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

Geometry
---------

We consider a reinforced concrete column of length :math:`\mathrm{0,7}m`, along the axis :math:`\mathrm{Ox}`, with a square cross section with a height and width equal to :math:`\mathrm{0,15}m`.


.. image:: images/10000201000004370000032A7BF090CEAEEEB4A9.png
    :width: 3.3366in
    :height: 2.3764in


.. _RefImage_10000201000004370000032A7BF090CEAEEEB4A9.png:

Figure 1: reinforced concrete column section.

The longitudinal frames are four :math:`\mathit{HA14}`.

The transverse reinforcements are not taken into account in the models below.

For modeling A, two reinforcing bars :math:`X` and :math:`Y` from :math:`\mathrm{2,053}\text{}{10}^{-3}{m}^{2}/m` are used.

For modeling B, a single steel fiber with section :math:`\mathrm{6,15}{\mathit{mm}}^{2}` is used.


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

The GLRC_DM law of behavior has the following parameters for concrete:


* Young's modulus: :math:`E\mathrm{=}28500\mathit{MPa}`


* Poisson's ratio: :math:`\nu \mathrm{=}0.2`


* Maximum compression stress: :math:`{\sigma }_{c}=25\mathrm{MPa}`


* Peak deformation under compression: :math:`{ϵ}_{c}=\mathrm{2,25}\mathrm{.}\text{}{10}^{-3}`


* Maximum tensile stress: :math:`{\sigma }_{t}=\mathrm{2,94}\mathit{MPa}`

The parameters for steel are:


* Young's modulus: :math:`E\mathrm{=}195000\mathit{MPa}`


* Poisson's ratio: :math:`\nu \mathrm{=}0.3`


* Elastic limit: :math:`{\sigma }_{y}=610\mathrm{MPa}`


* Tangent module (plastic slope): :math:`{E}_{t}\mathrm{=}\mathrm{19,5}\mathit{MPa}`

The operator DEFI_GLRC is used to obtain the parameters of the GLRC_DM law. Concrete stress has been reduced to :math:`{\sigma }_{t}=\mathrm{1,6}\mathit{MPa}`. In addition, the parameters :math:`{\gamma }_{c}=\mathrm{0,35}` and :math:`{\alpha }_{c}=60` are also set for the non-linear behavior in compression.

With these material data, the equivalent elastic modulus in membrane, cf. [R7.01.32], is equal to: :math:`{E}_{\mathrm{eq}}^{m}=34021.0\mathrm{MPa}`, i.e. membrane stiffness in the direction :math:`\mathrm{Ox}`: :math:`{E}_{\mathrm{eq}}^{m}\ast S=765.393\mathrm{MN}`.

The DEFI_MATER_GC operator was used to determine the parameters of laws MAZARS_UNIL and VMIS_CINE_GC.


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

One end of the beam, edge :math:`A`, is blocked and a distributed force of the resultant :math:`\mathit{FX}\mathrm{=}1\mathit{kN}` is imposed on the other end, edge :math:`B`, in the direction :math:`X`.


.. image:: images/10000000000002E70000013FB108272238DBC57A.png
    :width: 5.5118in
    :height: 2.3661in


.. _RefImage_10000000000002E70000013FB108272238DBC57A.png:


.. _DdeLink__1171_2114786994:

Figure 2: reinforced concrete column section.

Charging cycles are defined by:

.. csv-table::

    ":math:`t` ", "Multiplying factor
    on the :math:`\mathit{FX}` force"
    ":math:`\mathrm{0,0}` "," :math:`\mathrm{0,0}`"
    ":math:`\mathrm{1,0}` "," :math:`\mathrm{-}250`"
    ":math:`\mathrm{3,0}` "," :math:`55`"
    ":math:`\mathrm{5,0}` "," :math:`\mathrm{-}365`"
    ":math:`\mathrm{7,0}` "," :math:`176`"
    ":math:`\mathrm{9,0}` "," :math:`\mathrm{-}490`"
    ":math:`\mathrm{11,0}` "," :math:`298`"
    ":math:`\mathrm{13,0}` "," :math:`\mathrm{-}675`"
    ":math:`\mathrm{15,0}` "," :math:`368`"
    ":math:`\mathrm{17,0}` "," :math:`\mathrm{-}790`"
    ":math:`\mathrm{19,0}` "," :math:`376`"



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

Nil.