Reference problem
=====================


Geometry
---------

Piping bent in plane :math:`\mathrm{XY}`. The straight sections are :math:`L=1200\mathrm{mm}` in length.

The radius of curvature of the elbow is: :math:`\mathrm{Rc}=\mathrm{305mm}`


.. image:: images/Object_1.svg
    :width: 196
    :height: 149


.. _RefImage_Object_1.svg:

The average radius of the tubular section is :math:`R=\mathrm{105.5mm}` and the thickness is :math:`e=\mathrm{8.18mm}`.


Material properties
------------------------

:math:`E=200000\mathrm{MPa}`

:math:`\nu =0.3`


Boundary conditions and loads
-------------------------------------

Embedding in :math:`A`

2 load cases:


1. Moment :math:`\mathrm{MZ}` imposed in :math:`D`: :math:`\mathrm{MZ}=17000\mathrm{Nm}` (plane bending).


2. Off-plane bending: moment :math:`\mathrm{My}` imposed in :math:`D`

:math:`\mathrm{My}=17000\mathrm{Nm}`


Initial conditions
--------------------

Not applicable.