# Effect of Prestress Levels and Jacking Methods on Friction Losses in Curved Prestressed Tendons
## 4 Test Results and Discussion
### Comparison of Theoretical and Measured Prestress Forces  
Figures 5 and 6 compare the prestress forces at the jacking end and midspan when there was no friction loss, when only the theoretical friction loss was considered, and when two measured friction losses were considered. The first and second prestress forces for tendon 3 in the GBE girder jacked at both ends measured at the midspan were 83.7% and 89.2% of the prestress forces measured at the jacking ends on average, and the theoretical prestress forces corresponded to 88.9% of the actually introduced prestress force on average.  
Figure 5: Prestress forces between jacking end and midspan: GBE.  
Figure 6: Prestress forces between jacking end and midspan: GOE.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & & \multicolumn{3}{c}{GBE (kN)} & \\ \cline{3-8}
**Prefress** & **Prefress** & **Prefress Force** & \multicolumn{3}{c}{**Friction Loss**} \\ \cline{3-8}
**Forceat** & **Level** & \multicolumn{3}{c}{**Midspan**} & & \\ \cline{3-8}
**Live End** & & \multicolumn{3}{c}{**Theoretical**} & \multicolumn{3}{c}{**Measured**} & \multicolumn{3}{c}{**Measured**} \\ \cline{3-8}
**(kN)** & **(\%)** & \multicolumn{3}{c}{**Theoretical**} & **1 st** & **2 nd** & **1 st** & **2 nd** \\ \hline
303.9 & 13 & 270.3 & 233.3 & 258.9 & 33.6 & 70.6 & 45.0 \\
425.5 & 18 & 378.4 & 362.0 & 385.8 & 47.1 & 63.5 & 39.7 \\
547.0 & 24 & 486.5 & 458.1 & 490.2 & 60.5 & 88.9 & 56.8 \\
668.6 & 29 & 594.6 & 558.9 & 628.3 & 74.0 & 109.7 & 40.3 \\
790.1 & 34 & 702.7 & 664.7 & 710.4 & 87.4 & 125.4 & 79.7 \\
911.7 & 39 & 810.8 & 780.5 & 792.5 & 100.9 & 131.2 & 119.2 \\
1033.3 & 45 & 918.9 & 895.3 & 908.0 & 114.3 & 138.0 & 125.3 \\ \hline \hline \end{tabular}
\end{table}
Table 9: _Cont._The first and second prestress forces measured for tendon 1 in the GOE girder jacked at one end at the midspan were 79.5% and 82.8% of the prestress forces measured at the jacking end on average, and the theoretical prestress force was identical to that obtained when both ends were jacked. In the same girder, the second measured prestress force was greater than the first one, and greater prestress forces were observed with tension applied at both ends compared with that obtained when tension was applied only at one end. This phenomenon occurred because the friction between the sheath and the prestressing tendon was changed by the prestressing order and method. In other words, the contact surface between the sheath and the tendon was very rough in the first prestressing, but in the second prestressing, the contact surface became smooth due to the first prestressing. The changed contact surface generated smaller friction in the second prestressing than in the first prestressing. Furthermore, greater prestress forces were observed in the case of jacking at both ends than when jacking at only one end. This occurs because prestressing at both ends of the beam results in more and smoother contact surfaces between the sheath and prestressing tendons, compared to the situation when prestressing at only one end.