# Effect of Prestress Levels and Jacking Methods on Friction Losses in Curved Prestressed Tendons
## 4 Test Results and Discussion
### Measured Prestress Force  
The friction losses at the tendons from prestressing only one tendon in one girder were accurately measured in the experiment. The prestress forces were calculated at the girder end and midspan by using the strains of the prestressing tendon recorded from the strain gauges attached to one end and the center of the prestressing tendon, respectively. The difference between these prestress forces was the friction loss. Table 9 lists the prestress forces and friction losses measured in each experimental girder. The theoretical prestress forces and friction losses in this table were calculated by using Equations (3) and (4). The experimental results indicate that considerable friction losses occur when steel tendons are used to prestress PSC girders. The difference between the measured and theoretical losses was smaller when the prestress level was higher and both ends were jacked, compared to the difference obtained when only one end was jacked. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Tendon Number**} & \multicolumn{3}{c}{**Distance from Midspan (m)**} & \multicolumn{3}{c}{\(\Sigma\)**A\(\alpha\)**} \\ \cline{3-8}  & **14.8** & **12.0** & **9.0** & **6.0** & **3.0** & \\ \hline \multirow{2}{*}{1} & Degree & 957\({}^{\prime\prime}\)53\({}^{\prime\prime}\) & 804\({}^{\prime}\)51\({}^{\prime\prime}\) & 603\({}^{\prime}\)35\({}^{\prime\prime}\) & 402\({}^{\prime}\)22\({}^{\prime\prime}\) & 201\({}^{\prime}\)12\({}^{\prime\prime}\) & 957\({}^{\prime}\)53\({}^{\prime\prime}\) \\  & Radian & 0.1739 & 0.1410 & 0.1057 & 0.0705 & 0.03525 & 0.1739 \\ \hline \multirow{2}{*}{2} & Degree & 741\({}^{\prime}\)18\({}^{\prime\prime}\) & 614\({}^{\prime}\)02\({}^{\prime\prime}\) & 440\({}^{\prime}\)31\({}^{\prime\prime}\) & 307\({}^{\prime}\)01\({}^{\prime\prime}\) & 133\({}^{\prime}\)30\({}^{\prime\prime}\) & 741\({}^{\prime}\)18\({}^{\prime\prime}\) \\  & Radian & 0.1341 & 0.1088 & 0.0816 & 0.0544 & 0.0272 & 0.1341 \\ \hline \multirow{2}{*}{3} & Degree & 435\({}^{\prime}\)55\({}^{\prime\prime}\) & 343\({}^{\prime}\)43\({}^{\prime\prime}\) & 247\({}^{\prime}\)47\({}^{\prime\prime}\) & 151\({}^{\prime}\)51\({}^{\prime\prime}\) & 055\({}^{\prime}\)56\({}^{\prime\prime}\) & 435\({}^{\prime}\)55\({}^{\prime\prime}\) \\  & Radian & 0.0802 & 0.0650 & 0.0488 & 0.0325 & 0.0167 & 0.0802 \\ \hline \multirow{2}{*}{4} & Degree & 133\({}^{\prime}\)23\({}^{\prime\prime}\) & 115\({}^{\prime}\)43\({}^{\prime\prime}\) & 056\({}^{\prime}\)47\({}^{\prime\prime}\) & 037\({}^{\prime}\)51\({}^{\prime\prime}\) & 018\({}^{\prime}\)56\({}^{\prime\prime}\) & 133\({}^{\prime}\)23\({}^{\prime\prime}\) \\  & Radian & 0.0272 & 0.022 & 0.0165 & 0.011 & 0.005 & 0.0272 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Variation in angle with distance of tendons. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Tendon 1 in GOE**} & \multicolumn{3}{c}{**Tendon 3 in GBE**} \\ \hline \hline
**Prestress Force** & \multicolumn{3}{c}{**Prestress Force**} \\ \hline
**Live End** & **Midspan** & \multirow{2}{*}{**Frictional Loss**} & **Live End** & **Midspan** & **Frictional Loss** \\ \cline{3-6}
**(kN)** & **(kN)** & **(kN)** & **(kN)** & **(kN)** & **(kN)** \\ \hline
100 & 88.9 & 11.1 & 100 & 91 & 9 \\
200 & 177.8 & 22.2 & 200 & 182 & 18 \\
300 & 266.7 & 33.3 & 300 & 273.1 & 26.9 \\
400 & 355.7 & 44.3 & 400 & 364.1 & 35.9 \\
500 & 444.6 & 55.4 & 500 & 455.1 & 44.9 \\
600 & 533.5 & 66.5 & 600 & 546.1 & 53.9 \\
700 & 622.4 & 77.6 & 700 & 637.2 & 62.8 \\
800 & 711.3 & 88.7 & 800 & 728.2 & 71.8 \\
900 & 800.2 & 99.8 & 900 & 819.2 & 80.8 \\
1000 & 889.2 & 110.8 & 1000 & 910.2 & 89.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Initial prestress force and friction loss.