Code checks: DNV OS F201

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


Functional load specified by

To allow the environmental load to be separated from the function load, you must nominate a functional load case. You do this on the DNV functional load page.

The following data are specified on the DNV OS F201 properties and factors pages.



The minimum internal pressure that can be sustained. The default value ~ tells OrcaFlex to use the actual internal pressure, $p_\mathrm{i}$, of the line at the arc length for which we are calculating results; see line pressure effects for details. A value other than the default will be applied at all arc lengths which use this line type.


See DNV OS F201, section 5, C 203. The default value ~ means that $t_\mathrm{2}$ will be calculated as $(\ODs - \IDs)/2$.


See DNV OS F201, table 5-5.


See DNV OS F201, table 5-5.

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

The modulus of elasticity. Even if you have specified, separately, the line type Young's modulus, you must also supply a (non-zero) value here.

Out of roundness, $\boldsymbol{f_\mathrm{0}}$

See DNV OS F201, section 5, G 201.

Load factors

Functional, $\boldsymbol{\gamma_\mathrm{F}}$

See DNV OS F201, table 5-2.

Environmental, $\boldsymbol{\gamma_\mathrm{E}}$

See DNV OS F201, table 5-2.

Condition, $\boldsymbol{\gamma_\mathrm{c}}$

See DNV OS F201, table 5-11.

Moment condition, $\boldsymbol{\gamma_\mathrm{cm}}$

DNV OS F201, section 5, D 707 states that, if the bending moment can be assumed secondary, the bending moment used in the code checks may be multiplied by a condition factor. It is not, however, included explicitly in the DNV equations. We have implemented this by applying the condition factor, $\gamma_\mathrm{cm}$, to the bend moment contributions to the results in equations (\ref{LRFD}) and (\ref{WSD}) below.

Reduced functional, $\boldsymbol{\gamma_\mathrm{RF}}$

Defines an alternative, smaller functional load factor to satisfy the requirement (DNV OS F201, table 5-2) that, if the functional load effect reduces the combined load effect, a smaller functional load factor shall be used.

Reduced environmental, $\boldsymbol{\gamma_\mathrm{RE}}$

Defines an alternative, smaller environmental load factor to satisfy the requirement (DNV OS F201, table 5-2) that, if the environmental load effect reduces the combined load effect, a smaller environmental load factor shall be used.

Line type factors

Safety class factor, $\boldsymbol{\gamma_\mathrm{SC}}$

See DNV OS F201, table 5-3.

Material resistance, $\boldsymbol{\gamma_\mathrm{m}}$

See DNV OS F201, table 5-4.

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

See DNV OS F201, table 5-7.

WSD usage, $\boldsymbol{\eta}$

See DNV OS F201, table 5-8.


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

In order to calculate the results, derived values for burst resistance pressure and collapse pressure are required. These are calculated as follows.

The burst resistance pressure, $p_\mathrm{b}$, is used when the internal pressure is greater than the external pressure, and is calculated as \begin{equation} p_\mathrm{b} = \frac{2}{\sqrt{3}} \frac{2t_\mathrm{2}}{\ODs-t_\mathrm{2}} \min\left(f_\mathrm{y}, \frac{f_\mathrm{u}}{1.15}\right) \end{equation} The collapse pressure, $p_\mathrm{c}$, is used when the external pressure is greater than the internal pressure, and requires the solution of the third degree polynomial \begin{equation} \left(p_\mathrm{c}-p_\mathrm{el}\right) \left(p_\mathrm{c}^2 - p_\mathrm{p}^2\right) = p_\mathrm{c}p_\mathrm{el}p_\mathrm{p}f_\mathrm{0}\frac{\ODs}{t_\mathrm{2}} \end{equation} where \begin{align} p_\mathrm{p} &= 2f_\mathrm{y}\alpha_\textrm{fab}(t_\mathrm{2}/\ODs) \\ p_\mathrm{el} &= 2E\frac{(t_\mathrm{2}/\ODs)^3}{1-\nu^2} \\ \nu &= \href{LineTypes,StructureData.htm#PoissonRatio}{\text{Poisson ratio}} \end{align} The analytical solution to this polynomial is given in section 13, D 700, DNV OS F101 and is reproduced here in code checks: DNV ST F101.

Two different formats are defined by DNV OS F201, section 5: Load and resistance factor design, LRFD (in D 500), and the simpler working stress design, WSD (in D 600). These are implemented in OrcaFlex as separate results.

DNV OS F201 LRFD format

Here, the environmental load is separated from the functional load obtained from the functional load case. The load at time $t$ in the currently active model is taken to be the combined load, $L(t)$, which can be treated (see appendix C in DNV OS F201) as a linear superposition of the environmental load, $L_\mathrm{E}(t)$, and the functional load, $L_\mathrm{F}$. The loads can then be separated \begin{align} M_\mathrm{x,E}(t) &= M_\mathrm{x}(t) - M_\mathrm{x,F} \\ M_\mathrm{y,E}(t) &= M_\mathrm{y}(t) - M_\mathrm{y,F} \\ T_\mathrm{e,E}(t) &= T_\mathrm{e}(t) - T_\mathrm{e,F} \end{align} Note that the DNV OS F201 LRFD result, when the model is in the static state and the functional load is specified by the current model, will therefore have no environmental load contribution.

The required design load effects $T_\mathrm{e,d}$ and $|M_\mathrm{d}|$ are given by \begin{align} T_\mathrm{e,d} &= \gamma_\mathrm{F}T_\mathrm{e,F} + \gamma_\mathrm{E}T_\mathrm{e,E} \\ M_\mathrm{x,d} &= \gamma_\mathrm{F}M_\mathrm{x,F} + \gamma_\mathrm{E}M_\mathrm{x,E} \\ M_\mathrm{y,d} &= \gamma_\mathrm{F}M_\mathrm{y,F} + \gamma_\mathrm{E}M_\mathrm{y,E} \\ |M_\mathrm{d}| &= \sqrt{M_\mathrm{x,d}^2 + M_\mathrm{y,d}^2} \end{align} To account for the reduced environmental and functional load factors, each load effect is evaluated four times, using all the different permutations of the load factors ($\gamma_\mathrm{F}$ and $\gamma_\mathrm{E}, \gamma_\mathrm{RF}$ and $\gamma_\mathrm{RE}, \gamma_\mathrm{RF}$ and $\gamma_\mathrm{E}$, and $\gamma_\mathrm{F}$ and $\gamma_\mathrm{RE}$), and the combination yielding the largest magnitude is used in each case. This means that a different combination of factors might be used for the tension and the moment.

The LRFD code check result is calculated as \begin{equation} \label{LRFD} \begin{cases} \gamma_\mathrm{c}\gamma_\mathrm{m}\gamma_\mathrm{SC}\left[\gamma_\mathrm{cm}\cfrac{|M_\mathrm{d}|}{M_\mathrm{k}}\sqrt{1-\left(\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right)^2} + \left(\cfrac{T_\mathrm{e,d}}{T_\mathrm{k}}\right)^2\right] + \left(\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right)^2 & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$ and $p_\mathrm{i}-p_\mathrm{o} \lt p_\mathrm{b}$} \\ \gamma_\mathrm{c}\gamma_\mathrm{m}\gamma_\mathrm{SC}\left(\cfrac{T_\mathrm{e,d}}{T_\mathrm{k}}\right)^2 + \left(\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right)^2 & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$ and $p_\mathrm{i}-p_\mathrm{o} \geq p_\mathrm{b}$} \\ (\gamma_\mathrm{c}\gamma_\mathrm{m}\gamma_\mathrm{SC})^2\left[\gamma_\mathrm{cm}\cfrac{|M_\mathrm{d}|}{M_\mathrm{k}} + \left(\cfrac{T_\mathrm{e,d}}{T_\mathrm{k}}\right)^2\right]^2 + (\gamma_\mathrm{c}\gamma_\mathrm{m}\gamma_\mathrm{SC})^2\left(\cfrac{p_\mathrm{o} - P_\textrm{min}}{p_\mathrm{c}}\right)^2 & \text{otherwise ($p_\mathrm{i} \leq p_\mathrm{o}$)} \end{cases} \end{equation} where \begin{align} M_\mathrm{k} &= f_\mathrm{y}\alpha_\mathrm{c}(\ODs - t_\mathrm{2})^2t_\mathrm{2} \\ T_\mathrm{k} &= f_\mathrm{y}\alpha_\mathrm{c}\pi(\ODs - t_\mathrm{2})t_\mathrm{2} \\ \alpha_\mathrm{c} &= \min\left\{1.2, (1 - \beta) + \beta\frac{f_\mathrm{u}}{f_\mathrm{y}}\right\} \\ \beta &= \begin{cases} 0.4 + q_\mathrm{h} & \text{if $\ODs/t_\mathrm{2} \lt 15$} \\ (0.4 + q_\mathrm{h})(60 - \ODs/t_\mathrm{2})/45 & \text{if $15 \leq \ODs/t_\mathrm{2} \lt 60$} \\ 0 & \text{otherwise ($\ODs/t_\mathrm{2} \geq 60$)} \end{cases} \\ q_\mathrm{h} &= \frac{2}{\sqrt{3}} \frac{\max(p_\mathrm{i} - p_\mathrm{o}, 0)}{p_\mathrm{b}} \end{align}

Note: This analysis excludes the terms associated with accidental loads. Under DNV OS F201, accidental loads are not usually considered simultaneously with functional and environmental loads in global analyses. However, when conducting an SLS or ALS assessment, as per DNV OS F201, the environmental load effect factor, $\gamma_\mathrm{E}$, and the accidental load effect factor, $\gamma_\mathrm{A}$, both take the value 1.0, so the accidental loading could in principle be included in the OrcaFlex model alongside the environmental loading.

DNV OS F201 WSD format

The WSD code check result is calculated as \begin{equation} \label{WSD} \begin{cases} \cfrac{\gamma_\mathrm{cm}\cfrac{|M|}{M_\mathrm{k}}\sqrt{1-\left(\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right)^2} + \left(\cfrac{T_\mathrm{e}}{T_\mathrm{k}}\right)^2 + \left(\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right)^2}{\eta^2} & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$ and $p_\mathrm{i}-p_\mathrm{o} \lt p_\mathrm{b}$} \\ \cfrac{\left(\cfrac{T_\mathrm{e}}{T_\mathrm{k}}\right)^2 + \left(\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right)^2}{\eta^2} & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$ and $p_\mathrm{i}-p_\mathrm{o} \geq p_\mathrm{b}$} \\ \cfrac{\left[\gamma_\mathrm{cm}\cfrac{|M|}{M_\mathrm{k}} + \left(\cfrac{T_\mathrm{e}}{T_\mathrm{k}}\right)^2\right]^2 + \left(\cfrac{p_\mathrm{o} - P_\textrm{min}}{p_\mathrm{c}}\right)^2}{\eta^4} & \text{otherwise ($p_\mathrm{i} \leq p_\mathrm{o}$)} \end{cases} \end{equation}