## 4 Calculation Example
### Analysis Model
When synchronous equal proportion tension is adopted, the maximum CR radial deformation of 144 mm, which occurs at the short axis (axis 15), is still unsatisfactory. After the lifting is completed, the expansion of the short axis of the CR is basically large due to the analysis in Section 4.2.1. At the initial stage of synchronous equal proportional tension of the tie-downs, the changes in cable force in the cable net make the forces acted on the CR more uneven, and its uneven deformation further expands, resulting in more obvious outward expansion at the short axis. Therefore, the adjusting objective is set as: reduce radial deformation of the CR. The tie-down tension strategy is adjusted to proportional section tension according to the outward expansion degree of the CR. The initial tension proportion of the tie-downs at the short axis should be larger than that at the long axis and 45\({}^{\circ}\) angle, so as to control the outward expansion deformation at the short axis. Results of Proportional Section Tension  
According to the adjusted tension idea obtained from the analysis in the previous section, the tie-downs are divided into three areas: A, B, and C, as shown in Figure 39.  
According to the tie-down tension sequence, the tension process analysis is divided into six calculation conditions, as shown in Table 16. \begin{table}
\begin{tabular}{c c} \hline \hline
**Calculation Condition** & **State** \\ \hline C1 & Traction lifting completed \\ C2 & Tie-downs tensioned by 20\% in A, 10\% in B, and 5\% in C \\ C3 & Tie-downs tensioned 35\% in A, 20\% in B, and 15\% in C \\ C4 & Tie-downs tensioned 50\% in A, 40\% in B, and 30\% in C \\ C5 & Tie-downs tensioned 65\% in A, 60\% in B, and 50\% in C \\ C6 & All tie-downs tensioned 100\% (tension ring pulled down to design elevation, i.e., pull-down is completed) \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Calculation conditions during proportional section tension. Figure 39: Division of tie-downs. (1-56 represent the NO. of radial cables corresponding to Axis NO.) Tie-down force nephograms in Figure 42 show the distribution of tie-down forces during the tension process. All tie-down forces increase during the whole tension process. The maximum tension force is 547.6 kN, and the cable force of tie-downs at the long and short axes is significantly greater than at 45\({}^{\circ}\). Comparisons and Effects  
The envelope diagram of CR radial deformation before and after adjusting (Figure 43) shows that when the adjusted tie-down tension strategy is adopted, the maximum radial outward expansion deformation of CR can be reduced from 144 to 108 mm. Figure 42: Tie-down force nephograms (N): (**a**) C2, (**b**) C3 (**c**) C4, (**d**) C5, (**e**) C6. Figure 44 shows that the adjusted tension strategy can effectively reduce the CR stress during the tension process and has little effect on the stress level when tension is completed. The maximum equivalent stress is 145.3 MPa. Four representative tie-downs are selected: axis \(1\) (long axis), axis \(5\), axis \(8\) (45\({}^{\circ}\)), and axis \(15\) (short axis). The changes in cable force under various tension conditions before and after adjusting were drawn as cable force curve, shown in Figure 45. The slight difference in cable forces indicates that additional tooling cables will not be wasted due to different tension strategies of tie-downs. Figure 44: Maximum equivalent stress of CR before and after adjusting. Figure 45: Four selected groups of tie-down forces before and after adjusting.