## 3 Experimental Results
### Strengthened Beams
Prior to the post-tensioning, the measured stiffness after cracking \(K_{before}\) was 17.5 kN/mm. The stiffness of the strengthened specimen after post-tensioning \(K_{after}\) was 23.2 kN/mm. Post-tensioning was carried out after reducing the load from that at the state when it damaged the unstrengthened beam (\(P_{1 st}\) = 342.7 kN and \(\delta_{1 st}\) = 21.9 mm), to 226 kN. Post-tensioning aided the recovery of the deflection of approximately 4.1 mm at the center, and the tension strain applied to the steel rod \(\varepsilon_{se}\) was measured as 2163 \(\mu\varepsilon\). The beam specimen attained the maximum load \(P_{2 nd}\) and corresponding deflection \(\delta_{2 nd}\) of 469.4 kN and 55.5 mm, respectively, upon continuous reloading after post-tensioning. The deflection continued to increase without a significant increase in the load until the maximum load, followed by a decrease in the load. Although the strain of the concrete compressive-extreme fiber had already reached 0.003 prior to attaining the maximum strength, the strain of the concrete compressive extreme fiber could not be measured subsequently owing to the debonding of the top crack gauge, which was caused by crushing of the concrete. However, it was likely to have exceeded 0.005, considering the linearity of strains measured by crack gauges. The external rod strain of 2163 \(\mu\varepsilon\) with post-tensioning reached 2763 \(\mu\varepsilon\) and 5582 \(\mu\varepsilon\) when the compressive strain of the concrete extreme fiber \(\varepsilon_{cu}\) and the maximum load reached 0.003 and 469.4 kN, respectively. The steel rod yielded at a load of 463 kN and deflection of 71.0 mm between the time the compressive strain of the concrete extreme fiber reached 0.003 and the maximum load reached 469.4 kN. The test ended at the rod strain of 6260 \(\mu\varepsilon\). Figure 8: Crack pattern of strengthened beams: (a) S1 beams; (b) S2 beams; and (c) S3 beams. Figure 9b depicts the load-deflection and load-rod strain curves of S1-R28. The initial stiffness of 17.5 kN/mm immediately before post-tensioning increased to 22.3 kN/mm after strengthening with the steel rods. The mid-span deflection recovered by post-tensioning was approximately 6.4 mm; at this point, the measured steel rod strain was 1841 \(\mu\varepsilon\). The beam specimen attained the maximum load of 521.4 kN and deflection of 59.3 mm after post-tensioning. The strains of the concrete compressive extreme fiber were 0.003 and 0.005 at the deflection stages of 26.0 and 32.5 mm, respectively, prior to attaining the maximum strength. The load continued to increase beyond the yield strength up to the maximum strength and gradually decreased after the maximum load. The test ended at the point of deflection of 100 mm at the beam center. The external rod strain of 1841 \(\mu\varepsilon\) reached 2400, 2572, and 3536 \(\mu\varepsilon\) at \(\varepsilon_{cu}\) = 0.003, \(\varepsilon_{cu}\) = 0.005, and \(P_{2 nd}\) = 521.4 kN, respectively. The strain of the steel rod did not yield, even after attaining the maximum strength, until the completion of the experiment. Figure 10a shows the load-deflection and load-rod strain curves for S2-R22 strengthened with a steel rod of diameter \(\varphi\)22 mm. The stiffness prior to the post-tensioning of 12.5 kN/mm increased to 17.9 kN/mm after post-tensioning, which was performed after reducing the load from \(P_{1 st}\) = 230.2 kN to 154 kN. The post-tensioning recovered a deflection of approximately 5.7 mm, and the effective strain applied to the steel rod was 2153 \(\mu\varepsilon\). The continuous reloading resulted in a maximum load of 419.0 kN and deflection of 66.0 mm. The deflections were 30.4 mm and 41.5 mm at the measured strain of 0.003 and 0.005, respectively, in the concrete compressive extreme fiber; these deflections occurred well before attaining the maximum load capacity.