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

Geometry
---------

The test case is a metal frame composed of beams and columns.


.. image:: images/10000000000002920000028C79A433F80AF155F1.png
    :width: 5.2118in
    :height: 5.1591in


.. _RefImage_10000000000002920000028C79A433F80AF155F1.png:

Coordinates of the main nodes of the mesh:

.. csv-table::

    "Point", "Coordinator. :math:`X` (in :math:`m`)", "Coord. :math:`Y` (in :math:`m`)", "Coord. :math:`Z` (in :math:`m`)"
    ":math:`A` ", "2.0", "2.5", "0.0"
    ":math:`B` ", "4.0", "0.0", "0.0"
    ":math:`C` ", "2.0", "—2.5", "0.0"
    ":math:`D` ", "0.0", "0.0", "0.0"
    ":math:`E` ", "2.0", "2.5", "3.0"
    ":math:`F` ", "4.0", "0.0", "3.0"
    ":math:`G` ", "2.0", "—2.5", "3.0"
    ":math:`H` ", "0.0", "0.0", "0.0", "3.0"
    ":math:`I` ", "2.0", "0.0", "3.0"



Mechanical characteristics of beams
------------------------

The beams in the test case are standard profiles in metal construction. The units of their mechanical characteristics are homogeneous to meters away.


.. csv-table::

    "", ":math:`\mathrm{HEA200}` "," :math:`\mathrm{IPE220}` "," :math:`\mathrm{IPE160}` "," "," :math:`\mathrm{HEA140}` "," :math:`\mathrm{IPE120}`"
    "Beams", ":math:`\mathrm{BF},\mathrm{DH}` "," :math:`\mathrm{HF}` "," "," :math:`\mathrm{EI},\mathrm{CG}` "," :math:`\mathrm{AE}` "," :math:`\mathrm{FG},\mathrm{GH}`"
    ":math:`A` ", "5.39E—03", "3.34E—03", "3.34E—03", "2.01E—03", "3.14E—03", "1.32E—03"
    ":math:`\mathrm{IY}` ", "3.69E—05", "2.77E—05", "2.77E—05", "8.70E—06", "1.03E—05", "3.18E—06"
    ":math:`\mathrm{IZ}` ", "1.34E—05", "2.05E—06", "2.05E—06", "6.83E—07", "3.89E—06", "2.77E—07"
    ":math:`\mathrm{AY}` ", "1.474994", "1.789865", "1.789865", "1.792884", "1.464032", "1.774392"
    ":math:`\mathrm{AZ}` ", "4.466038", "2.633754", "2.633754", "2.586199", "4.464173", "2.590182"
    ":math:`\mathrm{JX}` ", "1.97E—07", "8.66E—08", "8.66E—08", "3.37E—08", "7.76E—08", "1.63E—08"
    ":math:`\mathrm{JG}` ", "1.06E—07", "2.23E—08", "2.23E—08", "3.89E—09", "1.47E—08", "8.73E—10"


The sizes :math:`\mathrm{EY}`, :math:`\mathrm{EZ}`, :math:`\mathrm{IYR2}`, :math:`\mathrm{IZR2}` are zero for all the beams.


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

Only one material is used:

Young :math:`2.10e+11\mathrm{Pa}`

Rho :math:`7.85e+03\mathrm{kg}/{m}^{3}`


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

Points :math:`A,B,C,D` are embedded.

.. csv-table::

    ":math:`\mathrm{DX}=0` "," :math:`\mathrm{DY}=0` "," :math:`\mathrm{DZ}=0` "," "," :math:`\mathrm{DRX}=0` "," :math:`\mathrm{DRY}=0` "," :math:`\mathrm{DRZ}=0`"