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


Geometry
---------


.. image:: images/10002A08000031D1000012EAC31A2205B2BD2B6E.svg
    :width: 642
    :height: 244


.. _RefImage_10002A08000031D1000012EAC31A2205B2BD2B6E.svg:

**Beam length:**

:math:`L=1m`

**Rectangular section:**


.. csv-table::

    "", "**Initial Straight Section**", "", "**Final Straight Section**"
    "", "**Case 1**", "**Case 2**", ""
    "height:", ":math:`{h}_{o}=0.04m` "," :math:`=0.04m` "," :math:`{h}_{1}=0.01m`"
    "width:", ":math:`{b}_{o}=0.04m` "," :math:`=0.05m` "," :math:`{b}_{1}=0.01m`"
    "do:", ":math:`{A}_{o}\mathrm{=}1.6{10}^{\mathrm{-}3}{m}^{2}` "," :math:`={2.10}^{-3}{m}^{2}` "," :math:`{A}_{1}={1.10}^{-4}{m}^{2}`"
    "inertia:", ":math:`{\mathrm{lz}}_{o}=2.1333{10}^{-7}{m}^{4}` "," :math:`=2.6667{10}^{-7}{m}^{4}` "," :math:`{\mathrm{Iz}}_{\mathrm{1 }}=8.3333{10}^{-10}{m}^{4}`"


**Point coordinates (** :math:`m` **) :**


.. csv-table::

    "", ":math:`A` "," :math:`B`"
    ":math:`x` ", "0. ", "1."
    ":math:`y` ", "0. ", "0."
    ":math:`z` ", "0. ", "0."



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

:math:`E={2.10}^{11}\mathrm{Pa}`

:math:`\rho =7800\mathrm{kg}/{m}^{3}`


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

Point :math:`A`: recessed :math:`u=v=0` :math:`\theta =0.`