## 4 Calculation Example
### Analysis Model
#### 4.2.3 Analysis of the Whole Construction Process
Finally, the deformation (especially vertical deformation) of the tension ring returns to a level close to 0 in C43. Figure 51 shows the variation in maximum equivalent stress of CR, roof radial truss, structural columns, and CR brackets, which clearly illustrates the three stages of the whole construction process. In the first stage (C1-C2), the maximum equivalent stress of the whole structure is low and increases rapidly, which reflects the cable net construction process. In the middle stage (C3-C40), tie-downs start to control the configuration of the cable net, resulting in stable stress for the whole structure. In the third stage (C41-C43), the maximum equivalent stress of the CR and the structural column further increases with the structure formation, and the maximum equivalent stress in the radial main truss and CR brackets will decrease after the tie-downs are removed. In the whole construction process:  
Figure 49: Vertical deformation Uz curve of typical nodes of tension ring (mm). Figure 50: Tension ring clamp nodes. (1–15 represent the tension ring cable clamps’ nodes NO. corresponding to the axis.) the maximum equivalent stress of the CR is 171 MPa, which occurs in the third stage (C42); the maximum radial main truss stress is 125 MPa, in the third stage (C41); the maximum structural column stress is 59.4 MPa, in the third stage (C43); and the maximum CR bracket stress is 82.5 MPa, in the middle stage. Figure 52 shows the change in radial cable forces under typical calculation conditions. Considering the symmetry of the structure, 1-15 axis 1/4 symmetrical cables are selected, as shown in Figure 53. At first (C1-C2), the pre-tension is preliminarily established inside the cable net while the radical cable forces are still relatively small. Then, in the subsequent tie-down tension and upper grid hoisting conditions (C3-C40), the tie-downs basically control the cable net configuration at the design position, and the radial cable forces are large and stable. Finally (C41-C43), the whole structure is lifted up and the radial cable forces decrease slightly after the tie-downs are removed, and then return to the stable middle stage level when the entire structure is finally formed. Figure 51: Maximum stress variation curve of four types of components under various calculation conditions (MPa). Figure 52: Cable force variation curve of three typical radial cables under various calculation conditions (kN). Figure 54 shows that during the whole construction process, the maximum internal force of all CR brackets is 792 kN, which occurs at 45\({}^{\circ}\), and the CR support force at the long and short axes is relatively small. Comparison between Analysis Results of Construction Process Forming State and Dead Load State  
(1). Comparison of vertical deformation of tension ring nodes  
Figure 55 compares the vertical deformation of 56 typical nodes of the tension ring in the construction forming state and the dead load state, which shows that the simulation results are slightly larger for the non-bracket construction forming method than the dead load state, with maximum deformation of \(-\)32.25 mm and minimum deformation of \(-\)22.26 mm. The maximum difference between the two results is 16.5 mm, which can be considered negligible. Figure 46:0 Variation curve of maximum internal force of each CR bracket (kN). Figure 46:1 Radial cables. (1\(\sim\)15 represent the radial cables’ NO. corresponding to the axis.) (2). Comparison of vertical deformation at the inner cantilever end of radial main beam  
Figure 56 compares the cantilever end deformation of 56 radial main beams in the construction forming state and the dead load state. The analysis results of the construction process are slightly larger than the dead load state results, with maximum deformation of \(-49.35\) mm and minimum deformation of \(-8.3\) mm, and the difference between the two results is small. (3).