## Line results: End loads |

The line end load results are based on the end force and end moment vectors at the line end.

Note that these results include the structural inertia load and added inertia load due to acceleration of the end node.

There are 3 groups of end load results:

- Standard results like effective tension, bend moment, etc. are available at line ends as well as at mid-segment points. For example to obtain the end tension at end A you can ask for the effective tension (or wall tension) at end A.
- Magnitude and individual components of the end force and end moment vectors.
- Bend restrictor load, which is a special end load result useful for bend restrictor design.

When considering the sign of end load components the question arises as to whether the load reported is that applied by the line to the parent object to which it is connected, or vice versa. The OrcaFlex convention is that the load reported at any point is that applied by the B side of that point to the A side. So at end A we report the end load applied *by* the line *to* its parent (e.g. a vessel), but at end B we report the end load applied *to* the line *by* its parent. This is in keeping with the OrcaFlex convention for the no-moment direction.

Normally, the end force and end moment are the total force and moment acting between the line end and the parent object to which it is connected. These totals include the appropriate contributions from any child objects themselves attached to the end node.

If, however, the line end is free (or has been released), then it is not connected to any parent object, and the end force and end moment are taken to be the total force and moment acting between the line end and any child lines, vessels, turbines, links or winches (but no other objects) connected to the end node. If the end node has no child lines, vessels, turbines, links or winches (or they have been released), the end load is zero.

Shear force, x shear force, y shear force,

Bend moment, x bend moment, y bend moment,

Curvature, x curvature, y curvature

These results are available at both end nodes and mid-segment points, and which are reported depends on the result point. If you ask for these results at end A or end B, or at an arc length that is closer to a line end than to the nearest mid-segment, then the results reported will be those at the line end; otherwise, the results for the nearest mid-segment point will be reported.

The mid-segment results are documented under line results: forces, line results: moments and line results: pipe stresses.

At line ends, these results report the components of the end loads in the local node directions of the end node, as follows:

- Effective tension is the component of the end force vector in the end node axial direction $\vec{N}_\mathrm{z}$.
- Wall tension is derived from the effective tension at the line end, using the pressure effects formula.
- Shear is the component of the end force vector normal to the end node axial direction.
- x-shear and y-shear are the components of the end force vector in the end node Nx and Ny directions.
- Torque is the component of the end moment vector in the end node axial direction.
- Bend moment is the component of the end moment vector normal to the end node axial direction.
- x-bend moment and y-bend moment are the components in the end node Nx and Ny directions.
- Stress results are based on the end load components in the end node axes directions.

The end values of these results differ from the corresponding values for the end segment for two reasons.

Firstly, they include the loads (weight, buoyancy, drag etc.) on the last half segment adjacent to the end.

Secondly, they are components in the local node directions Nxyz at the end node, whereas the end segment values are components with respect to the segment directions (Sx,Sy,Sz). The end node is often not aligned with the end segment because end connection stiffness turns it towards the end orientation direction. For example:

- If the end connection stiffness is zero, or if the line end is free or has been released, then the end node directions are aligned with the end segment directions. The end node values then differ from the end segment values only by the loads on the end half segment.
- If the end connection stiffness is infinity (and the end is not free or released) then the end node directions stay aligned with the line end axes $\Exyz$. The end node values are then usually in different directions to the end segment values.
- For intermediate values of end connection stiffness, the end node directions will be somewhere between the two. They will tend to be nearer to the end fitting directions if the end connection stiffnesses are stronger than the line bend stiffness and torsional stiffness, but nearer to the end segment directions if it is weaker.

End GX force, end GY force and end GZ force, end GX moment, end GY moment, end GZ moment,

End Lx force, end Ly force and end Lz force, end Lx moment, end Ly moment, end Lz moment,

End Ex force, end Ey force and end Ez force, end Ex moment, end Ey moment, end Ez moment

These results report the magnitude of the end force and end moment vectors, and their components in the following directions:

- The directions of the global axes $\GXYZ$.
- The directions of the local axes $\Lxyz$ of the parent object to which the line end is connected. For example, if the line end is connected to a vessel, the $\Lxyz$ axes are the directions of the vessel axes.
- The directions of the line end axes $\Exyz$.

For a line with a stiffener attached results are reported separately for the protected line and its stiffener. However, it is sometimes necessary (e.g. when designing end fittings) to report combined end loads including the load from both the protected line and its stiffener.

End load results are available for the protected line which include the stiffener end load, in addition to the protected line end load. These results are all prefixed with "Total", e.g. **Total end force**, **Total end moment**, **Total end GZ force** etc.

This is defined as bend restrictor load = end force*(1 - cos(end force Ez angle)). Another commonly used name for this variable is "pseudo-curvature". It is only available for line ends that are pin-connected (zero bending stiffness at the line end connection) and without a stiffener attached.