## 4 Analysis of Calculation Results
### Live Load Ratio of Cable Girder  
The live load ratio of cable and girder as determined by structural parameters were calculated from Equations (2) and (3) according to structural dimensions of some cable-stayed bridges [16]. The main influencing parameters were stiffness of the main girder and cable-stayed girder, inclination angle of the cable-stayed girder, anchorage spacing, and boundary conditions, among others. The effects of stiffness of the main girder and cables as well as the cable-free zone on overall structural forces were analyzed using the above finite element calculations, while live load ratios of the cable and girder in the background project were calculated using Equations (2) and (3).  
\[\eta=\frac{\sum_{i}E_{ci}A_{ci}\beta_{i}\sin^{2}\alpha\cos\alpha}{E_{\text{G}} I_{\text{G}}} \tag{2}\]  
Figure 9: Comparisons of the structural effects caused by changes in length of the uncorded area in the span. (**a**) midspan bending moment; (**b**) moment at the root of the main girder tower; (**c**) moment at the root of the tower; (**d**) midspan deflection; (**e**) tower top deflection. Note: \(M\)/\(\sum\)M(%), \(\gamma\)/\(\sum\)\(\gamma\)(%) have the same meaning as above.  
\[\beta_{i}=\frac{(l-x_{i})^{2}x_{i}}{24l} \tag{3}\]  
whereby \(\eta\) is the value of the live load ratio of the cable girder ; \(E_{ci},\ A_{ci},\ a_{i},\ x_{i}\) denotes the modulus of elasticity, cross-sectional area, angle and horizontal projection of the _ith cable_; \(E_{G},\ I_{G},\ l\) denotes the elastic modulus, cross-sectional moment of inertia and span diameter of the main girder; \(\beta_{i}\) is the arrangement parameter of the cable on the main girder, which is related to span diameter and support conditions. The background bridge is a multi-tower system with two main piers in the middle and towers and girders on the side. Based on the above equation, the live load ratio of the background bridge cable and girder under corresponding parameter settings was calculated (Table 3).  
The live load ratio of the cable girder decreased with increasing main girder stiffness, and the change amplitude significantly decreased when the stiffness multiplier was three. The large value of the live load ratio of the cable girder resulted in a large vertical load borne by stayed cable and high cable efficiency; with increasing main girder stiffness, the vertical load borne by the main girder increased while cable efficiency decreased, consistent with results from the finite element model. The live load ratio of the cable girder exhibited stable changes with changing stayed cable stiffness. The increase in cable stiffness led to increased vertical load borne by the cable, and the efficiency of the cable increased; when cable-free zone parameters changed in the range of \(l_{1}l_{0}\) = 0.08-0.29, the live load ratio of the cable girder proportionally changed to the parameter, the live load ratio decreased and then increased when \(l_{1}l_{0}\) > 0.29, and the overall change value was small. A reduction in the number led to an improvement in cable utilization efficiency, but with number reduction, the overall stiffness of the structure decreased. It is not better to have a longer length of the cable-free zone in the span.