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


Geometry
---------


.. image:: images/100011E400002EB700001E480BBD016A6C22E4FD.svg
    :width: 602
    :height: 390


.. _RefImage_100011E400002EB700001E480BBD016A6C22E4FD.svg:


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

:math:`E=200000\mathrm{MPa}`

:math:`\nu =0.3`

:math:`\nu =0.0` makes it possible to avoid the variation in orthogonal curvature induced by the Poisson effect in plates, which causes a discrepancy between the theories of beams and plates, outside the average fiber.


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


* force :math:`{F}_{y}=-1` (load 1) or torque :math:`{C}_{z}=1` (load 2)


* defined or applied to the neutral fiber


* embedding section :math:`x=0`


* continuity of translational movements on :math:`\mathrm{AB}`


* continuity of translational movements in :math:`C`


* equal rotation movements around :math:`z` on :math:`\mathrm{C1}-\mathrm{C2}`


* for points :math:`M` of the section (:math:`\mathrm{M1}` :math:`\mathrm{M2}` :math:`\mathrm{M4}`) the translational displacements :math:`u(M)` depend linearly on the rotational displacement :math:`{\varphi }_{z}` of the points :math:`P` of :math:`\mathrm{AB}`

:math:`u(M)=–{\varphi }_{z}(P)\mathrm{.}y+\mathrm{dx}(P)`