Code checks: API STD 2RD

Data

$\boldsymbol{p_\mathrm{c}}$ calculated by

API STD 2RD describes two different ways in which the elastic collapse pressure, $p_\mathrm{c}$, may be calculated (see section 5.3.3.1 of the code), and OrcaFlex offers you the same choice. We label these two calculations API RP 1111 and DNV OS F101, following the codes on which they are based.

$\boldsymbol{F_\mathrm{d}}$ for method 1

The design factor for use with method 1, see API STD 2RD, section 5.4.3.2.

$\boldsymbol{F_\mathrm{d}}$ for method 2

The design factor for use with method 2, see API STD 2RD, section 5.4.3.3.

Fabrication factor, $\boldsymbol{\alpha_\mathrm{fab}}$

The fabrication factor, used in determining the elastic collapse pressure, $p_\mathrm{c}$. It is only used if $\boldsymbol{p_\mathrm{c}}$ calculated by is DNV OS F101. See API STD 2RD, section 5.3.3.1.

Wall variability parameter, $\boldsymbol{k}$

A parameter to account for variability in mechanical properties and wall thickness, used in determining the burst pressure, $p_\mathrm{b}$. See API STD 2RD, section 5.3.2.

Corrosion allowance, $\boldsymbol{t_\textrm{corr}}$

Used to reduce the wall thickness when calculating the burst pressure, $p_\mathrm{b}$, and the elastic collapse pressure, $p_\mathrm{c}$.

Young's modulus, $\boldsymbol{E}$

The modulus of elasticity, used in calculating the elastic collapse pressure, $p_\mathrm{c}$, see API STD 2RD, section 5.3.3.1. Even if you have specified, separately, the line type Young's modulus, you must also supply a (non-zero) value here.

SMYS, $\boldsymbol{S}$

The material minimum yield strength, used to determine the pipe capacities: the burst pressure $p_\mathrm{b}$, the elastic collapse pressure $p_\mathrm{c}$, the yield tension $T_\mathrm{y}$, the yield moment $M_\mathrm{y}$, and the plastic moment $M_\mathrm{p}$. See API STD 2RD, section 5.3.

SMTS, $\boldsymbol{U}$

The specified minimum ultimate tensile strength, used in calculating the burst pressure, $p_\mathrm{b}$, see API STD 2RD, section 5.3.2.

Ovality, $\boldsymbol{\delta}$

Used in determining the elastic collapse pressure, $p_\mathrm{c}$ if $\boldsymbol{p_\mathrm{c}}$ calculated by is DNV OS F101. See API STD 2RD, section 5.3.3.1

Results

In order to calculate the results, a number of derived values are required:

Nominal thickness \begin{equation} t_\textrm{nom} = \frac{\ODs - \IDs}{2} \end{equation} Minimum thickness \begin{equation} t_\textrm{min} = t_\textrm{nom} - t_\textrm{corr} \end{equation} Tension capacity \begin{align} T_\mathrm{y} &= SA \\ A &= \frac{\pi}{4}\left(\ODs^2 - \IDs^2\right) \end{align} Plastic moment \begin{equation} M_\mathrm{p} = S\left(\ODs - t_\textrm{nom}\right)^2 t_\textrm{nom} \end{equation} Yield moment \begin{equation} M_\mathrm{y} = \frac{\pi}{4}M_\mathrm{p} \end{equation} Burst pressure \begin{equation} p_\mathrm{b} = k(S + U) \log_e\left(\frac{\ODs}{\ODs-2t_\textrm{min}}\right) \end{equation} The calculation of elastic collapse pressure, $p_\mathrm{c}$, depends on the $\boldsymbol{p_\mathrm{c}}$ calculated by option.

If $\boldsymbol{p_\mathrm{c}}$ calculated by is API RP 1111\begin{equation} p_\mathrm{c} = \frac{P_\mathrm{y}p_\mathrm{el}}{\sqrt{P_\mathrm{y}^2 + p_\mathrm{el}^2}} \end{equation} where \begin{align} P_\mathrm{y} &= 2S\left(t_\textrm{min}/\ODs\right) \\ p_\mathrm{el} &= \frac{2E\left(t_\textrm{min}/\ODs\right)^3}{1-\nu^2} \\ \nu &= \href{LineTypes,StructureData.htm#PoissonRatio}{\text{Poisson ratio}} \end{align} If $\boldsymbol{p_\mathrm{c}}$ calculated by is DNV OS F101, then calculating $p_\mathrm{c}$ requires the solution of a third degree polynomial (see API STD 2RD section 5.3.3.1). This solution is given in DNV OS F101, and is reproduced here in code checks: DNV ST F101. To translate between the notation of DNV OS F101 and that of API STD 2RD, replace $t_2$ with $t_\textrm{min}$ and $f_0$ with $\delta$.

The results themselves are as follows.

API STD 2RD method 1

This result presents the inequalities 18 and 19 in section 5.4.3.2, API STD 2RD in the form of a unity check. The inequalities 18 and 19 in API STD 2RD are satisfied if the value reported is no greater than one. It is given by \begin{equation} \begin{cases} \cfrac{\sqrt{(|T_\mathrm{e}/T_\mathrm{y}| + |M/M_\mathrm{y}|)^2 + \{(p_\mathrm{i}-p_\mathrm{o})/p_\mathrm{b}\}^2}}{F_\mathrm{d}} & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$} \\ \cfrac{\sqrt{(|T_\mathrm{e}/T_\mathrm{y}| + |M/M_\mathrm{y}|)^2 + \{(p_\mathrm{o}-p_\mathrm{i})/p_\mathrm{c}\}^2}}{F_\mathrm{d}} & \text{otherwise} \end{cases} \end{equation} where the design factor $F_\mathrm{d}$ is given by $\boldsymbol{F_\mathrm{d}}$ for method 1.

API STD 2RD method 2

The method 2 result corresponds to the inequalities 21 and 22 in section 5.4.3.3, API STD 2RD, recast as a unity check. The inequalities are satisfied if the value reported is no greater than one. It is given by \begin{equation} \begin{cases} \cfrac{\sqrt{\{M/(M_\mathrm{p}\cos \phi)\}^2 + \{(p_\mathrm{i}-p_\mathrm{o})/p_\mathrm{b}\}^2}}{F_\mathrm{d}} & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$ and $|\phi| \lt \pi/2$} \\ \cfrac{\sqrt{\{M/(M_\mathrm{p}\cos \phi)\}^2 + \{(p_\mathrm{o}-p_\mathrm{i})/p_\mathrm{c}\}^2}}{F_\mathrm{d}} & \text{if $p_\mathrm{i} \leq p_\mathrm{o}$ and $|\phi| \lt \pi/2$} \\ \infty & \text{otherwise} \end{cases} \end{equation} where \begin{equation} \phi = \begin{cases} \cfrac{\pi}{2}\cfrac{T_\mathrm{e}/T_\mathrm{y}}{\sqrt{F_\mathrm{d}^2 - \{(p_\mathrm{i}-p_\mathrm{o})/p_\mathrm{b}\}^2}} & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$} \\ \cfrac{\pi}{2}\cfrac{T_\mathrm{e}/T_\mathrm{y}}{\sqrt{F_\mathrm{d}^2 - \{(p_\mathrm{o}-p_\mathrm{i})/p_\mathrm{c}\}^2}} & \text{otherwise} \end{cases} \end{equation} and the design factor $F_\mathrm{d}$ is given by $\boldsymbol{F_\mathrm{d}}$ for method 2.