# Calculation Method of Rotational Constraint Stiffness for a New Tower-Pier Connected System
## 5 Case Study: An Inclined Single-Tower Cable-Stayed Bridge
### Verification of RCS Calculation Model Based on Monitoring Data  
The deformation along the longitudinal direction of the viewing platform is used to reflect the rotational displacement of the bridge tower to more clearly exhibit the rotational effect of the bridge tower. Reference point 1 (RP1) and reference point 2 (RP2) are set on the viewing platform, and are employed as the monitoring points for the rotation displacement of the bridge tower during the construction process, as shown in Figure 19.  
Two FE models considering the RCS of the UHS (the rotational restraint stiffness calculated from Equation (15)) and without considering the RCS of the UHS (the rotational stiffness is zero) are established, respectively, both of them include the entire construction process. The influence of the RCS on the attitude of the bridge tower in each construction stage is analyzed. The same tension is applied to the two models, respectively, and the bridge tower states at each construction stage are obtained. A comparison of the rotation angle of the bridge tower in each construction stage of the two models is shown in Figure 20.  
Figure 19: Layout of monitoring points.  
Figure 18: The critical torque and reaction torque under various conditions.  
Figure 20 shows that whether the RCS is considered or not will make a significant difference when designing the bridge tower during construction. The maximum difference occurs at stage 14, which is reflected by the maximum difference of the displacement at the monitoring point along the longitudinal direction of the bridge, which is about 265 mm, and this error is unacceptable for construction. If the inducement of the error caused by the failure to consider the RCS is not learned for engineers, it may mislead engineers into thinking about other induction factors, further leading to a wrong decision. Therefore, it is significant for accurately obtaining the rotational displacement of the tower to take into account the RCS at each construction stage.  
Readjust the tension of the cable according to the calculated RCS, analyze and calculate the deformation of the bridge tower at each construction stage, and compare it with the measured value, as shown in Figure 21.  
Figure 21 shows that the maximum difference between the theoretical rotation angle and the measured one occurs at stage 8 (tensioning the main beam cable B2), where its value is 0.04\({}^{\circ}\). This equates to about 15 mm through the displacement of the monitoring point along the longitudinal direction, and this error is acceptable in engineering. Analyze the reasons for the errors, which may be caused by a long measuring distance, systematic error of the measuring instrument, etc. In addition, compared with the condition that does not consider RCS, the error of the measured and calculated rotational displacements is reduced by about 90%. Therefore, the proposed method in this paper is a great approach to effectively calculate the RCS in practical applications.  
Figure 20: Comparison of the rotation displacement of the bridge tower.