## 6 Conclusions  
This paper describes aerodynamic admittance investigations conducted for the DDTG used in long-span rail-road cable-stayed bridges. A series of wind tunnel tests were performed based on force measurements to identify the AAFs. A long-span rail-road cable-stayed bridge was used to compare the identified AAFs with two other AAFs (AAF = 1.0 and the Sears function) in terms of the buffeting response. The following conclusions were obtained from this study:  
* The AAFs of the DDTG were successfully obtained in the target turbulent wind field through wind tunnel tests based on the force measurement method. Typical service/construction stages and multiple wind attack angles (0\({}^{\circ}\), 3\({}^{\circ}\) and 5\({}^{\circ}\)) were considered in the wind tunnel tests to identify the AAFs of the DDTG.
* In order to reduce fitting distortion caused by the resonance of the test system in the force measurement method, a modified nonlinear express was put forward to fit the AAFs of the DDTG in this paper. In the nonlinear expression, an additional item was introduced to fit the peak caused by resonance of the test system, and the traditional item was applied to fit the other unaffected experimental value. The combination of these two items can more efficiently match the experimental results of AAFs.
* According to the comparison between the identified AAFs of the DDTG and Sears functions, the Sears function is not applicable to the DDTG in both service and construction stages. With the \(\alpha\) changing from 0\({}^{\circ}\) to 5\({}^{\circ}\), the \(|\chi_{D}|_{con}\) has a greater sensibility to the wind attack angle. When \(\alpha\) = 0\({}^{\circ}\), the vertical and torsion vibration occur more easily in the DDTG because the \(|\chi_{L}|\)_and_\(|\chi_{M}|\) both have larger values than the other wind attack angles.
* A \"fish-bone\" model with an equal mechanical property to the DDTG is put forward in this paper to compensate for the computational insufficiency of the 3D finite element model in the transient  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Direction**} & \multicolumn{3}{c}{**Service Stage**} & \multicolumn{3}{c}{**Construction Stage**} \\ \cline{2-7}  & **Measured** & **Sears** & **1.0** & **Measured** & **Sears** & **1.0** \\ \hline Vertical disp.(m) & 0.346 & 0.198 & 0.215 & 0.312 & 0.156 & 0.171 \\ Lateral disp.(m) & 0.101 & 0.386 & 0.396 & 0.073 & 0.271 & 0.280 \\ Torsion disp. & 6.008 & 7.925 & 8.391 & 10.12 & 10.62 & 10.90 \\ (rad/\(\times\)10\({}^{-5}\)) & & & & & & \\ \hline \end{tabular}
\end{table}
Table 8: RMS maximum value of mid-span in the service and construction stages.  
analysis. Through modal analysis, these two models almost have a similar mode shape and frequency, which confirmed the equivalence of these two models in dynamic analysis.
* According to the buffeting response comparison for three kinds of AAFs (AAF = 1.0, the Sears function and the identified AAFs), the Sears function or AAF = 1.0 leads to an inaccurate response estimation for the DDTG. The Sears function and AAF = 1.0 underestimate the vertical vibration amplitude and overestimate the lateral vibration amplitude in DDTG wind-resistant design.  
All authors discussed and agreed upon the idea and made scientific contributions. [PERSON] designed the wind tunnel tests, obtained the test data and wrote the original paper; [PERSON] and [PERSON] reviewed and modified the paper.  
This research was funded by the National Natural Science Foundation of China grant number [51778043 and 51608031] and the technical research and development project grant number [2014-ZJKJ-03].  
The authors declare no conflict of interest.