## 3 Results and Discussion  
### Failure Modes and Flexural Moments  
The failure modes exhibited by the test beams can be classified into three distinct categories: (1) Typical Flexural Failure (Figure 4a,g). Once the yield moment is reached, the steel reinforcements within the beam begin to yield. The mid-span deflection demonstrates noticeable non-linearity until it reaches its maximum flexural bearing capacity. (2) Concrete Compression Failure in the compression zone (Figure 4e). In cases where the prestressing level of externally prestressed CFRP tendons is relatively low, a notable mid-span deflection arises following the yielding of steel reinforcements and persists until the beam failure stage. At this time, excessive compressive strain is generated in the compression zone, resulting in premature failure. (3) Failure of Beam Flexure due to Rupture of CFRP Tendon. In situations with significant external prestress, the CFRP tendons rupture and can no longer bear any load upon reaching their ultimate strain. At this point, the beam still supports a high level of external load, resulting in a rapid increase in mid-span deflection, leading to the beam's flexural failure. Figure 4: _Cont._  
Table 3 presents the characteristic flexural moments and failure modes of each test beam. The experimental results show that externally prestressed reinforcement using CFRP tendons can enhance the cracking moment, effectively delaying the yielding of the steel reinforcement and improving the ultimate flexural bearing capacity. Upon comparing specimens SCB, S-C-0-0, and S-C-30-0, it was noted that the application of prestressed CFRP tendons resulted in an increase in the ultimate flexural bearing capacities of the simply supported beams. Specifically, the flexural bearing capacities improved from 65.6 kN\(\cdot\)m to 160.6 kN-m (a 145% improvement) and 172.8 kN\(\cdot\)m (a 163% improvement) for specimens S-C-0-0 and S-C-30-0, respectively. In comparison to the beam CCB, the continuous beam C-C-30-0 experienced a significant increase in its ultimate flexural bearing capacity, rising from 75.1 kN\(\cdot\)m to 159.6 kN\(\cdot\)m (a 113% improvement). By applying an external prestress of 30% to the CFRP tendons, the flexural bearing capacity of the simply supported beam increased by 107.2 kN\(\cdot\)m, whilst the continuous beam saw an increase of 84.5 kN\(\cdot\)m in its flexural bearing capacity. This indicates that under the same external prestressing condition of the CFRP tendons, the increase in the ultimate flexural bearing capacity of the simply supported beams is greater than that of the continuous beams. The test beams S-C-0-0 and S-C-30-0 have ultimate flexural bearing capacities of 160.6 kN\(\cdot\)m and 172.8 kN\(\cdot\)m, respectively. In contrast, it can be observed that increasing the prestressing level in externally prestressed CFRP tendons results in a mere 7.6% increase in the ultimate flexural bearing capacity. This implies that merely altering the prestressing level of the CFRP tendons cannot significantly enhance the ultimate flexural bearing capacity of the concrete beams. The ultimate flexural bearing capacity of the specimen S-C-30-0.2 is 168 kN\(\cdot\)m. Compared to the specimen S-C-30-0, with a capacity of 172.8 kN\(\cdot\)m, the ultimate flexural bearing capacity decreased only by 2.8%. This indicates that the initial damage incurred by the reinforced test beams has a negligible impact on their ultimate flexural bearing capacity. It can therefore be concluded that the influence of the prestressing level and the initial cracks on the ultimate flexural load-carrying capability of the beams is relatively insignificant. In comparison to the SCB specimen, the beams S-SL-0-0 and  
Figure 4: Failure modes of concrete beams; (**a**) SCB; (**b**) S-SL-0-0; (**c**) S-C-30-0; (**d**) S-C-30-0.2; (**e**) S-C-0-0; (**f**) S-C-50-0.2; (**g**) CCB; (**h**) C-C-30-0.