B modeling
==============

Characteristics of modeling
-----------------------------------

The beam is modelled by elements DKTG and GRILLE_EXCENTREE. 16 elements are used in the longitudinal direction :math:`X` and only one in the transverse direction :math:`Z`.

Reinforced concrete is modelled by behavior law GLRC_DM. The parameters of the law of behavior GLRC_DM are obtained using the DEFI_GLRC macro-command. The material data used is defined in :ref:`1.2 <RefNumPara__10496_529633604>`. For the reinforcement layers of model GLRC, a reinforcement section :math:`\mathit{OMX}\mathrm{=}\mathit{OMY}\mathrm{=}\mathrm{8,04E-4}\mathit{m²}\mathrm{/}m` and the eccentricity :math:`\mathit{RX}\mathrm{=}\mathit{RY}\mathrm{=}\mathrm{0,872}` are defined. We use option PENTE =_F (

TRACTION =' PLAS_ACIER ',

FLEXION = 'UTIL',

KAPPA_FLEX = 3E-3,

),

The first two natural frequencies (calculated with*Code_Aster*) are :math:`{f}_{1}=38.7\mathit{Hz}` and :math:`{f}_{2}=153.2\mathit{Hz}`. For modal depreciations of 5%, the damping coefficients :math:`\alpha =8{.10}^{-5}` and :math:`\beta =20` are obtained. These coefficients are supplied to the macro command DEFI_GLRC.


Tested sizes and results
------------------------------

The reaction curves as a function of time as well as the arrow in the center as a function of time are shown in figures to.


.. image:: images/10000000000001E100000120F92E5ACC2ABB34B0.png
    :width: 5.0102in
    :height: 3in


.. _RefImage_10000000000001E100000120F92E5ACC2ABB34B0.png:

**Figure** 4.2-a: **Press reaction in A as a function of time for the first three seconds.**


.. image:: images/10000000000001E10000012109105D9C3F2D1CCE.png
    :width: 5.0102in
    :height: 3.0102in


.. _RefImage_10000000000001E10000012109105D9C3F2D1CCE.png:

**Figure** 4.2-b: f **arrow in the center according to the time for the first three seconds.**


.. image:: images/1000000000000257000001A7001B5DE853E4A4C4.png
    :width: 6.2398in
    :height: 4.4063in


.. _RefImage_1000000000000257000001A7001B5DE853E4A4C4.png:

**Figure** 4.2-c: **reaction-arrow curve for the first three seconds.**

The tests are carried out for the reaction on the first press and the arrow in the center. These values are tested for a few moments in the first three seconds of the earthquake, i.e. at times :math:`\mathrm{1.76s}` (at the very beginning of the non-linear domain), then :math:`\mathrm{2.05s}`, :math:`\mathrm{2.68s}` and :math:`\mathrm{2.87s}` when the structure is already heavily damaged.


.. csv-table::

    "**Instant**", "**Size**", "**Location**", "**Reference Type**", "**Tolerance**"
    "1.76 s", "FORC_NODA: DY", "Group:AA", "NON_REGRESSION ", "1.0E-06", "1.0E-06"
    "1.76 s", "DEPL: DY", "Group:CC", "NON_REGRESSION ", "1.0E-06", "1.0E-06"
    "2.05 s", "FORC_NODA: DY", "Group:AA", "NON_REGRESSION ", "1.0E-06"
    "2.05 s", "DEPL: DY", "Group:CC", "NON_REGRESSION ", "1.0E-06", "1.0E-06"
    "2.68 s", "FORC_NODA: DY", "Group:AA", "NON_REGRESSION ", "1.0E-06"
    "2.68 s", "DEPL: DY", "Group:CC", "NON_REGRESSION ", "1.0E-06", "1.0E-06"
    "2.87 s", "FORC_NODA: DY", "Group:AA", "NON_REGRESSION ", "1.0E-06", "1.0E-06"
    "2.87 s", "DEPL: DY", "Group:CC", "NON_REGRESSION ", "1.0E-06", "1.0E-06"


The figures below show the evolution of the reaction on support A and of the arrow in the center, for 15 seconds.


.. image:: images/10000000000001E1000001217565B56CA34CE128.png
    :width: 5.0102in
    :height: 3.0102in


.. _RefImage_10000000000001E1000001217565B56CA34CE128.png:

**Figure** 4.2-d: **Press reaction in A as a function of time, for 15 seconds.**


.. image:: images/10000000000001E1000001207C7EB9CD0BF654CE.png
    :width: 5.0102in
    :height: 3in


.. _RefImage_10000000000001E1000001207C7EB9CD0BF654CE.png:

**Figure** 4.2-e **: arrow in the center according to time, for 15 seconds.**


.. image:: images/100000000000035C000001AB6C783D7EF60F1ABE.png
    :width: 6.3083in
    :height: 3.1319in


.. _RefImage_100000000000035C000001AB6C783D7EF60F1ABE.png:

**Figure** 4.2-f: c**reaction-arrow curve, for 15 seconds.**