## 3 Experimental Results
### Strengthened Beams  
Figure 8a shows the crack distribution of the S1 beams strengthened with steel rods of diameters \(\varphi\)22 mm and \(\varphi\)28 mm. These strengthened specimens exhibited significantly fewer and narrower cracks in comparison to the unstrengthened specimens. However, in comparison with the S2-type specimens, the tensile flexural cracking was significantly reduced. Furthermore, the concrete collapse was deeper than that of the S2 specimens (reaching the deepened neutral axis) due to the relative increase in the tension reinforcements. The distribution of cracks after applying load on the S2 specimens strengthened with steel rods of diameters \(\varphi\)22 mm and \(\varphi\)28 mm is shown in Figure 8b. The two specimens manifested a significant decrease in the number and width of cracks in comparison to the unstrengthened control specimen S2-No. Although further reinforcement resulted in wider and deeper concrete collapse owing to the deepened neutral axis, the number and propagation of the flexural cracks observed at the beam bottom were relatively less. The specimen strengthened with a steel rod of diameter \(\varphi\)28 mm (S2-R28) cracked around the anchorage on top of the support upon attaining the ultimate strength. However, the anchorage did not fail until the completion of the test. Figure 8c indicates the crack patterns of the strengthened S3 beams. When compared to the basic beam, the width and number of the cracks decreased. At the cracking load, flexural cracks occurred near the loading point, and they grew to a height of 260-300 mm in the section at the completion of the test. In S3-R22, while the load increased from the yield load to the ultimate load, concrete crushing started on the left side of the loading point. In S3-R28, concrete crushing occurred over a wider range than in R22. Figure 7: Results of control RC beams: (**a**) measured total load versus mid-span deflection and (**b**) calculated mid-span moment versus curvature relationship. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**Before Cracking**} & \multicolumn{2}{c}{**After Cracking**} & \multicolumn{2}{c}{**At Yielding**} & \multicolumn{2}{c}{**At \(\varepsilon_{\alpha}\) = 0.003**} & \multicolumn{2}{c}{**At \(\varepsilon_{\alpha}\) = 0.005**} & \multicolumn{2}{c}{**At \(P_{max}\)**} \\ \cline{2-13}  & \(\mathbf{k_{initial}}\) & **Decrase** & \(\mathbf{k_{post}}\) & **Decrase** & \(\mathbf{P_{y}}\) & \(\mathbf{\delta_{y}}\) & \(\mathbf{P_{0,003}}\) & \(\mathbf{P_{0,005}}\) & \(\mathbf{\delta_{0,005}}\) & \(\mathbf{P_{max}}\) & \(\mathbf{\delta_{max}}\) \\  & **(dx/mm)** & **(\%)** & **(k/N/mm)** & **(\%)** & **(k/N)** & **(mm)** & **(k/N)** & **(mm)** & **(k/N)** & **(mm)** & **(k/N)** & **(mm)** \\ \hline S1-No & 30.3 & n/a & 16.5 & n/a & 331.3 & 24.8 & 333.4 & 32.8 & 326.6 & 43.9 & 335.6 & 30.1 \\ S2-No & 29.4 & \(-\)2.9 & 12.5 & \(-\)24.2 & 228.2 & 20.3 & 242.9 & 53.1 & 252.3 & 78.0 & 255.0 & 93.4 \\ S3-No & 26.0 & \(-\)14.1 & 10.1 & \(-\)38.5 & 181.2 & 18.2 & 203.9 & 98.1 & 205.5 & 129.2 & 205.9 & 137.0 \\ \hline \hline \end{tabular}  
* Notes: \(\varepsilon_{\alpha}\) is the compressive strain of the extreme concrete measured using crack gauges; \(K_{initial}\) is the initial stiffness before cracking; \(K_{post}\) is the post-stiffness after cracking; \(P_{y}\) and \(\delta_{y}\) are the yield load and its corresponding deflection, respectively; \(P_{0,003}\) and \(P_{0,005}\) are the loads and \(\delta_{0,003}\) and \(\delta_{0,005}\) are the corresponding deflections when \(\varepsilon_{\alpha}\) attained 0.003 and 0.005, respectively; \(P_{max}\) and \(\delta_{max}\) are the maximum load and its corresponding deflection, respectively; n/a = not applicable.  
\end{table} 
Table 3: Summary of measured results of control RC beams. Figure 9a shows the load-deflection and load-rod strain curves of S1-R22 strengthened with a steel rod of diameter \(\varphi\)22 mm.