# Preliminary Flutter Stability Assessment of the Double-Deck George Washington Bridge
## 4 The George Washington Bridge
### Steady-State Aerodynamic Coefficients and Flutter Derivatives  
Once the Fung formulation was validated, the steady-state aerodynamic coefficients of both the George Washington deck cross-sections were calculated in ANSYS FLUENT. For each section model and different wind attack angles, RANS simulations were performed modeling the turbulence by the \(k-\omega\)\(SST\) method, following the indications in [24; 37]. In order not to interrupt the logical flow of the speech, more information is given in Appendix A. The resulting steady-state aerodynamic coefficients of lift, \(C_{l}\), and moment, \(C_{m}\), are shown in Figure 6, where dashed lines represent the linear regressions. In the case of the double deck (Figure 6b), static coefficients deviate from linearity for higher angles of attack, so the linear regressions are restricted to the intervals \([-2^{\circ};2^{\circ}]\) and \([-1^{\circ};1^{\circ}]\) for lift and moment coefficients, respectively. The first derivatives of static coefficients at the origin, calculated as the slopes of linear regressions, are: \(C_{l}^{\prime}=-6.291\), \(C_{m}^{\prime}=1.902\) for the single-deck and \(C_{l}^{\prime}=-11.024\), \(C_{m}^{\prime+}=1.954\) for the double-deck configurations.  
Flutter derivatives, calculated accordingly by means of Equations (3a)-(3h), are shown in Figures 7 and 8. These were used to calculate the aerodynamic lift and moment actions to be applied to the bridge section.  
For the double-deck section, the lift and moment actions, based on static coefficients of the whole section, are applied to the top deck only, as sketched in Figure 9a. In addition, a second alternative method was adopted, which allows avoiding the use of data in Figure 6b and provides an additional model for comparison and validation of results. This latter method permits the same aeroelastic forces calculated for the single deck to be simultaneously applied to both upper and lower decks, as illustrated in Figure 9b. This procedure assumes that there is no aerodynamic interference between the two decks, whereas the mechanical interference is correctly modeled by the elements composing the truss. Furthermore, the pressure coefficients of the lower deck are assumed to be equal to those of the upper one and the aerodynamic influence of the secondary truss elements is also neglected. Despite the previous simplifications, the advantage of this procedure lies in the greater reliability of the results of CFD analysis for the single deck. Moreover, it can be conjectured that the simplified formulation previously introduced for the calculation of flutter derivatives (see Equations (3a)-(3h)), being based on the aerodynamics of the thin airfoil, is more suitable for the description of the behavior of a single deck rather than of a double deck.  
Figure 6: Steady-state aerodynamic coefficients of lift and moment for the George Washington Bridge. (a) Upper deck; (b) Double-deck.  
Figure 8: Flutter derivatives of the George Washington bridge’s double deck according to Equations (3a)–(3h).  
Figure 7: Flutter derivatives of the George Washington Bridge’s upper deck according to Equations (3a)–(3h).  
Figure 9: Sketch of the alternative methods adopted for the definition and application of aeroelastic loads to the double-deck cross-section. (**a**) Lift and moment actions, based on static coefficients of the whole section, applied to the top deck only; (**b**) Lift and moment actions, based on static coefficients of the single-deck section, applied to both upper and lower decks.