Code checks: PD 8010

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


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

Used to calculate the minimum thickness. See PD 8010, section If you wish to account for fabrication thickness, it should be incorporated into this value.

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

The modulus of elasticity used in calculating the collapse pressure $p_\mathrm{c}$, the characteristic torque $\tau_\mathrm{c}$, and the exponent $\gamma$ in PD 8010 load combinations check. See PD 8010, sections G.1.2, G.1.5, and G.1.6, respectively. Even if you have specified, separately, the line type Young's modulus, you must also supply a (non-zero) value here if you wish to calculate a PD 8010 torsion check or a PD 8010 load combinations check result.

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

The minimum yield strength of the pipe used in determining the allowable stress $\sigma_\mathrm{A}$, elastic collapse pressure $p_\mathrm{c}$, yield load $F_\mathrm{y}$, plastic moment capacity $M_\mathrm{p}$, characteristic torque $\tau_\mathrm{c}$, and the exponent $\gamma$ in the load combinations check. See PD 8010, sections, G.1.2, G.1.3, G.1.4, G.1.5, and G.1.6.

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

PD 8010, section general, note 1 requires that, for fabrication processes which introduce cold deformations giving different strength in tension and compression, a fabrication factor should be determined. In the absence of any more explicit guidance in PD 8010 ($\alpha_\mathrm{fab}$ is not explicitly included in any of the equations therein), we assume that it is applied in a fashion consistent with DNV OS F101, i.e. that it is considered in determining the elastic collapse pressure, $p_\mathrm{c}$, as reproduced here.

Ovalisation, $\boldsymbol{f_0}$

Used in determining the elastic collapse pressure, $p_\mathrm{c}$, see PD 8010, section G.1.2

Design factor, $\boldsymbol{f_\mathrm{d}}$

See PD 8010, section 6.4.1


Note: The wall tension $T_\mathrm{w}$, bend moment magnitude $M$, torque magnitude $T$, and shear force magnitude $S$, are all influenced by the stress loading factors or (with the exception of torque) are influenced by homogeneous pipe additional bending stiffness before being used in the calculations below.

The nominal thickness, $t_\textrm{nom}$, used throughout the calculations below, is given by \begin{equation} t_\textrm{nom} = \frac{\ODs - \IDs}{2} \end{equation} A number of PD 8010 code check results are available. All have been recast so as to present each one in the form of a unity check: to satisfy PD 8010 the result in each case should be less than one.

PD 8010 allowable stress check

Equivalent to equation 2, section, PD 8010, rewritten in the form of a unity check. It is calculated as \begin{equation} \frac{\sigma_\mathrm{A}}{f_\mathrm{d}\sigma_\mathrm{y}} \end{equation} where \begin{align} \sigma_\mathrm{A} &= \sqrt{\sigma_\mathrm{h}^2 + \sigma_\mathrm{L}^2 - \sigma_\mathrm{h}\sigma_\mathrm{L} + 3\tau^2} \\ \sigma_\mathrm{h} &= \begin{cases} \cfrac{(p_\mathrm{i} - p_\mathrm{o})\ODs}{2t_\textrm{min}} & \text{ if $\ODs/t_\textrm{min} \gt 20$} \\ (p_\mathrm{i} - p_\mathrm{o}) \cfrac{\ODs^2 + \IDs^2}{\ODs^2 - \IDs^2} & \text{ otherwise} \end{cases} \\ t_\textrm{min} &= t_\textrm{nom} - t_\textrm{corr} \\ \tau &= \frac{\ODs T}{2I_\mathrm{z}} + \frac{2S}{A} \\ I_\mathrm{z} &= \frac{\pi}{32}\left(\ODs^4 - \IDs^4\right) \\ A &= \frac{\pi}{4}\left(\ODs^2 - \IDs^2\right) \end{align} The longitudinal stress, $\sigma_\mathrm{L}$, which varies over the pipe wall cross section, is chosen to ensure that the equivalent stress, $\sigma_\mathrm{A}$, evaluates to the largest possible value. This is done by calculating the equivalent stress twice, using the minimum and the maximum longitudinal stress in the pipe wall cross section and choosing the largest of the two resulting values. The minimum and maximum longitudinal stresses are given by \begin{equation} \sigma_\mathrm{L} = \textrm{direct tensile stress} \pm \textrm{max bending stress} \end{equation}

PD 8010 axial compression check

This result represents the axial compression requirement in section G.1.3, PD 8010 in the form of a unity check. It is given by \begin{equation} \frac{F_\mathrm{x}}{F_\mathrm{xc}} \end{equation} where \begin{align} F_\mathrm{x} &= \max(-T_\mathrm{w}, 0) \\ F_\mathrm{xc} &= F_\mathrm{y} = \pi(\ODs-t_\textrm{nom})t_\textrm{nom}\sigma_\mathrm{y} \end{align}

PD 8010 bending check

The bending moment requirement in section G.1.4, PD 8010, rewritten as a unity check. It is given by \begin{equation} \frac{M}{M_\mathrm{c}} \end{equation} where \begin{align} M_\mathrm{c} &= M_\mathrm{p}\left(1 - 0.0024\frac{\ODs}{t_\textrm{nom}}\right) \\ M_\mathrm{p} &= \left(\ODs-t_\textrm{nom}\right)^2t_\textrm{nom}\sigma_\mathrm{y} \end{align}

PD 8010 torsion check

The torsion requirement in section G.1.5, PD 8010, as a unity check. It is calculated as \begin{equation} \frac{\tau_\mathrm{shear}}{\tau_\mathrm{c}} \end{equation} where \begin{align} \tau_\mathrm{shear} &= \textrm{maximum shear stress due to torsion} \\ &= \frac{\ODs T}{2I_\mathrm{z}} \\ \tau_\mathrm{c} &= \begin{cases} 0.542\tau_\mathrm{y}\alpha_\tau & \text{if $\alpha_\tau \lt 1.5$} \\ \tau_\mathrm{y}(0.813 + 0.068\sqrt{\alpha_\tau - 1.5}) & \text{if $1.5 \leq \alpha_\tau \leq 9$} \\ \tau_\mathrm{y} & \text{otherwise} \\ \end{cases} \\ \tau_\mathrm{y} &= \frac{\sigma_\mathrm{y}}{\sqrt{3}} \\ \alpha_\tau &= \frac{E}{\tau_\mathrm{y}} \left(\frac{t_\textrm{nom}}{\ODs}\right)^{3/2} \end{align}

PD 8010 load combinations check

This is equation G.14, section G.1.6, PD 8010, written as a unity check. It is given by \begin{align} & \left(\frac{M}{M_\mathrm{c}} + \frac{F_\mathrm{x}}{F_\mathrm{xc}}\right)^\gamma + \frac{p_\mathrm{o}-p_\mathrm{i}}{p_\mathrm{c}} & \text{if $p_\mathrm{o} \gt p_\mathrm{i}$} \\ & \frac{M}{M_\mathrm{c}} + \frac{F_\mathrm{x}}{F_\mathrm{xc}} & \text{otherwise} \end{align} where \begin{align} \gamma &= 1 + 300 \frac{t_\textrm{nom}}{\ODs} \frac{\sigma_\mathrm{hb}}{\sigma_\mathrm{hcr}} \\ \sigma_\mathrm{hb} &= \frac{(p_\mathrm{o}-p_\mathrm{i})\ODs}{2t_\textrm{nom}} \\ \sigma_\mathrm{hcr} &= \begin{cases} \sigma_\mathrm{hE} & \text{if $\sigma_\mathrm{hE} \leq (2/3)\sigma_\mathrm{y}$} \\ \sigma_\mathrm{y}\left[1-\cfrac{1}{3}\left(\cfrac{2\sigma_\mathrm{y}}{3\sigma_\mathrm{hE}}\right)^2\right] & \text{otherwise} \end{cases} \\ \sigma_\mathrm{hE} &= E\left(\frac{t_\textrm{nom}}{\ODs-t_\textrm{nom}}\right)^2 \end{align}

PD 8010 bending strain check

This result is equivalent to equation G.19, section G.1.7, PD 8010, in terms of a unity check. The calculation is \begin{equation} \frac{\epsilon_\mathrm{b}}{\epsilon_\mathrm{bc}} + \frac{\max(p_\mathrm{o}-p_\mathrm{i}, 0)}{p_\mathrm{c}} \end{equation} where \begin{align} \epsilon_\mathrm{b} &= \href{Lineresults,Stressstrain.htm#LineMaxBendingStrain}{\text{max bending strain}} \\ \epsilon_\mathrm{bc} &= 15\left(\frac{t_\textrm{nom}}{\ODs}\right)^2 \end{align}

Collapse pressure, $\boldsymbol{p_\mathrm{c}}$

The load combinations check and bending strain check both refer to the collapse pressure, $p_\mathrm{c}$, the calculation of which is described in section G.1.2, PD 8010 and also detailed here under DNV ST F101. To translate from the DNV ST F101 description to PD 8010, replace DNV's $t_2$ with $t_\textrm{nom}$. The fabrication factor $\alpha_\textrm{fab}$ is treated as described in the DNV ST F101 documentation.