## 2 Stress-Calculation Methodologies for High-Temperature Steam Pipes
### TRD-Code-Based Method  
The main steam pipe (MSP) of the Manjung power plant has straight, bent, and T-piece components, and it measures 445 mm in outer diameter with a thickness of 41.5 mm and a tolerance of 12.5%. The piping stiffness and section modulus are based on the nominal wall thickness, which decreases by tolerance percentage. The formula for calculating the stress according to the pipe shape in the TRD code is shown in Table 1.  
To verify the calculations for the completed components, the wall thickness, straight pipe, and cross-section values should be calculated as shown in Table 1. The \(s_{v}\), \(s_{e}\), and  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Geometry** & **Dominant Formula** \\ \hline Straight & \(\sigma=\frac{p}{2}\left(\frac{d_{s}-2s_{v}}{s_{v}s_{v}}\right)\) \\  & \(s_{v}=s_{e}-c_{1}-c_{2}\), \(s_{v}=\frac{s_{e}}{s_{v}}\) \\ \hline Bent & \(\frac{\sigma_{i}}{2s_{v}s_{v}}=\frac{p\left(d_{s}-s_{v}s_{v}\right)}{2s_{v}s_{ v}}\frac{2R-0.5d_{s}+1.5s_{v}-0.5s_{v}}{2R-d_{s}+s_{v}}\) & \(\frac{p}{2}\) \\  & \(r=s_{v}\sqrt{\frac{1}{2}\left[\left(\frac{d_{s}}{2s_{v}}\right)^{2}+\left( \frac{R}{s_{v}}\right)^{2}\right]+\sqrt{1}\left[\left(\frac{d_{s}}{2s_{v}} \right)^{2}+\left(\frac{R}{s_{v}}\right)^{2}\right]^{2}-\frac{d_{s}}{2s_{v}} \left(\frac{d_{s}}{2s_{v}}-1\right)\left(\frac{R}{s_{v}}\right)^{2}}\) \\ \hline T/Y piece & \(A_{p}=\frac{d_{s}}{2}\left(\epsilon_{G}+\frac{d_{s}}{2}\right)+\frac{d_{s}}{2} \left(\epsilon_{A}+s_{v}\right)\) \\  & \(A_{\sigma}=s_{v}\cdot\epsilon_{G}+s_{A0}\cdot\epsilon_{A}+s_{v}\cdot s_{A0}\) \\  & \(\epsilon_{G}=\sqrt{(d_{i}+s_{v})s_{v}}\), \(e_{A}=1.25\sqrt{(d_{Ai}+s_{A0})s_{A0}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Stress-calculation formula based on the TRD code.  
\(s_{o}\) are the wall thicknesses of many bodies; \(c_{1}\) and \(c_{2}\) are allowance under tolerances or corrosion; and \(v_{N}\) indicates the weld joint factor. Solving for the reference Tresca, i.e., the stress used for the remaining life calculations based on uniaxial test results, the stresses of the external diameter can be calculated. When the pressure is 19.4 MPa, the welding coefficient is 1, and when \(s_{v}\) is 36.3125, the calculated stress is 99.471 MPa. According to the TRD code, two stresses must be calculated for the elbows: the average stress inside the bend and the average stress outside of the bend. The four stresses (two stresses each for the given inside/outside diameters) are calculated according to Table 1. Depending on the given values (either the outside diameter of the cylindrical shell (\(d_{a}\)) or the inside diameter of the cylindrical shell (\(d_{i}\))), the average stress of both outside the bend (\(\overline{v_{i}}\)) and inside the bend (\(\overline{\sigma_{a}}\)) must be calculated. When the bending radius is 2250 mm and the curvature radius is 2757 mm, the internal stress is 110.23 MPa and the external stress is 110.14 MPa. For the stress calculation of T-pieces, it is necessary to distinguish among three types: extruded branch, forged branch, and branch with/without reinforcement. In the case of the Manjung power plant, the forged branch should be considered to calculate the stress for the T-piece piping components. Nevertheless, for all three types of T-pieces, the values \(e_{G}\) and \(e_{A}\) in Table 1 must be calculated. Drawings suitable for the planimeter are used to obtain the pressure loaded area (\(A_{P}\)) and cross-sectional area (\(A_{\sigma}\)) as functions of \(e_{G}\) and \(e_{A}\), respectively. For the extruded branches, if the extension radii are not considered, the cross-sectional area \(A_{\sigma}\) should be multiplied by a factor of 0.9. The average stress is then calculated by geometrical conditions. The stress of the T-piece pipe calculated using the equation in Table 1 is 103.9 MPa.