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

Geometry
---------

Geometric values are expressed in meters.

Straight beam of length :math:`L=1`, direction :math:`x`.


.. image:: images/100000000000032E000000B10B745D3C987624CE.png
    :width: 4.9217in
    :height: 1.0665in


.. _RefImage_100000000000032E000000B10B745D3C987624CE.png:

Two types of section are calculated simultaneously:

+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Rectangular section                                                                                                                                                 |Circular section                                                                                                                                                  |
+                                                                                                                                                                    +                                                                                                                                                                  +
|                                                                                                                                                                    |                                                                                                                                                                  |
+ .. image:: images/10000000000001060000011BC8363945E0463E5B.png                                                                                                     + .. image:: images/1000000000000074000000732A48C99847FF9367.png                                                                                                   +
|    :width: 2.1791in                                                                                                                                                |    :width: 0.9598in                                                                                                                                              |
+    :height: 2.352in                                                                                                                                                +    :height: 0.9508in                                                                                                                                             +
|                                                                                                                                                                    |                                                                                                                                                                  |
+                                                                                                                                                                    +                                                                                                                                                                  +
|                                                                                                                                                                    |                                                                                                                                                                  |
+                                                                                                                                                                    +                                                                                                                                                                  +
|                                                                                                                                                                    |                                                                                                                                                                  |
+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------+


For modeling D, 1 thin tube section is calculated:


.. image:: images/100000000000007800000078436C191CC3DB6F4F.png
    :width: 0.9937in
    :height: 0.9902in


.. _RefImage_100000000000007800000078436C191CC3DB6F4F.png:


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

:math:`E=2.{10}^{11}\mathrm{Pa}`

:math:`\nu =0.3`

.. csv-table::

    "ECRO_LINE:"
    ":math:`\mathrm{SY}={\sigma }_{y}=150{10}^{6}\mathrm{Pa}`"
    ":math:`H` = D_ SIGM_EPSI = :math:`2{10}^{9}\mathrm{Pa}` or 0"



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

Embedding in :math:`O`

Displacement imposed in :math:`B`

:math:`{\mathrm{DX}}^{e}=\frac{\mathrm{L.}{\sigma }_{y}}{E}={0.7510}^{-3}m`

:math:`\mathrm{DX}` varies from :math:`{\mathrm{DX}}^{e}` to :math:`{\mathrm{3DX}}^{e}`

Rotation imposed in :math:`B`

:math:`{\mathrm{DRZ}}^{e}={0.7510}^{-2}m`

:math:`\mathrm{DRZ}` varies from :math:`{\mathrm{DRZ}}^{e}` to :math:`20\mathrm{\times }{\mathit{DRZ}}^{e}` and then decreases to :math:`\mathrm{-}2\mathrm{\times }{\mathit{DRZ}}^{e}`

**Note:**

*In pure bending,* :math:`\mathrm{MZ}` *and* :math:`\mathrm{DRZ}` *do not depend on* :math:`x`\ *. The curvature* :math:`\varphi =\frac{d(\mathrm{DRZ})}{\mathrm{dx}}=\mathrm{DRZ}(B)`