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Code checks: DNV ST F101 |
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Code checks: DNV ST F101 |
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 ST F101 properties, factors and CRA properties 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 ST F101, section 5, table 5-5. The default value ~ means that $t_\mathrm{2}$ will be calculated as $(\ODs - \IDs)/2$.
See DNV ST F101, section 5.3.3.3.
See DNV ST F101, section 5.3.3.3.
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.
See DNV ST F101, section 5.4.6.11, and section 7, table 7-5 and table 7-11.
See DNV ST F101, section 5.4.4.2.
See DNV ST F101, section 13, table 13-5.
See DNV ST F101, section 4, table 4-4.
See DNV ST F101, section 4, table 4-4.
See DNV ST F101, section 4, table 4-5.
Defines an alternative, smaller functional load factor to satisfy the requirement (DNV ST F101, section 4, table 4-4) that, if the functional load effect reduces the combined load effect, a smaller functional load factor shall be used.
See DNV ST F101, section 5, table 5-2.
See DNV ST F101, section 5, table 5-2.
See DNV ST F101, section 5, table 5-1.
See DNV ST F101, section 5, table 5-4.
See DNV ST F101, section 13.4.9.
See DNV ST F101, section 5.4.6.8.
A factor, not named in the standard, allowing for modification of the strain curvature capacity. See DNV ST F101, section 5.4.6.13.
See DNV ST F101, section 5.4.6.11. The default value ~ means that $\alpha_\mathrm{mat}$ will be calculated as shown below.
See DNV ST F101, section 5, table 5-5.
See DNV ST F101, section 5.3.3.4.
See DNV ST F101, section 5.3.3.4.
| 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. |
To calculate the DNV ST F101 code check results, 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 local buckling – combined loading criteria are implemented as separate results for the load-controlled and displacement-controlled conditions defined in section 5, DNV ST F101, and the precise nature of the load $L(t)$ differs between these two results. For the load-controlled case, the load is the effective tension, $T_\mathrm{e}$, and the $x$ and $y$ bend moments, $M_\mathrm{x}$ and $M_\mathrm{y}$, while for displacement-controlled, it is the compressive strain, $\epsilon$, given by max bending strain - direct tensile strain.
The loads are separated, using an obvious subscript notation \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} \\ \epsilon_\mathrm{E}(t) &= \epsilon(t) - \epsilon_\mathrm{F} \end{align} The design load effects (design tension effect, $T_\mathrm{e,Sd}$, design moment effect, $M_\mathrm{Sd}$, and design compressive strain effect, $\epsilon_\mathrm{Sd}$) are given by \begin{align} T_\mathrm{e,Sd} &= \max(|\gamma_\mathrm{F}\gamma_\mathrm{c}T_\mathrm{e,F} + \gamma_\mathrm{E}T_\mathrm{e,E}|, |\gamma_\mathrm{RF}\gamma_\mathrm{c}T_\mathrm{e,F} + \gamma_\mathrm{E}T_\mathrm{e,E}|) \\ M_\mathrm{Sd} &= \max(|\gamma_\mathrm{F}\gamma_\mathrm{c}M_\mathrm{F} + \gamma_\mathrm{E}M_\mathrm{E}|, |\gamma_\mathrm{RF}\gamma_\mathrm{c}M_\mathrm{F} + \gamma_\mathrm{E}M_\mathrm{E}|) \\ \epsilon_\mathrm{Sd} &= \max(\gamma_\mathrm{F}\gamma_\mathrm{c}\epsilon_\mathrm{F} + \gamma_\mathrm{E}\epsilon_\mathrm{E}, \gamma_\mathrm{RF}\gamma_\mathrm{c}\epsilon_\mathrm{F} + \gamma_\mathrm{E}\epsilon_\mathrm{E}) \end{align} In order to calculate the results, a number of derived values are required as follows.
The pressure containment resistance (or burst pressure), $p_\mathrm{b}$, is used in the case where the internal pressure is greater than the external pressure, and is given by \begin{equation} p_\mathrm{b} = \frac{2}{\sqrt{3}} \frac{2 t_\mathrm{2}}{\ODs-t_\mathrm{2}} f_\mathrm{cb} \end{equation} Or accounting for liner/clad material \begin{equation} p_\mathrm{b,com} = \frac{2}{\sqrt{3}} \frac{2 \left(t_\mathrm{2} f_\mathrm{cb} + t_\mathrm{CRA} f_\mathrm{y,CRA} \right)}{\ODs-t_\mathrm{2}-t_\mathrm{CRA}} \end{equation} where \begin{equation} f_\mathrm{cb} = \min\left(f_\mathrm{y}, \frac{f_\mathrm{u}}{1.15}\right) \end{equation} The characteristic resistance for external pressure (or collapse pressure), $p_\mathrm{c}$, is used in the case where the external pressure is greater than the internal pressure, and requires the solution of the third degree polynomial \begin{equation} \label{p_cPoly} \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}O_\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} An analytical solution to the polynomial (\ref{p_cPoly}) is given in section 13.4.7, DNV ST F101\begin{equation} p_\mathrm{c} = y - \frac{b}{3} \end{equation} where \begin{align} b &= -p_\mathrm{el} \\ c &= -\left(p_\mathrm{p}^2 + p_\mathrm{p}p_\mathrm{el}O_\mathrm{0}\frac{\ODs}{t_\mathrm{2}}\right) \\ d &= p_\mathrm{el}p_\mathrm{p}^2 \\ u &= \frac{1}{3}\left(\frac{-b^2}{3} + c\right) \\ v &= \frac{1}{2}\left(\frac{2b^3}{27} - \frac{bc}{3} + d\right) \\ \Phi &= \cos^{-1}\left(\frac{-v}{\sqrt{-u^3}}\right) \\ y &= -2\sqrt{-u} \cos\left(\frac{\Phi}{3} + \frac{60\pi}{180}\right) \end{align} To calculate the collapse pressure, $p_\mathrm{c,com}$, accounting for liner/clad material, $t_\mathrm{2}$, $p_\mathrm{p}$, and $p_\mathrm{el}$ are replaced by $t_\mathrm{2} + t_\mathrm{CRA}$, $p_\mathrm{p,com}$, and $p_\mathrm{el,com}$ respectively in the above, where \begin{align} p_\mathrm{p,com} &= f_\mathrm{y}\alpha_\textrm{fab}\frac{2t_\mathrm{2}}{\ODs} + f_\mathrm{y,CRA} \frac{2t_\mathrm{CRA}}{\ODs - 2t_\mathrm{2}} \\ p_\mathrm{el,com} &= 2E\left(\frac{t_\mathrm{2} + t_\mathrm{CRA}}{\ODs}\right)^3\frac{\alpha_\mathrm{el}}{1-\nu^2} \\ \alpha_\mathrm{el} &= 1 - 1.85 \frac{t_\mathrm{CRA}}{t_\mathrm{2}} + 1.7 \left(\frac{t_\mathrm{CRA}}{t_\mathrm{2}}\right)^2 \end{align}
The load-controlled code check result is calculated as \begin{equation} \begin{cases} \left[\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{|M_\mathrm{Sd}|}{\alpha_\mathrm{pm} \left( \alpha_\mathrm{c,BS} M_\mathrm{p} + \alpha_\mathrm{c,CRA}M_\mathrm{p,CRA} \right)} + \left(\cfrac{\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}T_\mathrm{e,Sd}}{\alpha_\mathrm{c,BS}S_\mathrm{p} + \alpha_\mathrm{c,CRA}S_\mathrm{p,CRA}}\right)^2\right]^2 + \left(\gamma_\mathrm{p,com}\cfrac{p_\mathrm{i} - p_\mathrm{o}}{\alpha_\mathrm{c,com}p_\mathrm{b,com}}\right)^2 & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$} \\ \left[\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{|M_\mathrm{Sd}|}{\alpha_\mathrm{pm} \left(\alpha_\mathrm{c,BS}M_\mathrm{p} + \alpha_\mathrm{c,CRA}M_\mathrm{p,CRA} \right)} + \left(\cfrac{\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}T_\mathrm{e,Sd}}{\alpha_\mathrm{c,BS}S_\mathrm{p} + \alpha_\mathrm{c,CRA}S_\mathrm{p,CRA}}\right)^2\right]^2 + \left(\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{p_\mathrm{o} - P_\textrm{min}}{p_\mathrm{c,com}}\right)^2 & \text{otherwise} \end{cases} \end{equation} where \begin{align} S_\mathrm{p} &= f_\mathrm{y}\pi(\ODs - t_\mathrm{2})t_\mathrm{2} \\ M_\mathrm{p} &= f_\mathrm{y}(\ODs - t_\mathrm{2})^2t_\mathrm{2} \\ S_\mathrm{p,CRA} &= f_\mathrm{y,CRA}\pi(\ODs - 2t_\mathrm{2} - t_\mathrm{CRA})t_\mathrm{CRA} \\ M_\mathrm{p,CRA} &= f_\mathrm{y,CRA}(\ODs - 2t_\mathrm{2} - t_\mathrm{CRA})^2t_\mathrm{CRA} \\ \alpha_\mathrm{c,BS} &= 1 + \beta_\mathrm{com}\left( \frac{f_\mathrm{u}}{f_\mathrm{y}} - 1 \right) \\ \alpha_\mathrm{c,CRA} &= 1 + \beta_\mathrm{com}\left( \frac{f_\mathrm{u,CRA}}{f_\mathrm{y,CRA}} - 1 \right) \\ \gamma_\mathrm{p,com} &= \begin{cases} 1 - \beta_\mathrm{com} & \text{if $\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b,com}} \lt \cfrac{2}{3}$} \\ 1 - 3\beta_\mathrm{com}\left(1 - \cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b,com}}\right) & \textrm{otherwise} \end{cases} \\ \beta_\mathrm{com} &= \frac{1}{90} \left(60 - \frac{\ODs}{t_\mathrm{2} + t_\mathrm{CRA}}\right) \\ \alpha_\mathrm{c,com} &= 1 + \frac{\beta_\mathrm{com}}{t_\mathrm{2} + t_\mathrm{CRA}}\left( t_\mathrm{2} \frac{f_\mathrm{u}}{f_\mathrm{y}} + t_\mathrm{CRA} \frac{f_\mathrm{u,CRA}}{f_\mathrm{y,CRA}} \right) - \beta_\mathrm{com} \end{align}
Legacy support for the DNV OS F101 2012 load-controlled code check result, calculated as \begin{equation} \begin{cases} \left[\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{|M_\mathrm{Sd}|}{\alpha_\mathrm{c}(\alpha_\mathrm{pm}M_\mathrm{p})} + \left(\cfrac{\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}T_\mathrm{e,Sd}}{\alpha_\mathrm{c}S_\mathrm{p}}\right)^2\right]^2 + \left(\alpha_\mathrm{p}\cfrac{p_\mathrm{i} - p_\mathrm{o}}{\alpha_\mathrm{c}p_\mathrm{b}}\right)^2 & \text{if $p_\mathrm{i} \gt p_\mathrm{o}$} \\ \left[\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{|M_\mathrm{Sd}|}{\alpha_\mathrm{c}(\alpha_\mathrm{pm}M_\mathrm{p})} + \left(\cfrac{\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}T_\mathrm{e,Sd}}{\alpha_\mathrm{c}S_\mathrm{p}}\right)^2\right]^2 + \left(\gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{p_\mathrm{o} - P_\textrm{min}}{p_\mathrm{c}}\right)^2 & \text{otherwise} \end{cases} \end{equation} where \begin{align} \alpha_\mathrm{c} &= (1 - \beta) + \beta \frac{f_\mathrm{u}}{f_\mathrm{y}} \\ \alpha_\mathrm{p} &= \begin{cases} 1 - \beta & \text{if $\cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}} \lt \cfrac{2}{3}$} \\ 1 - 3\beta\left(1 - \cfrac{p_\mathrm{i} - p_\mathrm{o}}{p_\mathrm{b}}\right) & \textrm{otherwise} \end{cases} \\ \beta &= \frac{1}{90} \left(60 - \frac{\ODs}{t_\mathrm{2}}\right) \end{align}
This result is calculated as \begin{equation} \frac{T_\mathrm{e,Sd}}{S_\mathrm{p}} \end{equation} The valid range for the above load-controlled criteria is given as $T_\mathrm{e,Sd}/S_\mathrm{p} \lt 0.4$, in section 5.4.6.6 and section 5.4.6.10, DNV ST F101.
The displacement-controlled code check result is \begin{equation} \begin{cases} \gamma_\mathrm{SC,DC}\cfrac{\epsilon_\mathrm{Sd}}{\epsilon_\mathrm{c}(t_\mathrm{2} + t_\mathrm{CRA}, P_\textrm{min} - p_\mathrm{o})} & \text{if $\epsilon_\mathrm{Sd} \geq 0$ and $p_\mathrm{i} \geq p_\mathrm{o}$} \\ \left[\gamma_\mathrm{SC,DC}\cfrac{\epsilon_\mathrm{Sd}}{\epsilon_\mathrm{c}(t_\mathrm{2}, 0)}\right]^{0.8} + \gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{p_\mathrm{o} - P_\textrm{min}}{p_\mathrm{c}} & \text{if $\epsilon_\mathrm{Sd} \geq 0$ and $p_\mathrm{i} \lt p_\mathrm{o}$} \\ 0 & \text{otherwise ($\epsilon_\mathrm{Sd} \lt 0$)} \end{cases} \end{equation} where \begin{align} \epsilon_\mathrm{c}(t, p_\textrm{net}) &=\alpha_\mathrm{\epsilon c} \alpha_\mathrm{p} \alpha_\mathrm{mat} \tilde{\epsilon}(t) \\ \tilde{\epsilon}(t) &= \left(\frac{t}{\ODs} - 0.01\right)\left(\frac{0.85}{\alpha_\mathrm{h}}\right)^{1.5}\alpha_\mathrm{gw} \\ \alpha_\mathrm{p} &= 1 + \frac{20}{3} \left(\frac{p_\textrm{net}}{p_\mathrm{b,com}}\right)^2 \end{align} The Lüder factor, $\alpha_\mathrm{mat}$, can be user specified. If a value of ~ is given, it will be calculated as \begin{equation} \begin{cases} 1 & \text{if $\tilde{\epsilon} \alpha_\mathrm{p} \gt 0.025$} \\ 0.6 & \text{if $\tilde{\epsilon} \alpha_\mathrm{p} \lt 0.015$} \\ 0.6 + 40(\tilde{\epsilon} \alpha_\mathrm{p} - 0.015) & \text{otherwise} \end{cases} \end{equation}
| Note: | This result is not available at arc lengths where the line type uses hysteretic or externally calculated axial stiffness. These axial stiffness data sources do not permit derivation of the direct tensile strain result, or this result which is calculated with direct tensile strain as input. |
Legacy support for the DNV OS F101 2012 displacement-controlled code check, calculated as \begin{equation} \begin{cases} \gamma_\mathrm{SC,DC}\cfrac{\epsilon_\mathrm{Sd}}{\epsilon_\mathrm{c}(t_\mathrm{2}, P_\textrm{min} - p_\mathrm{o})} & \text{if $\epsilon_\mathrm{Sd} \geq 0$ and $p_\mathrm{i} \geq p_\mathrm{o}$} \\ \left[\gamma_\mathrm{SC,DC}\cfrac{\epsilon_\mathrm{Sd}}{\epsilon_\mathrm{c}(t_\mathrm{2}, 0)}\right]^{0.8} + \gamma_\mathrm{m}\gamma_\mathrm{SC,LB}\cfrac{p_\mathrm{o} - P_\textrm{min}}{p_\mathrm{c}} & \text{if $\epsilon_\mathrm{Sd} \geq 0$ and $p_\mathrm{i} \lt p_\mathrm{o}$} \\ 0 & \text{otherwise ($\epsilon_\mathrm{Sd} \lt 0$)} \end{cases} \end{equation} where \begin{equation} \epsilon_\mathrm{c}(t, p_\textrm{net}) = 0.78\left(\frac{t}{\ODs} - 0.01\right)\left(1 + 5.75\frac{p_\textrm{net}}{p_\mathrm{b}}\right)\alpha_\mathrm{h}^{-1.5}\alpha_\mathrm{gw} \end{equation}
| Note: | This result is not available at arc lengths where the line type uses hysteretic or externally calculated axial stiffness. These axial stiffness data sources do not permit derivation of the direct tensile strain result, or this result which is calculated with direct tensile strain as input. |
This result represents the simplified laying criteria for the overbend, given in section 13, DNV ST F101, and is given by \begin{equation} \frac{|\epsilon_\mathrm{zz}|}{\epsilon_\textrm{lim}} \end{equation} where $\epsilon_\mathrm{zz}$ is the worst zz strain and the simplified strain limit, $\epsilon_\textrm{lim}$, is given the appropriate value from table 13-5, DNV ST F101, using criterion I or II for static or dynamic analysis respectively.
| Note: | This result is not available at arc lengths where the line type uses hysteretic or externally calculated axial stiffness. These axial stiffness data sources do not permit derivation of the direct tensile strain result, or this result which is calculated with direct tensile strain as input. |
This result represents the simplified laying criteria for the sagbend, section 13, DNV ST F101, and is given by \begin{equation} \frac{\sigma_\mathrm{vm}}{0.87f_\mathrm{y}} \end{equation} where $\sigma_\mathrm{vm}$ is the max von Mises stress.