## 3 Applications
### Example Calculation
#### 3.2.2 Stress of PCCP under Combined Loads  
The stress of the adopted PCCP under combined loads, involving the vertical earth pressure at the top of the pipe, the lateral earth pressure, the variable load, weight of the pipe, and weight of water in the pipe, is presented in Table 5.  
2.3 Calculation of Area of Prestressed Strands, Considering the Concrete Core Compression of Ultimate Limit States  
Assuming that the area of prestressed strands is \(A_{st}=2223\) mm\({}^{2}\)/m, the calculation process of the area of prestressed strands, considering the concrete core compression of ultimate limit states, can be depicted in Table 6.  
The value of \(M_{max}^{l}\) is negative, indicating that the outer surface of the concrete core is subjected to tension. The absolute value is taken when substituting the formula for reinforcement. Therefore, \(A_{st}\geq\frac{A_{y}}{f_{pyk}}\Big{(}N^{l}+\frac{M_{max}^{l}}{d_{0}}-A_{sc}f_{ yy}^{\prime}\Big{)}=1069.413\) m\({}^{2}\)/m \begin{table}
\begin{tabular}{l c} \hline \hline
**Item** & **Value** \\ \hline Prestress loss related to the bending loss, \(F\) & 276.099 \\ Correction coefficient accounting for the bending loss and the deviation loss, \(c_{1}\) & 1.01 \\ Prestress loss caused by friction resistance, \(\sigma_{1\text{I}}\)/(N/mm\({}^{2}\)) & 278.860 \\ Prestress loss caused by anchorage deformation, \(\sigma_{1\text{Z}}\)/(N/mm\({}^{2}\)) & 158.802 \\ Prestress loss caused by elastic compression of concrete during batch tensioning, \(\sigma_{1\text{S}}\)/(N/mm\({}^{2}\)) & 0 \\ Maximum width of the visible cracks in the concrete core before the reinforcement, w\({}_{1}\)/m & 0.0022 \\ Maximum width of the visible cracks in the concrete core after the reinforcement, w\({}_{2}\)/m & 0.0001 \\ Prestress loss due to the crack reduction and closure, \(\sigma_{1\text{A}}\)/(N/mm\({}^{2}\)) & 0.3434 \\ Prestress loss caused by shrinkage and creep of concrete, \(\sigma_{1\text{S}}\)/(N/mm\({}^{2}\)) & 0 \\ The relaxation coefficient of the strand, k & 0.045 \\ Prestress loss due to long-term relaxation of the strand, \(\sigma_{1\text{S}}\)/(N/mm\({}^{2}\)) & 52.731 \\ Total prestress loss of prestressed wires, \(\sigma_{\text{stJ}}\)/(N/mm\({}^{2}\)) & 490.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The calculation results of the prestress loss. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Vertical earth pressure at the top of the pipe, \(F_{sp,k}\)/(kN/m) & 164.245 \\ Lateral earth pressure, \(F_{ep,k}\)/(kN/m) & 25.026 \\ Variable load, \(q_{mk}\)/(kN/m) & 10 \\ Weight of the pipe, \(G_{1k}\)/(kN/m) & 29.157 \\ Weight of water in the pipe/(kN/m) & 31.416 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The calculation results of the stress. 2.4. Checking Calculation of Prestressed Strands Considering the Concrete Core Compression of Serviceability Limit States  
The conversion coefficient of the elastic resistance moment of the tensioned edge of the pipe wall can be obtained by interpolation, where \(\omega_{c}=1.017\) and \(\omega_{m}=0.9932\). The checking calculation process of the prestressed strands, considering the concrete core compression of serviceability limit states, is depicted in Table 7.  
Therefore, the area of prestressed strands should meet the requirement of \(A_{st}\geq\Big{(}\sigma_{ss}-K\gamma f_{ty}\Big{)}\frac{A_{st}}{\sigma_{st}^{ 2}}=222.300\) mm\({}^{2}\)/m. Above all, the area of prestressed strands is \(A_{st}=2223\) mm\({}^{2}\)/m.