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


Geometry
---------


.. image:: images/100007CE000029220000087A8E419B683BC9BD2C.svg
    :width: 530
    :height: 109


.. _RefImage_100007CE000029220000087A8E419B683BC9BD2C.svg:

The geometric characteristics of the beam constituting the mechanical model are as follows:

Length: :math:`L=10m`


.. csv-table::

    "Cross Section", "Area", ":math:`\mathrm{IZ}=\mathrm{IY}` "," :math:`\mathrm{JX}`"
    "", ":math:`3.439{10}^{-3}{m}^{2}` "," :math:`1.377{10}^{-5}{m}^{4}` "," :math:`2.754{10}^{-5}{m}^{4}`"


The coordinates (in meters) of the characteristic points of the beam are:


.. csv-table::

    "", ":math:`A` "," :math:`B`"
    ":math:`x` ", "0. ", "10."
    ":math:`y` ", "0. ", "0."



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

The properties of the material from which the beam is made are:

:math:`E=1.658\times {10}^{11}\mathit{Pa}`

:math:`\nu =0.3`

:math:`\mathrm{\rho }=1.3404106104\mathit{kg}\mathrm{.}{m}^{-3}`

:math:`\alpha =\text{AMOR\_ALPHA}=0.001`

:math:`\beta =\text{AMOR\_BETA}=0.`


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

The boundary condition that characterizes this problem is the embedment of point :math:`A` and is written as:

:math:`u=v=0.`

:math:`\mathrm{\theta }=0.`

For charging we have:


.. csv-table::

    ":math:`\mathrm{Fx}=3000.N` ", "", ":math:`\mathrm{Fy}=\mathrm{Fz}=0.` ", "(tractive force)"
    ":math:`\mathrm{Fx}=0.` "," :math:`\mathrm{Fy}=3000.N` "," :math:`\mathrm{Fz}=0.` ", "(bending force)"