## 4 Test Results
### AAFs Identified by a Nonlinear Expression  
Figures 8-10 display the identified equivalent AAFs of the DDTG for the service and construction stages under \(\alpha=0^{\circ}\), \(\alpha=3^{\circ}\) and \(\alpha=5^{\circ}\), respectively. According to some previous studies [18; 26], the AAFs can always be fitted by nonlinear expressions, such as the first item in Equation (13). When the test system is installed completely, the system has natural frequencies of vibration in all three measured directions, which have a strong influence on the test accuracy of the force measured method. Limited by the model materials, the manufacturing technique and the connection of each component in the test system, the model resonance cannot be avoided. If only the traditional expression (the first item in Equation (13)) is used to fit AAFs, a serious distortion will occur near the natural frequencies. In this paper, a peak item is introduced to improve the fitting accuracy. Through many trials, the measured AAFs are effectively fitted using the following target nonlinear function:  
\[\left|\chi_{i}(K)\right|_{eq}=\frac{\alpha}{\tau+\beta K^{\prime}}+\frac{c_{1} K^{2}+c_{2}}{(K-c_{3})^{4}+c_{4}K^{2}+c_{5}} \tag{13}\]  
where \(i=D\), \(L\), \(M\); \(K=fB/U\) is the reduced frequency; \(\alpha\), \(\tau\), \(\beta\), \(\gamma\), \(c_{1}\), \(c_{2}\), \(c_{3}\), \(c_{4}\), and \(c_{5}\) are the nine parameters to be fitted; and the second item of Equation (13) on the right-hand side is used to fit the peak of the AAF in the low frequency range. Normally, for a long-span road-rail cable-stayed bridge, the wind-induced sensitive modes usually appear in the first 50 natural modes, and the reduced frequency is usually below 3.0 [30]. Thus, the reduced frequency range was chosen as 0-3.6 in this paper. When the undetermined parameters in Equation (13) were fitted, an undesired peak appeared due to model resonance. The actual AAFs used in the buffeting response analysis of the long-span bridge can be modified by eliminating the fractions in the second item of Equation (13). The identified parameters in the first item of Equation (13) are shown in Table 4.  
In each figure, the modulus of the Sears function derived for the lift force of an aerofoil or a flat plate is also plotted. The Sears function significantly deviates from most measured AAFs of the DDTG in the service and construction stages. The major reason is probably that the Sears function is appropriate only for the lift force AAF of an aerofoil, an ideal flat plate or a flat streamlined box girder section, and the aerofoil section greatly differs from the truss bridge section in this study. In the turbulence, the vertical and oblique web members (see Figure 1) changed the inner flow field between roadway and railway decks, and led the changes of the energy transfer from turbulence to buffeting forces. As the DDTG has a high ventilation rate (58%), there is less wind energy transfer to the structural wind load than the ideal flat with the same height of the DDTG. Therefore, the value of identified \(\left|\chi_{D}\right|\) is always below the Sears function. Comparing the measured \(\left|\chi_{L}\right|\) with the Sears function, similar tendencies are observed between these two AAFs because the double decks of the DDTG have wide flat characteristics and little aerodynamic impact between them. It is generally recognized that the \(\left|\chi_{L}\right|\) and \(\left|\chi_{M}\right|\) have the approximate frequency of peak value in box girder or ideal flat [18]. However, unlike an ideal flat, the different peak frequencies of the DDTG between the lift and torsional equivalent admittances in each stage is significant. The reason is probably that the influence degrees and frequency ranges of the vertical and torsional resonances of the measured system for the lift and pitch moment are different.