## 3 Result Analysis
### Analysis of the Failure Mechanism  
In order to comprehensively assess the failure mechanism of PC beams subjected to impact loading, Figure 15 presents the mid\(-\)span displacement-time history curves, support reaction force, and impact force. The stages of local impact damage, global impact failure, and elastic rebound can be used to categorize the impact process. The start and end positions of each stage are shown in Figure 15a. Along with the failure mode and crack distribution of each specimen, the dynamic reaction of the impact process, the shifting mode of the failure mode, and their interaction are evaluated. (A) Local impact damage \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **QF (J)** & **QR (J)** & **E (J)** & **\(\gamma\)F (\%)** & **\(\gamma\)R (\%)** \\ \hline A1 & 931 & 5720 & 16,464 & 5.65 & 34.74 \\ B1 & 1216 & 11,999 & 16,464 & 7.38 & 72.88 \\ B2 & 1653 & 11,324 & 16,464 & 10.04 & 68.78 \\ B3 & 1402 & 11,405 & 16,464 & 8.52 & 69.27 \\ \hline \hline \end{tabular}  
* **Note:** QF stands for the total energy consumption, which is calculated by integrating the impact force-displacement curve at the span’s midpoint. QR stands for total energy consumption, which is calculated by integrating the reaction force–displacement curve at the span’s midpoint. E represents the input energy. \(\gamma\)F = QF/E, and \(\gamma\)R = QR/E.  
\end{table} 
Table 3: Percentage of the specimen’s entire energy use. stage: the time history curve of the impact force increases rapidly and reaches the primary peak when the falling weight hits the top of the beam. Because the inertial force effect is apparent at the time of contact, the impact force opposes the stiffness of the beam itself, and the material has a higher yield stress at a rapid strain rate; the impact force-time history curve rapidly increases to a higher value. At this point, minute oblique abdominal shear cracks with symmetrical distributions began to appear in the middle span of the test beam. Concrete close to the contact area of the hammerhead undergoes crushing, and there is a localized peeling off of concrete samples. Transverse cracks develop in the superimposed layer when there is no reinforcement or when a 2 mm\(-\)thick steel plate is bonded, and microcracks gradually develop in the beam web as a result of the transmission of the stress wave from the top of the beam downward. Then, the impact force drops to near zero within a short period of time and the local impact damage response phase ends. The local impact damage stage is mainly caused by the major peak portion of the impact force. This can be inferred from the curve above and the failure mechanism of the test beam. Due to the propagation of stress waves, neither the displacement nor the support response force respond at this stage, as their response times are slower than those of the impact force. At the same time, it is shown that the main peak section of the impact force is the main influencing factor in the local impact damage stage, and it has little effect on the overall dynamic response and failure mode of the test beam. (B) Overall impact failure stage: the impact force-time history curve enters the oscillation section after the local impact damage stage, at which point the impact load continues to act. At this point, the displacement-time history curve and the support reaction force-time history curve begin to respond, with the displacement response time being slightly earlier than the support response force. The experimental beam has now reached the stage of global impact failure, which is characterized by an increase in the number of bending fractures that travel upward and inward in the mid\(-\)span stress zone of the bottom of  
Figure 15: The PC beam’s typical dynamic response–time history curve: (**a**) A1, (**b**) B1, (**c**) B2, and (**d**) B3. the beam and the development of oblique downward\(-\)moving cracks in the beam's web. Increased beam deflection and localized concrete damage near the hammerhead contact point occur.