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


Geometry
---------

We consider an arc :math:`\mathit{AB}` with radius :math:`100\mathit{cm}`, center :math:`C` and aperture :math:`45°`


.. image:: images/10000000000004AD000003E951804794D7A8C1B5.png
    :width: 6.889in
    :height: 5.7602in


.. _RefImage_10000000000004AD000003E951804794D7A8C1B5.png:

Illustration 1.1.1: arc geometry

Coordinates of the points (in :math:`\mathit{cm}`):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C`"
    ":math:`x` ", "0", "29.3", "100"
    ":math:`y` ", "0", "70.7", "0"
    ":math:`z` ", "0", "0", "0"



Characteristics of the section
------------------------------

The arc has a square cross section of :math:`1\mathit{cm}` by :math:`1\mathit{cm}`.


.. csv-table::

    ":math:`A\mathrm{=}1{\mathit{cm}}^{2}`"
    ":math:`{I}_{y}\mathrm{=}{I}_{z}\mathrm{=}0.0833{\mathit{cm}}^{4}`"
    ":math:`{A}_{y}\mathrm{=}{A}_{z}\mathrm{=}1.2`"



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


.. csv-table::

    ":math:`E\mathrm{=}1\mathit{MPa}`"
    ":math:`\nu \mathrm{=}0.0`"



Boundary conditions and loading
------------------------------------


.. csv-table::

    "1)", "Boundary conditions are imposed at point :math:`A` (arc embedment):
    :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}\mathit{DRX}\mathrm{=}\mathit{DRY}\mathrm{=}\mathit{DRZ}\mathrm{=}0`"
    "2)", "At the free end at point :math:`B`, a vertical loading (perpendicular to the plane of the arc) is imposed at the free end at point: :math:`\mathrm{600N}`
    :math:`\mathit{FZ}\mathrm{=}\text{600}\mathrm{\times }t`"