## 4 Results and Comparison
### Thermal Prestressing Effect  
#### 4.3.1 Optimal Heating Region and Effects of the Closing Method  
For the three cases, which have different heating regions, structural behaviors are examined using the new closing method. First, the girder moments are compared for the three cases. Figure 7a shows the girder moments generated by the heating and heat removal processes. Case-L1 with the heating region near the pylons shows the smallest moments in the main span, while Case-L3, which has a heating region near the center of the main span, shows the largest moments. In the side span, the heat removal process gives only the new member forces, and there is little difference among the three thermal cases. For a completed construction state, the girder moments are compared with those in the case without using the new closing method, which assumes only set back and reset back processes ignoring the difficulty of the installation process. Case-L3 shows the increase of girder moments in the center of the main span, whereas Case-L1 and Case-L2 show similar moments to those in the case without thermal prestressing effects (Figure 7b). In the side span, all cases with thermal prestressing show similar or decreased moments resulting from the new member forces using the heat removal process. The peak girder moment in the side span is reduced by about 23%. Figure 7: Girder moments according to the heating region. (**a**) Girder moments generated by heating and heat removal processes; (**b**) Girder moments after completed construction. Variations of axial forces according to the various heating regions are represented in Figure 8. As for the girders near the pylons, the three cases show similar axial forces generated by the heating and heat removal processes. In the main span, Case-L3 with the heating region near the center of the main span shows the largest generated tensile force among the three cases. Thus, after construction is completed, Case-L3 shows the largest tensile force in the main span girder. Since tensile forces in the girder generated by heat removal are accumulated in the bridge system, the peak compressive axial force near the pylons is reduced in cases with thermal prestressing after construction. The peak values are reduced by about 3%. The cable forces are compared for the completed construction state (Figure 9). In the earth-anchored cables, the cable forces are increased by about 3% using the proposed method. However, cables near the earth-anchored cables show decreased cable forces. From the cable forces of the main span, it is found that Case-L3 shows the variation of cable forces, whereas Case-L1 and Case-L2 show similar cable forces to those in the case without thermal prestressing. Figure 8: Girder axial forces according to the heating region. (**a**) Axial forces generated by heating and heat removal processes; (**b**) Axial forces after completed construction. The deflections of the girders are compared. Figure 10 represents the girder deflections caused by the heating and heat removal processes according to the heating region. Among the three cases, Case-L1 with the heating region near the pylons shows the smallest slope during the heating process, while Case-L3 with the heating region near the center of the main span has the steepest curve. In addition, Case-L1 shows the smallest variation of displacements during the heat removal process. Table 7 represents the displacements at the end of the cantilever girder caused by the heating process. Even though Case-L3 has the smallest displacements, this case has the largest rotation because it has the steepest curve. This is because the deflection occurs in a small region. Case-L1 shows the smallest value for the slope of the deflections and girder end rotation since it contains the large-deflection region. Figure 10: Girder deflections generated by thermal prestressing for different heating regions. Figure 9: Cable forces according to the heating region. (**a**) Cable forces after completed construction; (**b**) Cable force ratio.