# Research on Effective Design Methods of Core Beam of Full Bridge Aeroelastic Model
## 5 Practical Application
### Core Beam Design of the Bridge Tower  
The rectangular section is used for the cross-section of the bridge tower, the sizes of which vary vertically along the tower height. Due to the changing nature of the tower, it is discretized into ten segments, as shown in Figure 23. The section dimensions of each segment are averaged over its length. In so doing, tower B has ten groups of section properties as the targeted values. The optimization is accomplished by the genetic algorithm, \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mode** & **Targeted (Hz)** & **Measured (Hz)** & **Error (\%)** \\ \cline{2-5} core beam of the deck girder & 1 st-Vertical bending & 1.00 & 0.98 & \(-\)1.93 \\  & 1 st-Side bending & 8.47 & 8.3 & \(-\)2.04 \\  & 1 st-Torsional & 20.49 & 20.3 & \(-\)0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Major modal properties of the tower models. Figure 21: Time history of side-bending-free decay. Figure 22: Time history of torsion-free decay. of which the results are listed in Table 8. According to the properties listed in Table 8, the core beams of the bridge towers are manufactured as shown in Figure 24. The tested torsional and vertical acceleration time histories of the core beam of tower B are given in Figures 25 and 26, and the natural frequencies can be obtained by Fourier transforms. When mass properties are concerned, it can be seen from Table 9 that additional mass is needed for all segments to meet the similarity of mass distribution with the prototype. This is realized by winding thin lead sheets around the core beams. Finally, the aeroelastic models of the two towers are shown in Figure 27. The tested torsional and vertical acceleration time histories of tower B are given in Figures 28 and 29, and the corresponding spectral analysis is also presented. All the tested frequencies and the theoretical ones of the models of bridge tower A and bridge tower B are listed in Table 10 and it shows that the tested frequencies agree very well with the targeted values. Figure 23: The elevation and sectional views of bridge tower B.  
Figure 24: The core beam model test of bridge tower A and B. **(a)** The core beam of bridge tower B. **(b)** The core beam of bridge tower A.  
Figure 25: Time history of torsion-free decay of tower B. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Segment**} & \multicolumn{4}{c}{**Moment of Inertia**} & \multicolumn{2}{c}{**Core Beam**} & \multirow{2}{*}{**Error (\%)**} \\ \cline{2-3} \cline{5-9}  & \multicolumn{2}{c}{**Prototype (m\({}^{4}\))**} & \multicolumn{2}{c}{**Model (mm\({}^{4}\))**} & \multicolumn{2}{c}{**Section (mm)**} & \multicolumn{2}{c}{**Error (\%)**} \\ \cline{2-9}  & **Iz** & **Ix** & **Iz** & **Ix** & **Width** & **Height** & **Iz** & **Ix** \\ \hline B-top & 135.35 & 203.95 & 571.72 & 954.86 & 9.15 & 8.95 & 0.14 & 0.03 \\ B-C & 144.89 & 212.61 & 848.96 & 1426.5 & 10.09 & 9.93 & 0.20 & 0.35 \\ C-D & 154.83 & 221.31 & 907.98 & 1486.0 & 10.34 & 9.86 & 0.03 & 0.30 \\ D-E & 165.18 & 230.05 & 969.42 & 1545.7 & 10.56 & 9.89 & 0.05 & 0.32 \\ E-F & 175.93 & 238.83 & 1033.3 & 1605.7 & 10.80 & 9.84 & 0.01 & 0.08 \\ F-G & 187.10 & 247.65 & 1099.7 & 1666.0 & 11.02 & 9.84 & 0.37 & 0.08 \\ G-H & 198.69 & 256.49 & 1168.7 & 1726.4 & 11.27 & 9.81 & 0.01 & 0.01 \\ H-I & 210.71 & 265.36 & 1240.2 & 1787.1 & 11.49 & 9.80 & 0.03 & 0.14 \\ I-J & 223.17 & 274.27 & 1314.4 & 1848.0 & 11.77 & 9.73 & 0.51 & 0.51 \\ J-K & 226.43 & 276.55 & 1362.0 & 1886.3 & 11.88 & 9.75 & 0.03 & 0.33 \\ L & 84.29 & 145.63 & 510. 7 & 997.42 & 8.55 & 9.80 & 0.04 & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Geometric sizes of core beam sections of bridge tower B.  
Figure 27: Model test of the bridge towers. (**a**) The model of bridge tower B. (**b**) The model of bridge tower A.