## 4 Results and Comparison
### Thermal Prestressing Effect
#### 4.3.2 Change of Elongation Length  
Various elongation lengths are considered in order to examine the influence of the elongation length in the new closing method. For Case-L1 selected from the previous section, which has an elongation length of 100 mm and the heating regions near the pylons, two additional cases with elongation lengths of 150 mm and 200 mm are added (Table 8 and Figure 11).  
Figure 12 represents the variations of the girder moments according to various elongation lengths. As elongation length increases, positive moments generated at the side spans by the heat removal process increase (Figure 12a). Thus, after construction is completed, the negative moments at the side spans are reduced remarkably with increasing elongation length (Figure 12b). In the center of the main span, there is a small increase in girder moments with increasing elongation length.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Bridge Axis (mm)** & **Vertical (mm)** & **Rotation (Radians \(\times\) 10\({}^{-3}\))** \\ \hline Case-L1 & 100.0 & 265.7 & \(-\)0.52057 \\ Case-L2 & 100.0 & 273.8 & \(-\)0.58151 \\ Case-L3 & 100.2 & 261.5 & \(-\)1.92691 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Displacements at the end of the cantilever girders caused by the heating process.  
Figure 11: Heating regions for various elongation lengths.  
The generated axial girder forces show increases in proportion to the elongation length (Figure 13a). For the state of completed construction, the ratio of the peak compressive axial force to that in the case without using prestressing method is 0.97 for an elongation length of 100 mm, 0.96 for 150 mm, and 0.95 for 200 mm (Figure 13b).  
Figure 12: Girder moments for various elongation lengths. (**a**) Moments generated by heating and heat removal processes; (**b**) Moments after completed construction.  
The variations of cable forces relative to the various elongation lengths are plotted in Figure 14. Only in the side span do the cable forces show variation with changing elongation length. As the elongation length increases, the earth-anchored cables show increased tensile forces whereas the cables anchored to the side span girders show decreased tensile forces.  
Figure 13: Axial girder forces for various elongation lengths. (**a**) Axial forces generated by heating and heat removal processes; (**b**) Axial forces after completed construction.  
For the state of completed construction, the deflections of the girders are plotted in Figure 15 for various elongation lengths. The generated deflections increase in proportion to the elongation length during the thermal prestressing procedure.  
Figure 14: Cable forces for various elongation lengths. (**a**) Cable forces after completed construction; (**b**) Cable force ratio.  
Figure 15: Girder deflections generated by heating and heat removal for various elongation lengths.  
Summarizing the results of major member forces for the various elongation lengths, the increase of the target elongation length generates increased moments and axial forces in the girders and cable forces. In determining the elongation length for the closure of partially earth-anchored cable-stayed bridges, the elongation length is an important factor for enhancing the behavior of cable-stayed bridges. However, the condition of a construction site should be also considered.