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

Geometry
---------


.. image:: images/1000000000000179000001369BF8DBD499E24E3F.png
    :width: 3.2575in
    :height: 2.7126in


.. _RefImage_1000000000000179000001369BF8DBD499E24E3F.png:

Gantry geometry :math:`(m)`:

• :math:`l=20`

• :math:`h=8`

• :math:`a=4`

Quadratic moments of beams :math:`({m}^{4})`:

• Sections :math:`\mathrm{AD}`, :math:`\mathrm{EB}`: :math:`{I}_{1}=5.0{E}^{-4}`

• Sections :math:`\mathrm{DC}`, :math:`\mathrm{CE}`: :math:`{I}_{1}=2.5{E}^{-4}`

The gantry consists of beams with symmetrical sections, so that :math:`\mathrm{IY}=\mathrm{IZ.}`

Only the flexural energy is taken into account, because the beams are very slender. This is why the other beam cross-section characteristics do not come into play.


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

Isotropic linear elastic material: :math:`E=2.1\mathrm{E11}\mathrm{Pa}`


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

Articulated :math:`A` and :math:`B` post legs.

**Loading**

.. csv-table::

    "Nodal strength in :math:`C`:", ":math:`Fy=–2000N=F1`"
    "Nodal strength in :math:`D`:", ":math:`Fx=–10000N=F2`"
    "Moment in :math:`D`:", ":math:`\mathrm{Mx}=–100000\mathrm{N.m}=M`"
    "Force distributed over section :math:`\mathrm{DC}`:", ":math:`Pz=–3000N/m`"