## 6 Conclusions  
In summary, through comparison and analysis, the following conclusions are drawn.  
1. The internal structural force and deformation sensitivity are higher when \({E_{\mathrm{G}}}^{\prime}{I_{\mathrm{G}}}/{E_{\mathrm{G}}}{I_{\mathrm{G}}}<1\). When this condition is met, a change in main girder stiffness of the rigid girder and flexible tower type partially cable-stayed bridge has less effect on the internal force of the main tower. However, when the main girder stiffness multiplier exceeds three, the maximum deflection of the bridge tower and the span mid-span lower deflection do not change significantly.
2. The influence of cable stiffness on the main girder moment and deformation is significant. As the stiffness increases, the main girder midspan bending moment and deflection show a large reducing trend; the main tower bending moment and deflection change value is small, and the main girder tower root moment produces a very small change in cable stiffness with a multiplier of 0.8-1. The influence of cable stiffness change on the side and middle towers also varies.
3. The change in the length of the cable-free zone in the span has a greater influence on the bridge force and deformation of the main girder than that of the cable-free zone at the tower root and the main tower. As the length of the cable-free zone at the bottom of the tower increases, the negative bending moment at the main girder's root also increases proportionally. In addition, the main tower deflection decreases gradually and stops when the length of the cable-free zone in the span rises to a specific value.
4. The change in the live load ratio of the three parameters is consistent with the conclusion obtained from the finite element analysis. In addition, the overall stiffness of the structure can be improved by increasing the stiffness of the main girder and the stayed cable.
5. Combined with the multi-parameter coupling model, the three parameters of main girder stiffness (\({E_{\mathrm{G}}}{I_{\mathrm{G}}}\)), stayed cable stiffness (\({E_{\mathrm{C}}}{A_{\mathrm{C}}}\)) and mid-span cable-free zone length (\({I_{1}}\)) are calculated. From this calculation, the optimal range of values for the parameters are as follows: \({E_{\mathrm{G}}}^{\prime}{I_{\mathrm{G}}}/{E_{\mathrm{G}}}{I_{\mathrm{G}}}=1 \)-3, \({E_{\mathrm{C}}}{A_{\mathrm{C}}}^{\prime}/{E_{\mathrm{C}}}{A_{\mathrm{C}}}=0.8 \)-1.4 and \({I_{1}}/{I_{0}}=0.08\)-0.15, with a medium to high coupling coordination among them. Through this coordination, the parameters promote each other, resulting in good static performance of the background project bridge.  
Conceptualization, W.H.; software, W.H. and X.T.; validation, Y.Z.; formal analysis, Y.Z.; writing--original draft preparation, W.H.; writing--review and editing, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the Natural Science Foundation of China (Grant Nos.52078059), the Science and Technology project of Powerhina Roadbridge Group Co., Ltd. (No. LOKY2016-02).  
Not applicable.  
The data in this article are available from the corresponding author.  
The authors declare no conflict of interest.