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


Geometry
---------


A to G models
~~~~~~~~~~~~~~~~~~~~~

We consider a semi-ring of concrete, with a square cross section, with a cable in the center of the section. The half ring has a radius :math:`r\mathrm{=}5m`, from the center to the origin, in a :math:`(\mathit{xy})` plane and the half of the ring in question is :math:`y` positive. A section of the ring in plane :math:`y\mathrm{=}0` is given by the following two points on the diagonal :math:`(4.5;\mathrm{0 };\mathrm{-}0.5)` and :math:`(5.5;\mathrm{0 };\mathrm{0,5})` (i.e. an area of :math:`1m` by :math:`1m`). The cable cross section is :math:`\mathrm{2,5}\mathrm{\times }{10}^{\mathrm{-}3}m`.

For models A to E, the concrete modeling is solid, for models F and G, the modeling is flat.


.. image:: images/1000000000000394000001F857B568B5FD478AC2.png
    :width: 5.1835in
    :height: 2.8354in


.. _RefImage_1000000000000394000001F857B568B5FD478AC2.png:

Figure 1-1: view of the concrete mesh used (models A to E)


.. image:: images/1000000000000396000001F57B357D2520C0AD5B.png
    :width: 4.3791in
    :height: 2.6819in


.. _RefImage_1000000000000396000001F57B357D2520C0AD5B.png:

Figure 1-2: view of the concrete mesh used (F and G models)


.. image:: images/100000000000031A0000015A9C4D31592E6F7161.png
    :width: 5.1193in
    :height: 2.1035in


.. _RefImage_100000000000031A0000015A9C4D31592E6F7161.png:

Figure 1-3: view of the prestressing cable embedded in concrete

H modeling
~~~~~~~~~~~~~~~

We consider a concrete beam with a length :math:`10m`, a square cross section of :math:`1m` on a side with a cable in the center of the section. The cable cross section is :math:`\mathrm{2,5}\times {10}^{-3}{m}^{2}`.


.. image:: images/10000201000004020000023C2006FCC64EE967C4.png
    :width: 4.9661in
    :height: 2.6575in


.. _RefImage_10000201000004020000023C2006FCC64EE967C4.png:

Figure 1-4: View of the concrete mesh from the H model


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

Concrete is isotropic elastic, its properties are:


* :math:`E=45000\mathit{MPa}`


* :math:`\nu =0`

Steel is isotropic elastic, its properties are:


* :math:`E=185000\mathit{MPa}`


* :math:`\nu =0`


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


A to G models
~~~~~~~~~~~~~~~~~~~~~

The section at :math:`y\mathrm{=}0` and :math:`x<0` of the ring is embedded (side containing ANCR2).


H modeling
~~~~~~~~~~~~~~~

The face in plane :math:`x\mathrm{=}0` is embedded and a pressure is exerted distributed on the lower face of the beam (:math:`z\mathrm{=}\mathrm{-}\mathrm{0,5}`) with a value of :math:`{10}^{5}\mathit{Pa}`. There is no pretension in this test.


Initial conditions
--------------------

Nil.