General characteristics
==========================

Geometry
---------

The three-point bending beam studied is 5m long. Its section is 0.2x0.5m. Its geometry as well as the positioning of the steels that constitute it are defined on the.


.. image:: images/1000000000000368000003CCC6FA11DD0FAE7FD7.png
    :width: 5.1665in
    :height: 5.5118in


.. _RefImage_1000000000000368000003CCC6FA11DD0FAE7FD7.png:

**Figure** 1.1-a: plane of the beam.


.. _RefNumPara__13770_529633604:


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

• Concrete:

Young's module: :math:`E\mathrm{=}37272\mathit{MPa}`

Poisson's ratio: :math:`\nu =0.2`

Tensile elasticity threshold: :math:`{\sigma }_{\mathrm{ft}}=3.9\mathrm{MPa}`

Threshold of elasticity in compression: :math:`{\sigma }_{\mathrm{fc}}=38.3\mathrm{MPa}`

Threshold of elastic deformation under compression: :math:`{\varepsilon }_{\mathrm{fc}}={\mathrm{2.0.10}}^{-3}`

Cracking energy :math:`{G}_{f}^{1}\mathrm{=}110J\mathrm{/}\mathit{m²}`

• Steel:

Young's module: :math:`E=200000\mathrm{MPa}`

Poisson's ratio: :math:`\nu =0.33`

Elastic limit: :math:`{\sigma }_{e}\mathrm{=}400\mathit{MPa}`

Tangent module (plastic slope) :math:`{E}_{T}\mathrm{=}3280\mathit{MPa}`

*AND*

.. image:: images/10000000000000F7000000DEDDD725A2B2B746C2.png
    :width: 1.6835in
    :height: 1.4583in


.. _RefImage_10000000000000F7000000DEDDD725A2B2B746C2.png:

**Figure** 1.2-a: c **stress curve — steel deformation**


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

Simple press in :math:`B`: :math:`\mathit{DY}=0`.

Double press in :math:`A`: :math:`\mathit{DX}=\mathit{DY}=\mathit{DZ}=0` as well as :math:`\mathit{DRX}=\mathit{DRY}=0`.

Quasi-static loading: monotonic downward displacement :math:`\mathit{DY}` applied halfway through :math:`C` (3-point flexure test), according to a linear function of time:

.. csv-table::

    ":math:`t` "," :math:`\mathit{DY}`"
    ":math:`\mathrm{0,0}` "," :math:`\mathrm{0,0}\mathrm{cm}`"
    ":math:`\mathrm{3,0}` "," :math:`\mathrm{-}\mathrm{3,0}\mathit{cm}`"
    ":math:`\mathrm{5,0}` "," :math:`\mathrm{-}\mathrm{5,0}\mathit{cm}`"


The final displacement applied for modeling A is :math:`\mathrm{-}\mathrm{3,0}\mathit{cm}`.

For the D modeling, the imposed displacement is done according to :math:`\mathit{DZ}`.

**Note:** transverse reinforcements are not taken into account in the calculations.