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


Calculation method used for the reference solution
--------------------------------------------------------


.. image:: images/Object_7.svg
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.. _RefImage_Object_7.svg:

The ruin of the beam occurs when there are plastic joints at points :math:`A`, :math:`D` and :math:`E` (figure b). The static equilibrium of the left half of the beam makes it possible to determine the limit pressure (figure c)


.. image:: images/Object_8.svg
    :width: 574
    :height: 246


.. _RefImage_Object_8.svg:

=>

.. image:: images/Object_9.svg
    :width: 574
    :height: 246


.. _RefImage_Object_9.svg:

where:

:math:`{q}_{L}` represents the limit pressure

:math:`{M}_{p}` represents the plastic moment (

.. image:: images/Object_10.svg
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    :height: 246


.. _RefImage_Object_10.svg:

)

The appearance of the first plastic dot on the outer fiber of the beam takes place at points :math:`A` and :math:`D`, the other fibers being in an elastic regime. The elastic limit pressure is

.. image:: images/Object_11.svg
    :width: 574
    :height: 246


.. _RefImage_Object_11.svg:

.


Benchmark results
----------------------

Pressure limit :math:`{q}_{L}\mathrm{=}39166.67N\mathrm{/}m`


Uncertainties about the solution
----------------------------

Analytical solution


Bibliographical references
---------------------------


1. WILLIAM A. NASH: Theory and Problems of Strength of Material, Schaum's Outline Series, 2/Ed, Mc GRAW - HILL