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Homogeneous pipe |
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Homogeneous pipe |
The line type wizard for homogeneous pipe creates data for a general category line type with properties appropriate for a pipe constructed from a single homogeneous material, such as a steel riser.
| Note: | If you are modelling a homogeneous pipe then it is usually more effective to do so directly in OrcaFlex with a line type of the homogeneous pipe category. |
| Figure: | Homogeneous pipe |
Using the following notation for the input data\begin{align*} \rho &= \text{material density} \\ E &= \text{Young's modulus} \\ \nu &= \text{Poisson ratio} \\ O\!D &= \text{outer diameter} \\ t &= \text{wall thickness} \end{align*}
and calculating the value \begin{equation} I\!D = O\!D-2t \end{equation} for the inner diameter, we derive the line type properties as follows.
Mass per unit length is calculated as \begin{equation} \rho\ \frac{\pi}{4} \left( O\!D^2 - I\!D^2 \right) \end{equation}
The line type outer and inner diameters are simply $O\!D$ as given and $I\!D$ as calculated, respectively.
The line type contact diameters are set to '~'.
The line type axial stiffness is given by \begin{equation} \begin{aligned} \text{axial stiffness} &= EA \\ &= E\ \frac{\pi}{4} \left( O\!D^2 - I\!D^2 \right) \end{aligned} \end{equation} since $A$ is the cross sectional area
The line type bending stiffness is given by \begin{equation} \text{bending stiffness} = EI \end{equation} where $I$ is the second moment of area, about an axis in the plane of the cross section through the centroid (e.g. NN'), so \begin{equation} \text{bending stiffness} = E\ \frac{\pi}{64} \left( O\!D^4 - I\!D^4 \right) \end{equation}
As the bending stiffness is significant, compression is limited.
The torque experienced by a pipe of length $l$ when twisted through an angle $\theta$ is given by \begin{equation} \text{torque} = \frac{G\theta}{l}\,J \end{equation} where $J$ is the second moment of area about the axial axis OO' (often called the polar moment of inertia) and $G$ is the shear modulus (or modulus of rigidity). For homogeneous pipes, $J = 2I$; $G$ is calculated as \begin{equation} G = \frac{E}{2(1+\nu)} \end{equation} The torsional stiffness, representing the torque resisting a twist of 1 radian, per unit length, is therefore given by \begin{equation} \text{torsional stiffness} = \frac{E}{2(1+\nu)}\ \frac{\pi}{32} \left( O\!D^4 - I\!D^4 \right) \end{equation}
The line type stress diameters are set to '~', since they are the same as the pipe diameters.
These are set to one, as a simple homogeneous pipe carries all the loads.
