# Collapse Analysis of a Two-Span Reinforced Concrete Bridge Model
## 4 Analysis of Collapse Mode
### Influence of Pier Height  
The influence of different pier heights on the collapse process of the model bridge was studied. We assumed that the substructure form of the two-span continuous beam bridge model was unchanged; that is, the pier section size and reinforcement were completely the same, with only the pier height changed to 1.2 m, 1.8 m, 2.4 m, 3 m, and 3.6 m. The selected longitudinal ground motions were still the El Centro wave and Chi\(-\)chi wave. Without considering the influence of vertical ground motions, the longitudinal collapse modes of these five structures under two different ground motions were specified by finite element analysis, as shown in Tables 7 and 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Span/m** & **PGA/g** & **Cracking Time of Upper Edge of Beam/s** & **Collapse Mode** \\ \hline
3.3 & 1.6 & 17.09 & Excessive relative \\
5.3 & 1.4 & 17.3 & displacement between \\
6.7 & 1.2 & 17.48 & pier and beam led to \\
8.3 & 1.2 & 24.26 & falling beam \\ \hline \hline \end{tabular}
\end{table}
Table 6: Longitudinal collapse information of Chi\(-\)chi wave input condition.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pier Height/m** & \
\begin{tabular}{c} **Natural Period** \\ **of Vibration/s** \\ \end{tabular} & **PGA/g** &
\begin{tabular}{c} **Failure Time of** \\ **Middle Pier/s** \\ \end{tabular} & **Collapse Mode** \\ \hline
1.2 & 0.283 & 1.2 & 1.05 & Structural \\
1.8 & 0.338 & 1.2 & 1.07 & collapse caused \\
2.4 & 0.409 & 1.4 & 1.04 & by failure of \\
3 & 0.495 & 1.4 & 1.37 & middle pier \\
3.6 & 0.594 & 2.2 & 1.97 & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Longitudinal collapse information of El Centro wave input condition.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Span/m** & **PGA/g** & **Failure Time of Middle Pier/s** & **Collapse Mode** \\ \hline
3.3 & 1.4 & 1.94 & Structural collapse \\
5.3 & 1.2 & 0.93 & caused by failure of \\
6.7 & 1.2 & 0.9 & middle pier \\
8.3 & 1.0 & 0.91 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Longitudinal collapse information of El Centro wave input condition.  
The higher the pier column, the smaller the longitudinal stiffness of the model bridge. The variation of the seismic response of the bridge model with pier height varied with different types of ground motion.  
The predominant period of the El Centro wave was 0.19 s. When the pier height of the bridge model increased from 1.2 m to 3.6 m, the longitudinal self-vibration period of the bridge was greater than the predominant period and gradually moved away from the predominant period. Thus, the acceleration response of the main beam decreased, and the bridge model could withstand a greater intensity of this kind of earthquake.  
In contrast, the predominant period of the Chi\(-\)chi wave was 0.57 s, which was more than the natural periods of vibration of these five bridge models. With the increase of the height of the pier column, the natural periods of vibration moved closer to the predominant period of Chi-chi wave, meaning that the acceleration response and displacement response of the structure increased and the collapse state appeared earlier, as shown in Table 7 and Figure 19.