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

Geometry
---------

Problem plan


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    :height: 2.0362in


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.. csv-table::

    "Beam", "Length", "Moment of inertia"
    ":math:`\mathrm{AB}` "," :math:`{l}_{\mathrm{AB}}=\mathrm{4m}` "," :math:`{I}_{\mathrm{AB}}=\frac{64}{3}{10}^{-8}{m}^{4}`"
    ":math:`\mathrm{AC}` "," :math:`{l}_{\mathrm{AC}}=\mathrm{1m}` "," :math:`{I}_{\mathrm{AC}}=\frac{1}{12}{10}^{-8}{m}^{4}`"
    ":math:`\mathrm{AD}` "," :math:`{l}_{\mathrm{AD}}=\mathrm{1m}` "," :math:`{I}_{\mathrm{AD}}=\frac{1}{12}{10}^{-8}{m}^{4}`"
    ":math:`\mathrm{AE}` "," :math:`{l}_{\mathrm{AE}}=\mathrm{2m}` "," :math:`{I}_{\mathrm{AE}}=\frac{4}{3}{10}^{-8}{m}^{4}`"


:math:`G` is in the middle of :math:`\mathrm{DA}`.

Another characteristic of beams that are not used for calculations: the beams have a square cross section.

:math:`\begin{array}{}{A}_{\mathrm{AB}}=16{10}^{-4}m\\ {A}_{\mathrm{AD}}=1{10}^{-4}m\\ {A}_{\mathrm{AC}}=1{10}^{-4}m\\ {A}_{\mathrm{AE}}=4{10}^{-4}m\end{array}`


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

Isotropic linear elastic material: :math:`E=2.{10}^{11}\mathrm{Pa}`


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


1. Point :math:`C`: articulated :math:`({u}_{C}={v}_{C}=0)`.


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Punctual force in :math:`G`: :math:`F=-{10}^{5}N`

Force distributed on the beam :math:`\mathrm{AD}`: :math:`p=-{10}^{3}N/m`