## 3 Results and Discussion
### Moment-Deflection Behavior  
Figure 5 illustrates the relationship between mid-span deflection and flexural moment for all specimens. The deflection-moment behavior exhibited by the test beams can be approximated as a tri-linear response. In Phase I, when the beam is uncracked, it demonstrates the highest rigidity. During Phase II, the beam exhibits characteristics of multi-point micro-cracking caused by the combined force-bearing of steel reinforcement and CFRP tendons. The rigidity of the beam in this phase is lower than that of Phase I. During Phase III, the steel reinforcement undergoes yielding, leading to a subsequent decrease in rigidity. This leads to a significant increase in mid-span deflection, ultimately culminating in the failure of the test beam. During the course of these three phases, there is a gradual reduction in the flexural rigidity of the beam. This implies that a strong correlation exists between the short-term deflection of beams reinforced with externally prestressed CFRP tendons and the initial cracks. In Phase I, the slopes of all curves are essentially consistent. Once the breaking load is attained, the disparities in mid-span deflection among the test beams are relatively minor. The reason for this phenomenon is that applying external prestress with CFRP tendons results in an inverted arch in the mid-span of the concrete beams. As the external load surpasses the de-compression load, the concrete beams exhibit downward deflection. Hence, upon reaching the moment of cracking, it can be observed that the CFRP tendons have yet to undergo significant strain. Consequently, the variations in mid-span deflections among the tested beams are rather minor. As the second phase commences, there is a noticeable alteration in the slope of the curve. As illustrated in Figure 5a, the mid-span deflection values of all reinforced beams at the yield point are close to each other, whereas their corresponding flexural moments have shown a notable rise. This finding suggests that the application of CFRP tendons significantly contributes to the enhancement of the beam's rigidity, and the extent of this enhancement is positively correlated to the level of prestress applied. Upon comparing the curves of specimens S-SL-0-0 and S-C-0-0, it becomes apparent that the slope of the curve for S-SL-0-0 becomes steeper during Phase II compared to S-C-0-0. This finding implies that the straight-line arrangement is more effective in enhancing the flexural rigidity of specimens than the curved arrangement. When comparing specimens S-C-30-0 and S-C  
Figure 5: Deflection–moment curves: (**a**) Deflection–moment curves in the span of a simply supported beam; (**b**) comparison of deflection–moment curves in the span of a continuous beam and a simply supported beam. 30-0.2, it can be observed that the slopes of their curves exhibit a high degree of similarity. This suggests that the reinforcement effect is minimally affected by the initial cracks in the reinforced beams. Upon transitioning into Phase III, it can be observed that the slopes of the curves for all reinforced beams exhibit a high degree of similarity, with negligible disparities in terms of the ultimate flexural bearing capacity. The mid-span deflection exhibits a negative correlation with the prestress level, such that a rise in the prestress level results in a decrease in the mid-span deflection. The cooperative deformation of the CFRP tendons with the beams is responsible for this phenomenon. When subjected to excessive prestress, the occurrence of smaller mid-span deflections can result in the CFRP tendons reaching their ultimate strength, thus causing the test beams to undergo failure. Figure 4(b) illustrates the deflection-moment curves for singly supported beams and continuous beams, both subjected to identical reinforcing circumstances. It can be observed that the mid-span deflection of the continuous beam reinforced with a CFRP tendon is lower than that of the simply supported beam.