## 3 Result Analysis
### Analysis of the Time History Curves for Impact and Support Response Forces  
Figure 11 illustrates the time\(-\)history curves of the impact force and the support response force for test beams A1-B3. Time history curves for impact forces and support response forces are shown in black and red, respectively. It is generally possible to divide the impact\(-\)force-time history curve into segments for the primary wave peak, oscillation peak, secondary wave peak, and attenuation peak. The beginning and end points of each segment are shown in Figure 11a. (A) Main wave peak segment: at the beginning of the impact, the impact force resists the stiffness of the beam itself, and the impact force value increases rapidly and reaches the main peak value within 1 ms. The main peak value of each test beam is between 3353 and 3684 kN. The beam moves downward due to the impact force. When the speed of the hammerhead is the same as that of the beam body, the impact force decreases to zero. At this time, the main peak of the impact force ends. The duration of this process is between 1.06 and 1.21 ms. However, during the impact phase, the impact force has a negative value. There is a lack of rigorous display programs and the impact force value is high, indicating an overflow, which is to blame. (B) Oscillation segment: after the impact force reaches the main peak, the impact force-time history curve fluctuates slightly. This is because the hammerhead is still at the top of the beam body at this time, and the stress wave is continuously reflected in the beam body along the height direction, which is a manifestation of the energy dissipation of the beam body itself. (C) Secondary wave peak segment: after a relatively long period of low vibrations, the impact force gradually increases and appears as a secondary peak caused by the test beam's secondary impact after the hammerhead rebounds. The peak value of the secondary peak is low, between 406 and 442 kN, which is only 11.7% to 13.8% of the peak value of the main peak; however, the duration of the secondary peak is longer, ranging from 3.96 to 4.93 ms. The secondary wave peak segment ends when the hammerhead speed is the same as the test beam speed. Figure 11: Time history curve of the impact and support reaction forces of the specimen: (**a**) A1, (b) B1, (c) B2, and (**d**) B3. (D) Attenuation segment: the impact force value gradually decreases after two wave peaks and remains close to zero. Since the energy level of the hammerhead is low and the energy of the beam body rapidly diminishes, there is no visible fluctuation or shock at this point. As the thickness of the bonded steel plate increases, the peak value of the main wave of the impact force does not change as much as compared to the impact force-time history curves of the A1, B1, and B2 test beams. This is because the impact force is mainly affected by the local contact state and stiffness between the drop hammer and the PC beam, so the strengthening of the beam bottom has little effect on the impact force. There is a similar duration in the main peak section of the impact force, and the curve has a faster initial response. However, the rate of increase in the impact force slows down and the impact area of the impact force-time history curve has a smaller range of fluctuations. The most moderate oscillation segment belongs to the time history curve of the impact force of the B2 test beam. The reason behind this is the significant increase in local damage to the contact surface of the hammerhead with the 4 mm\(-\)thick steel plate. The impact\(-\)force-time history curves of test beams B1 and B3 are comparable when compared to each other. However, the impact force value increases when the beam is strengthened with U\(-\)shaped steel plate hoops, indicating that the U\(-\)shaped steel plate hoop increases the stiffness of the test beam. While the duration of the secondary wave peak segment increases significantly and its generation time is delayed, the duration of the main wave peak segment is marginally reduced.