Code checks: API RP 2RD

$\newcommand{\us}{_\textrm{stress}}$ $\newcommand{\IDs}{I\!D\us}$ $\newcommand{\ODs}{O\!D\us}$


Design case factor, $\boldsymbol{C_\mathrm{f}}$

See API RP 2RD, section 4.4, table 2 and section

Corrosion thickness, $\boldsymbol{t_\mathrm{corr}}$

Used to determine the minimum thickness, $t_\textrm{min}$, using the equation \begin{equation} t_\textrm{min} = t_\textrm{nom} - t_\textrm{corr} \end{equation} where $t_\textrm{nom}$ is the nominal thickness \begin{equation} t_\textrm{nom} = \frac{\ODs - \IDs}{2} \end{equation}

SMYS, $\boldsymbol{\sigma_\mathrm{y}}$

The material minimum yield strength (SMYS), denoted $\sigma_\mathrm{y}$ in API RP 2RD, section


Note: The wall tension, $T_\mathrm{w}$, and bend moment magnitude, $M$, are influenced by the stress loading factors or by homogeneous pipe additional bending stiffness before being used in the calculations below.

API RP 2RD stress, $\sigma_\textrm{API}$, is a von Mises type stress defined in section 5.2 of API RP 2RD as \begin{equation} \label{sigma_API} \sigma_\textrm{API} = \max \sqrt{\frac{\left(\sigma_\mathrm{pr}-\sigma_\mathrm{p\theta}\right)^2 + \left(\sigma_\mathrm{p\theta}-\sigma_\mathrm{pz}\right)^2 + \left(\sigma_\mathrm{pz}-\sigma_\mathrm{pr}\right)^2}{2}} \end{equation} where \begin{align} \sigma_\mathrm{pr} &= - \frac{p_\mathrm{o}\ODs + p_\mathrm{i}\IDs}{\ODs + \IDs} \\ \sigma_\mathrm{p\theta} &= \frac{(p_\mathrm{i} - p_\mathrm{o})\ODs}{2t_\textrm{min}} - p_\mathrm{i} \\ \sigma_\mathrm{pz} &= \frac{T_\mathrm{w}}{A} \pm \frac{M}{2I}\left(\ODs - t_\textrm{nom}\right) \label{sigma_pz} \\ A &= \frac{\pi}{4} \left(\ODs^2 - \IDs^2\right) \\ I &= \frac{\pi}{64}\left(\ODs^4 - \IDs^4\right) \end{align} The max in equation (\ref{sigma_API}) for $\sigma_\textrm{API}$ is to account for the fact that $\sigma_\mathrm{pz}$ is double-valued, due to the $\pm$ sign in (\ref{sigma_pz}).

API RP 2RD utilisation, $U_\textrm{API}$, is defined as \begin{equation} U_\textrm{API} = \frac{\sigma_\textrm{API}}{C_\mathrm{f}C_\mathrm{a}\sigma_\mathrm{y}} \end{equation} where $C_\mathrm{a} = 2/3$. The strength check for API RP 2RD then corresponds to the test $U_\textrm{API} \leq 1$.