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


Geometry
---------


.. image:: images/1000039A0000154A0000054548BF3DCEC0A40115.svg
    :width: 219
    :height: 54


.. _RefImage_1000039A0000154A0000054548BF3DCEC0A40115.svg:

**Figure** 1.1-a

:math:`\mathrm{7,5}m` length straight beam.

**Section features:**

This is the :math:`U` beam shown [:ref:`Figure 1.1-b <Figure 1.1-b>`].


.. image:: images/Object_1.svg
    :width: 219
    :height: 54


.. _RefImage_Object_1.svg:

**Figure** 1.1-b **:** **Section of the beam in** :math:`U`

:math:`h=200\mathrm{mm}`

:math:`b=273\mathrm{mm}`

:math:`e=\mathrm{8,2}\mathrm{mm}`

For [:ref:`bib1 <bib1>`] we have the following data:

:math:`{I}_{y}={I}_{z}=\mathrm{5,022}{10}^{-5}{m}^{4}`

:math:`\mathrm{ZGC}=\mathrm{221,5}\mathrm{mm}`

From the geometry of the section, we calculate:


.. csv-table::

    ":math:`S=\mathrm{6,117}{10}^{-3}{m}^{2}`"
    ":math:`{J}_{x}=\mathrm{1,28}{10}^{-7}{m}^{4}`"



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


.. csv-table::

    "Young's module:", ":math:`E=2.07{10}^{11}\mathrm{Pa}`"
    "Poisson's ratio:", ":math:`\nu =\mathrm{0,3}`"
    "Density:", ":math:`\rho =7850\mathrm{kg}/{m}^{3}`"



Boundary conditions
----------------------

**Boundary condition:**

Problem plan: :math:`\mathrm{DZ}` and :math:`\mathrm{DRY}` stuck.

Knots :math:`A` and :math:`B` supported: :math:`\mathrm{DX}` and :math:`\mathrm{DY}` blocked

The eccentricity is taken into account using the LIAISON_DDL operand of the AFFE_CHAR_MECA command.

The degrees of freedom are always in :math:`G`, and eccentricity is taken into account by: :math:`\mathrm{DY}(G)=\mathrm{DY}(C)+\mathrm{GC}\wedge {\Theta }_{x}`