## 4 Conclusions  
This study experimentally evaluated and verified the strengthening effect of post-tensioning on an RC beam using external unbonded steel rods. The objective was to examine the effect of such strengthening on damaged RC beams as a technique for rehabilitation or reinforcement. Reinforced concrete beams with different tensile rebar quantities were prepared, and three-point bending tests were performed with different diameters (\(\varphi\)22 mm and \(\varphi\)28 mm) of steel rods in order to evaluate the performance of the steel rods as strengthening members. The beam specimens were damaged by repetitive loading before applying the reinforcement system. Subsequently, the loading was controlled up to the service load after the yield load was attained, and post-tensioning was applied to the steel rod. Tension was applied by tightening the nut of the anchorage, and the initial tension was set to the amount of force required to recover the deflection up to the service load stage or about 2000 \(\mu\varepsilon\) (the strain in the steel rods that two adult men could achieve conveniently). The following conclusions were derived from the flexural strength tests:  
1. External post-tensioning was highly effective in strengthening the RC beams because the strengthened test specimens generally exhibited stable load-deflection behavior after reaching the maximum load, without a rapid decrease in strength. 2. The rehabilitation or reinforcement of the beams using external unbonded post-tensioning steel rods resulted in enhancements exceeding 28% and 40% in stiffness and strength, respectively. Furthermore, the external post-tensioning was effective in controlling the crack width and re-establishing the service load deflections of the RC beams. This method reduced the crack widths or closed the cracks and resulted in a stiffer load-deflection behavior. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Specimen** & \(M_{n,tot}\) & \(M_{n,003}\) & \(M_{n,003}\)/\(M_{n,test}\) & \(M_{n,005}\) & \(M_{n,005}\)/\(M_{n,tot}\) & \(M_{n,Pmax}\) & \(M_{n,Pmax}\)/\(M_{n,test}\) & \(M_{n,mod}\)/\(M_{n,tot}\) \\ \cline{2-10}  & **(kN-m)** & **(kN-m)** & **(v)** & **(kN-m)** & **(v)** & **(kN-m)** & **(v)** & **(kN-m)** & **(v)** \\ \hline S1-No & 318.8 & 260.7 & 0.82 & 265.7 & 0.83 & 259.8 & 0.81 & 265.7 & 0.83 \\ S1-R22 & 445.9 & 403.3 & 0.90 & 414.2 & 0.93 & 414.2 & 0.93 & 414.1 & 0.93 \\ S1-R28 & 495.3 & 446.0 & 0.90 & 470.5 & 0.95 & 480.1 & 0.97 & 480.1 & 0.97 \\ S2-No & 242.3 & 179.4 & 0.74 & 181.7 & 0.75 & 183.2 & 0.76 & 183.2 & 0.76 \\ S2-R22 & 398.1 & 347.4 & 0.87 & 352.3 & 0.89 & 352.1 & 0.88 & 351.9 & 0.88 \\ S2-R28 & 488.1 & 420.9 & 0.86 & 430.3 & 0.88 & 430.0 & 0.88 & 429.8 & 0.88 \\ S3-No & 195.6 & 137.4 & 0.70 & 138.1 & 0.71 & 138.3 & 0.71 & 138.8 & 0.71 \\ S3-R22 & 388.6 & 313.5 & 0.81 & 318.3 & 0.82 & 311.0 & 0.80 & 318.0 & 0.82 \\ S3-R28 & 415.1 & 299.0 & 0.72 & 318.0 & 0.77 & 401.1 & 0.97 & 401.0 & 0.97 \\  & Average & 0.81 & & 0.84 & & 0.86 & & 0.86 \\ Standard deviation & 0.08 & & 0.08 & & 0.09 & & 0.09 \\  & Minimum & 0.70 & & 0.71 & & 0.71 & & 0.71 \\  & Maximum & 0.90 & & 0.95 & & 0.97 & & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Sensitivity analysis of moment capacities with respective to loading step. * 3. Comparing the effects of the external rod diameter, the maximum strength of the beams strengthened with the thicker steel rods was higher; however, the depth of concrete crushing at the ultimate strength was also higher in these beams. * 4. Notably, tensioning played a highly important role in external strengthening. It was also observed that the initial tension of the steel rod was sufficiently effective for recovering the deflection up to the service load stage or approximately 2000 \(\mu\varepsilon\). * 5. The ultimate moment determined using moment capacity analysis was found to be sufficiently accurate and computationally efficient at various loading steps, i.e., \(\varepsilon_{cut}\) = 0.003, 0.005, \(P_{\text{max}}\), and test completion.