## 5 Analysis of Deformation Performance of CFRP-Strengthened Corroded RC Beams under Fatigue Loading
### Formulation and Verification of Mid-Span Deflection for CFRP-Strengthened Beams
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Beam ID**} & \multirow{2}{*}{\(\mathbf{\eta_{5}}\)**(\%)**} & \multirow{2}{*}{**Fatigue Cycles \(\mathbf{N}\)**} & \multirow{2}{*}{**Experimental Result**} & \multirow{2}{*}{**Calculated Result**} & \multirow{2}{*}{**[\(\mathbf{f_{e}}-\mathbf{f_{ca}}\)]/\(\mathbf{f_{e}}\)] (\%)**} & \multirow{2}{*}{**[\%)**} & \multirow{2}{*}{**\(\mathbf{f_{e}}\)**/\(\mathbf{f_{ca}}\)**} \\ \cline{5-8}  & & 1 & 3.68 & 4.39 & \(-\)19.29 & 0.84 \\ \multirow{5}{*}{Beam 19 [8]} & & 10 & 4.00 & 4.44 & \(-\)11.00 & 0.90 \\  & & 100 & 4.08 & 4.54 & \(-\)11.27 & 0.90 \\  & & 1000 & 4.09 & 4.70 & \(-\)14.91 & 0.87 \\  & & 10,000 & 4.23 & 4.93 & \(-\)16.55 & 0.86 \\  & & 100,000 & 4.66 & 5.25 & \(-\)12.66 & 0.89 \\ \hline \multirow{5}{*}{Beam 20 [8]} & & 1 & 3.61 & 4.30 & \(-\)19.11 & 0.84 \\  & & 10 & 3.74 & 4.35 & \(-\)16.31 & 0.86 \\ \multirow{5}{*}{Beam 20 [8]} & \multirow{2}{*}{14.3} & 100 & 3.91 & 4.45 & \(-\)13.81 & 0.88 \\  & & 1000 & 4.32 & 4.60 & \(-\)6.48 & 0.94 \\  & & 10,000 & 4.60 & 4.83 & \(-\)5.00 & 0.95 \\ \hline \multirow{5}{*}{Beam 21 [8]} & & 1 & 3.32 & 4.07 & \(-\)22.59 & 0.82 \\  & & 100 & 3.40 & 4.21 & \(-\)23.82 & 0.81 \\ \multirow{5}{*}{Beam 21 [8]} & \multirow{2}{*}{13.6} & 1000 & 3.72 & 4.36 & \(-\)17.20 & 0.85 \\  & & 10,000 & 3.93 & 4.57 & \(-\)16.28 & 0.86 \\  & & 100,000 & 4.17 & 4.87 & \(-\)16.79 & 0.86 \\  & & 150,000 & 4.26 & 4.93 & \(-\)15.73 & 0.86 \\ \hline \multirow{5}{*}{Beam No. 8 [23]} & & 1 & 0.93 & 0.88 & 5.38 & 1.06 \\  & & 50,000 & 1.11 & 1.04 & 6.31 & 1.07 \\  & & 250,000 & 1.19 & 1.09 & 8.40 & 1.09 \\  & & 500,000 & 1.21 & 1.12 & 7.44 & 1.08 \\  & & 1,100,000 & 1.34 & 1.15 & 14.18 & 1.17 \\ \hline \multirow{5}{*}{Beam No. 10 [23]} & & 1 & 1.00 & 1.01 & \(-\)1.00 & 0.99 \\  & & 10,000 & 1.16 & 1.13 & 2.59 & 1.03 \\  & & 200,000 & 1.42 & 1.24 & 12.68 & 1.15 \\  & & 500,000 & 1.50 & 1.28 & 14.67 & 1.17 \\ \hline \multirow{5}{*}{A3 [29]} & & 1 & 1.25 & 1.40 & \(-\)12.00 & 0.89 \\  & & 15,000 & 1.49 & 1.58 & \(-\)6.04 & 0.94 \\  & & 30,000 & 1.52 & 1.61 & \(-\)5.92 & 0.94 \\ \multirow{5}{*}{B3 [29]} & \multirow{2}{*}{13.4} & 40,000 & 1.54 & 1.63 & \(-\)5.84 & 0.94 \\  & & 300,000 & 1.68 & 1.73 & \(-\)2.98 & 0.97 \\  & & 500,000 & 1.81 & 1.76 & 2.76 & 1.03 \\  & & 1,200,000 & 2.07 & 1.87 & 9.66 & 1.11 \\ \hline \multirow{5}{*}{B3 [29]} & & 1 & 8.72 & 9.64 & \(-\)10.55 & 0.90 \\  & & 10,000 & 9.85 & 10.82 & \(-\)9.85 & 0.91 \\ \cline{1-1}  & & 50,000 & 10.08 & 11.29 & \(-\)12.00 & 0.89 \\ \cline{1-1}  & & 75,000 & 10.20 & 11.43 & \(-\)12.06 & 0.89 \\ \cline{1-1}  & & 100,000 & 10.38 & 11.53 & \(-\)11.08 & 0.90 \\ \cline{1-1}  & & 300,000 & 11.07 & 11.95 & \(-\)7.95 & 0.93 \\ \hline \multirow{5}{*}{D3 [29]} & & 1 & 2.54 & 2.81 & \(-\)10.63 & 0.90 \\ \cline{1-1}  & & 10,000 & 3.00 & 3.15 & \(-\)5.00 & 0.95 \\ \cline{1-1}  & & 50,000 & 3.16 & 3.29 & \(-\)4.11 & 0.96 \\ \cline{1-1}  & & 100,000 & 3.33 & 3.36 & \(-\)0.90 & 0.99 \\ \cline{1-1}  & & 500,000 & 3.29 & 3.55 & \(-\)7.90 & 0.93 \\ \cline{1-1}  & & 1,000,000 & 3.42 & 3.64 & \(-\)6.43 & 0.94 \\ \cline{1-1}  & & 2,000,000 & 3.55 & 3.75 & \(-\)5.63 & 0.95 \\ \hline \multicolumn{5}{c}{Average value} & & & & 0.95 \\ \multicolumn{5}{c}{Standard deviation} & & & & 0.09 \\ \multicolumn{5}{c}{Coefficient of variation} & & & & 0.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Verification of mid-span deflection calculation Formula (24).