## 3 Experimental Results and Analysis
### Load-Deflection Analysis  
The deflections were measured as negative values after subtracting the vertical displacements from both ends of the support pedestal. The deflections along the beam were recorded at each loading cycle. The load-deflection curves are shown in Figure 10. To provide a clearer representation of the deflection changes with respect to the applied load, the deflections at the mid-span position for each loading level were extracted separately, as shown in Figure 11.  
Figure 10: Load–deflection curves along the length of the beam. Figure 9: Experimental site beam crack diagram. During the loading process, the stiffness of the T-beam gradually decrease as its deflection increases, thus affecting the carrying capacity and normal service performance of the bridge components. Figure 10 shows the load-deflection curves at the mid-span position of the experimental results, and the slope of the curve can reflect the change in the stiffness of the components in different stages. It can be observed in the Figure 11 that there are two distinct inflection points, corresponding to the initiation of cracking in the component and the onset of full plastic stage. By using these two inflection points, the mechanical behavior of the T-beam during the destructive test can be classified into three stages: complete linear stage, incomplete linear stage, and non-linear plastic stage, which is consistent with the observed results in the article [18]. The specific analysis results are as follows:  
1. Complete linear stage: During the initial stage of loading, when the load value is small, the deflection of the beam increases gradually. The load-deflection curve shows a linear relationship between the deflections and the applied load. The slope of the load-deflection curve is the highest during this stage. No cracks are observed, and the stiffness of the T-beam remains essentially unchanged. The material in the T-beam does not reach the yield state. 2. Incomplete linear stage: With the increase in the cyclic loads, the structural carrying capacity gradually decreases. In this process, the deflection verification factor shows an exponential growth trend as the cyclic load value increases. This indicates that, under the criterion of deflection verification factor assessment, the structural carrying capacity fails to meet the requirements for normal use. When the load reached 1030 kN, the deflection at the mid-span section of the beam reached 36.62 mm, marking the occurrence of the first inflection point on the load-deflection curve. At this point, the test beam emitted a continuous sound, and cracks began to appear at the bottom of the beam's mid-span section. Crack dispersion was observed predominantly within the 2.5 m vicinity of the mid-span of the beam, exhibiting a skewed orientation. The average crack width was approximately 0.08 mm, with the maximum crack width measuring 0.12 mm, which corresponded to the cracking load. This cracking load of 1030 kN was almost equal to the predicted cracking load. After the first inflection point, the deflection continued to change linearly with the load, but the slope of the load-deflection curve decreased, indicating a decrease in stiffness. The cracks gradually propagated towards the two ends of the beam as the load increased during this stage. 3. Non-linear stage: As the load further increased to 2380 kN, the deflection at the mid-span section of the beam reached 279.32 mm, marking the occurrence of the second inflection point on the load-deflection curve. The rate of deflection growth accelerated, indicating that the beam has entered the plastic stage. At a load of 2550 kN, the deflection at the mid-span section reached 473.28 mm. At this point, the  
Figure 11: Load-deflection curve at the mid-span position of the T-beam. crack height at the mid-span section is close to the top of the beam, and the maximum crack width was measured at 4.7 mm. A sound was heard from the pre-stress breaking, and the tensile steel bars in the beam began to yield.