# Assessment of Modal Characteristics of Steel-Concrete Composite Grider Bridge with V-Shaped Piers
## 6 The Effects of Shear Connector on Self-Vibration Characteristics
### Effect of Local Damage of Shear Joints
#### 6.2.1 Shear-Resistant Connectors Vulnerable to Regional Damage  
In the actual use process, the damage location of the shear connectors is difficult to determine; in the negative moment zone of the bridge, as the concrete deck slab is subjected to tensile stress compared with the positive moment zone of the compressive state, the concrete deck slab for the shear nail restraint effect is decreased. Therefore, in the  
Figure 14: First-order vertical vibration diagram of rigid connection/m. Figure 15: One-half design stiffness elastic connection first-order vertical vibration diagram/m. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Modal Order**} & \multicolumn{2}{c}{**One-Half Design Stiffness**} & \multirow{2}{*}{**Design Stiffness**} & \multirow{2}{*}{
\begin{tabular}{c} **Rigid** \\ **Connection** \\ \end{tabular} } \\  & **Stiffness** & & **Connection** \\ \hline
1 & 1.396 & 1.403 & 1.410 \\
2 & 1.882 & 1.911 & 1.939 \\
3 & 3.678 & 3.729 & 3.777 \\
4 & 3.924 & 3.945 & 3.967 \\
5 & 4.283 & 4.366 & 4.446 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Effect of shear-resistant connectors on the self-vibration frequencies of the original structure. background bridge, the shear nail density is much higher than that of the span section at the connection between the bearing and the steel beam and V-shaped piers, which reduces the damage probability of the shear nails to some extent. Therefore, the shear connectors are considered to be damaged first in the mid-span area in which the deflection is the largest. The deflection diagram of the whole bridge is shown in Figure 16.  
From the above figure, it can be seen that the deflection value of the background bridge is higher in the second span, the fifth span and the seventh span mid-span area, and the damage of shear connectors is considered to occur preferentially in this third span mid-span area. In the second span (the fifth span and the seventh span), a shear joint damage zone with a length of 0.1 m was set up to simulate the local shear joint damage by changing the shear joint stiffness in this area. The shear joint damage zone is shown in Figure 17.  
As the shear connectors are flexible connections in the form of shear nails, the form of damage incurred is generally ductile damage, so the damage zone shear connector stiffness were set to design stiffness, one half of the design stiffness, and stiffness to zero (complete damage); the self-vibration frequencies of the original bridge as shown in Table 11. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Modal** & & \multicolumn{2}{c}{**Degree of Damage**} & \\
**Orders** & **Complete** & **One-Half Design** & **Design Stiffness** \\  & **Destruction** & **Stiffness** & **Design Stiffness** \\ \hline
1 & 1.40 & 1.40 & 1.40 \\
2 & 1.91 & 1.91 & 1.91 \\
3 & 3.73 & 3.73 & 3.73 \\
4 & 3.94 & 3.94 & 3.95 \\
5 & 4.36 & 4.36 & 4.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Effect of damage to the vulnerable area of shear joints on the self-vibration frequency of the structure. Figure 16: Schematic diagram of full bridge deflection. Figure 17: Schematic diagram of the damage zone of the shear resistant connector. From the above table, it can be seen that the local damage of the shear connectors has little effect on the self-vibration frequencies of the bridge, especially the first two orders of self-vibration frequencies, which undergo almost no change; the third to fifth-order self-vibration frequency decreases with local damage to the shear connectors. This indicates that the local damage to the shear joint has almost no effect on the overall lateral stiffness of the bridge, but has a certain effect on the slight reduction of the vertical stiffness, and the vibration modes do not change with local damage to the shear joints.