## 3 Applications
### Example Calculation  
#### 3.2.1 Calculation of Prestress Loss, \(\sigma_{st,l}\)  
For the utilized split wedge without jacking force, \(\Delta l_{re}=6\) mm (measured in the prototype test [29]). Given \(\mu=0.1\), the calculated radius of the strand wrapped outside the pipe, \(r_{st}\), and the retraction length, \(l_{re}\), can be known as follows:  
\[r_{st}=\frac{D_{i}}{2}+h_{c}+\frac{d_{st}}{2}=1.1726\) m,\(l_{re}=\sqrt{\frac{\Delta l_{re}E_{st}r_{st}}{\mu\sigma_{st}}}=3.4217\) m  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Key Parameter** & **Value** & **Key Parameter** & **Value** \\ \hline Designed 28-day compressive strength & 44 & Modulus of concrete, \(E_{c}\)/(N/mm\({}^{2}\)) & \(3.55\times 10^{4}\) \\ of the core concrete, \(f_{c}^{\prime}\)/(N/mm\({}^{2}\)) & 45 & Modulus of mortar, \(E_{m}\)/(N/mm\({}^{2}\)) & \(2.416\times 10^{4}\) \\ \hline Poisson’s ratio of concrete, \(v_{c}\) & 0.167 & Modulus of cylinder, \(E_{y}\)/(N/mm\({}^{2}\)) & \(2.068\times 10^{5}\) \\ \hline Poisson’s ratio of mortar, \(v_{m}\) & 0.2 & Modulus of wire, \(E_{s}\)/(N/mm\({}^{2}\)) & \(1.93\times 10^{5}\) \\ \hline Minimum tensile strength of the & 1570 & Designed tensile or compressive yield strength of steel cylinder, \(f_{yy}\)/(N/mm\({}^{2}\)) & 227.5 \\ \hline Gross wrapping tensile stress in wire, & 0.75\(f_{su}\) & Designed tensile strength of steel cylinder at pipe burst, \(f_{yy}^{\prime}\)/(N/mm\({}^{2}\)) & 215 \\ \hline Design tensile strength of core concrete, & 1.95 & Unit weight of the pipe, \(\gamma_{c}\)/kN/m\({}^{3}\) & 25 \\ \hline Standard tensile strength of core & 2.75 & Unit weight of mortar, \(\gamma_{m}\)/kN/m\({}^{3}\) & 23.5 \\ \hline Unit weight of backfill soil, \(\gamma_{s}\)/kN/m\({}^{3}\) & 18 & Unit weight of water, \(\gamma_{w}\)/kN/m\({}^{3}\) & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Key parameters of the materials.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Key Parameter** & **Value** & **Key Parameter** & **Value** \\ \hline Nominal diameter without & 15.2 & Control coefficient for the & 0.63 \\ polyethylene \(\mathrm{d_{st}/mm}\) & & tensioning of the steel strands, \(\alpha\) & \\ \hline Nominal section area without & 140 & \
\begin{tabular}{c} Tension stress of the prestressed \\ steel strands, \(\sigma_{st}\)/(N/mm\({}^{2}\)) \\ \end{tabular} & 1171.8 \\ \hline Nominal tensile strength, & 1860 &
\begin{tabular}{c} Standard tensile yield strength, \\ \(f_{yy}\)/(N/mm\({}^{2}\)) \\ \end{tabular} & 1580 \\ \hline Modulus of the strand, & \(1.95\times\) & Designed tensile yield strength, & 1110 \\ \(E_{sl}\)/(N/mm\({}^{2}\)) & \(10^{5}\) & \(f_{yy}\)/(N/mm\({}^{2}\)) & [17] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Key parameters of the adopted strand.  
The corresponding angle of the retraction length, \(\theta_{re}\), is \(\pi\), which is consistent with the value of \(\theta\), indicating that the assumption is reasonable (Equation (10)).  
The prestress loss caused by friction resistance, anchorage deformation, elastic compression of concrete during batch tensioning, crack reduction and closure, shrinkage and creep of concrete, and long-term relaxation of the strand is given in Table 4.