Benchmark solution
=====================

Reference quantities and results
------------------------

.. csv-table::

    "Arrow to :math:`B` next :math:`Z` ", "Arrow to :math:`B` next ", "Arrow to next :math:`Y`"
    ":math:`{\delta }_{z}=\frac{{F}_{z}\mathrm{.}{L}^{3}}{2E{I}_{y}}` "," :math:`{\delta }_{y}=\frac{{F}_{y}\mathrm{.}{L}^{3}}{2E{I}_{z}}`"


Stress at a point :math:`C` with coordinates :math:`({v}_{y},{v}_{z})` of the section of the beam

.. math::
: label: EQ-None

    \ sigma =\ frac {N} {S} +\ frac {{M} _ {y}} {{I} _ {y}}}\ mathrm {.} {v} _ {z} -\ frac {{M} _ {z}} {{z}} {{I} _ {z}}\ mathrm {.} {v} _ {y}

from where:

 :math:`\sigma =\frac{N}{S}-\frac{3E\mathrm{Lo}}{{L}^{3}}({\delta }_{y}{v}_{y}+{\delta }_{z}{v}_{z})` [:ref:`éq2.1-1 <éq2.1-1>`]


Bibliographical reference
-------------------------

[:ref:`1 <1>`] "Project M7-01-72. Elasto-plastic behavior of beams. New approach." Note HM77 /01/140/A.