\beta\)-mV correlation curve of the flexural beam can be proposed by integrating the \(\beta\)-mV correlation, as expressed by Equation (15), with respect to \(\phi\).