## 3 Experimental Results  
### Unstrengthened Beams  
Figure 6 indicates the typical crack distributions in an RC beam. Generally, the cracking behavior of an RC beam can be described as composed of three stages: the first is the initiation of cracking, the second is the yield of the tensile rebar, and the third is the concrete crushing collapse [38]. Similarly, in this test, flexural cracking occurred from the bottom of the beam center upon attaining the crack load. The gradual loading resulted in a wider crack and the propagation of the crack toward the support. As the propagation of the cracks involved simultaneous shear cracking and flexural cracking, diagonal cracking was observed toward the support. After the tensile rebar yielded, a plastic hinge occurred around the loading point, causing the cracking to propagate further, and the collapse of the concrete around the loading point started. Moreover, at this point of tensile rebar yielding, the increase in load was not significant and only the deflection increased. Upon attaining the final failure of the specimens, the compressive collapse of concrete in the specimens S1-No, S2-No, and S3-No was observed at the distances of 1200, 1000, and 600 mm, respectively, on the left and right sides of the loading point. The more the number of tensile rebars in the test specimen, the fewer were the hairline cracks and the narrower were the cracks observed.  
Figure 7a shows the load-deflection curves of the control specimens. The yield load for the specimen S1-No was 331 kN, and the corresponding mid-span deflection was 24.8 mm. This specimen manifested ductility until the strain of the compressive concrete extreme fiber attained 0.013 with no indication of rapid load decrease. The specimen S2-No yielded at the deflection of 20.3 mm and load of 228 kN. The specimen S3-No started to yield at the deflection of 18.2 mm and load of 181.2 kN. Moreover, the two beams exhibited sufficient ductility until the strain of the compressive concrete extreme fiber attained 0.016 and 0.007, respectively, with no indication of load decrease.  
The mid-span curvature curves in Figure 7b are plotted with the strain of the section as measured using the crack gauges installed as illustrated in Figure 4. The curvature of S1-No could not be computed until the completion of the experiment owing to an early debonding of the crack gauge caused by the compressive collapse of the extreme concrete fiber.  
Table 3 summarizes the experimental results such as the stiffness, load capacity, and corresponding deflection of the unstrengthened control specimens. All the specimens exhibited similar crack load \(P_{cr}\) and deflection \(\delta_{cr}\) of approximately 50 kN and 2.3 mm, respectively. The initial stiffness \(K_{initial}\) of about 30 kN/mm decreased to the post-stiffness \(K_{post}\) of 16.5 kN/mm for S1-No and 12.5 kN/mm for S2-No. For S3-No, the initial stiffness was 26.0 kN/mm, and the post-stiffness after cracking was 10.1 kN/mm. Comparing the deflections, when the compressive strains \(\epsilon_{cu}\) of the extreme concrete fiber were 0.003 or 0.005, as measured using the crack gauges, the deflection tended to decrease with a higher number of tensile rebars. The strain of 0.003 represents the maximum strain (or ultimate strain or failure strain) of the compressive extreme fiber as assumed during the typical flexural design of the RC beam [37].  
Figure 6: Experimental crack pattern of unstrengthened beams.  
The strain of 0.005 refers to the maximum value of the strain of the compressive concrete as used more practically in the rehabilitation and reinforcement of RC structures [39; 40]. This study investigated the stepwise change at strains exceeding 0.003 in the compressive extreme fiber.