## 4 Results of Vehicle-Bridge Coupling Analysis
### Impact Analysis of Vehicle Parameters
#### 4.1.2 Influence of Different Vehicle Weights  
With the continuous development of the highway traffic industry, the phenomena of heavy loads and excessive loads are becoming more and more frequent. The above situation will cause the static load stress of the bridge to become very large over a period of time; furthermore, it will make the damage caused by the dynamic load on the bridge more serious. Therefore, this section chooses six working conditions to study the dynamic response of the bridge. The vehicle weights are \(35\) t, \(45\) t, and \(55\) t, respectively. The stiffness reduction coefficients are \(1\) and \(0.76\), respectively.  
Through the analysis of different vehicle weight conditions, the stress peak values of the lower edge of the concrete section at the midspan, the one-fourth section of the middle span, and the one-third section of the middle span were obtained, and the change rule is shown in Figure 18.  
Figure 16: Peak displacement of each section at different vehicle speeds.  
Figure 17: Dynamic amplification factor of each section at different vehicle speeds.  
It can be seen from Figure 18 that the peak stresses of each section of the damaged bridge under different vehicle weight conditions have obvious changes. When the vehicle weight increases from 35 t to 55 t, the increase rate of the peak stress of the middle section of the middle span is 16.21%, that of the one-fourth section of the middle span is 38.11%, and that of the one-third section of the middle span is 58.58%. Although the dynamic response of the midspan section is the largest, the one-third section has the fastest stress increase rate.  
For the undamaged bridges, with the increase in vehicle weight the stress change of each section is similar to that of the damaged bridges. Under different vehicle weights, the stress at the midspan position is the largest, followed by the one-fourth section, and the one-third section is the smallest. When the vehicle weight increases from 35 t to 55 t, the stress increase rate of the middle span section is 31.03%, the stress increase rate of the one-fourth section is 32.76%, and the stress increase rate of the one-third section is 34.65%. It can be seen that the vehicle weight parameter has a significant effect on the dynamic response of the bridge under the vehicle-bridge coupling vibration, and the impact on the dynamic response of the damaged bridge is more significant.  
The variation laws of the peak value and impact coefficient of the displacement at the one-fourth section and one-third section are shown in Figures 19 and 20. It can be seen that with the increase in vehicle weight, the displacement of each section also increases significantly. Among them, the increase is more obvious in the midspan position. When the vehicle weight increases from 35 t to 55 t, the peak increase rate of the midspan displacement is 22.49%. Figure 20 shows that the displacement impact coefficient of each section of the damaged bridge is different under the condition of vehicle weight, and the impact coefficient keeps increasing with the increase in vehicle weight. The increase in vehicle weight occurs at the same rate, but the impact coefficient increases in a nonlinear way. When the vehicle weight increases from 35 t to 55 t, the midspan impact coefficient increases by about 16.24%. The impact coefficient at the position of the one-fourth section increases by about 13.15%, and the impact coefficient at the position of the one-third section increases by about 11.10%. Although the increase in vehicle weight did not result in a large increment in the impact coefficient, the impact coefficient only reflected the ratio relationship between the dynamic response and the static response. The increase in the dynamic response of each section can indicate that the increase in vehicle weight has a significant impact on the dynamic response of the bridge.  
Figure 18: Stress peak values of each section under different vehicle weights.