## 4 Full Bridge Aeroelastic Model
### Model Design and Manufacture  
Because some structural properties, such as axial stiffness of beams or bending stiffness of cables, have little impact on bridge response, it is usually impracticable or unnecessary to represent all structural properties precisely. As a result, the relevance of each property is given due consideration in the modeling of each element, and the modeling simplification is done accordingly.  
The model's deck was comprised of aluminum core beam (simulating the deck stiffness), high-dense foam coats (simulating the deck appearance), auxiliary equipment, and lead compensating weights. The aluminum core beam employed a \"U\" shaped skeleton to meet the identical requirements of lateral, vertical and torsional stiffness of the deck. To replicate the aerodynamic shape, the shape of the concrete deck was simulated with plexiglass, while the shape of the steel deck was simulated with light wood. Auxiliary facilities, such as the central separation belt, various railings, and the maintenance vehicle track and its deflector, were simulated. Lead compensating weights were pasted into the coat to adjust the deck's mass and mass moment of inertia.  
The stay cable was made up of constant wire and spring to simulate its shape and tension. Steel core beams, light wood coats, and compensating weights made up the model's towers and piers. The steel core beams were selected with rectangular sections and their parameters were established to fulfill identical stiffness requirements, and the towers and piers were generally simulated in longitudinal and transverse bending. Furthermore, all support conditions for the deck and towers or piers must be precisely simulated, with the appropriate restrictions and motion releases. This was accomplished by combining the use of leaf springs, wires, and rigid connections. After installation, the full bridge aeroelastic model placed in TJ-3 wind tunnel is shown in Figure 13.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Property** & **Name** & **Scaling Factor** & **Value** & **Property** & **Name** & **Scaling Factor** & **Value** \\ \hline Length & \(\lambda_{\text{L}}\) & — & \(1/150\) & Frequency & \(\lambda_{\text{f}}\) & \(1/(\lambda_{\text{L}}/\lambda_{\text{V}})\) & \(150^{1/2}/1\) \\ Wind speed & \(\lambda_{\text{V}}\) & \({\lambda_{\text{L}}}^{1/2}\) & \(1/150^{1/2}\) & Damping ratio & \(\lambda_{\text{f}}\) & — & \(1/1\) \\ Density & \(\lambda_{\rho}\) & — & \(1/1\) & Time & \(\lambda_{\text{t}}\) & — & \(1/150^{1/2}\) \\ Mass per unit & \(\lambda_{\text{m}}\) & \(\lambda_{\rho}\times{\lambda_{\text{L}}}^{2}\) & \(1/150^{2}\) & Mass moment of inertia per unit length & \(\lambda_{\rho}\times{\lambda_{\text{L}}}^{4}\) & \(1/150^{4}\) \\ Axial stiffness & \(\lambda_{\text{EA}}\) & \(\lambda_{\rho}\times\lambda\
u^{2}\times{\lambda_{\text{L}}}^{2}\) & \(1/150^{3}\) & Torsional stiffness & \(\lambda_{\text{GJ}}\) & \(\lambda_{\rho}\times\lambda\
u^{2}\times{\lambda_{\text{L}}}^{4}\) & \(1/150^{5}\) \\ Acceleration & \(\lambda_{\text{a}}\) & — & \(1/1\) & Bending stiffness & \(\lambda_{\text{EI}}\) & \(\lambda_{\rho}\times\lambda\
u^{2}\times{\lambda_{\text{L}}}^{4}\) & \(1/150^{5}\) \\ Length & \(\lambda_{\text{L}}\) & — & \(1/150\) & Frequency & \(\lambda_{\text{f}}\) & \(1/(\lambda_{\text{L}}/\lambda_{\text{V}})\) & \(150^{1/2}/1\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Scaling parameters for Froude number similitude.