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


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

Analytical solution for each of the 4 loading cases:

In beam theory, within the framework of the Euler-Bernouilli hypotheses, the solution of the reference problem is that of a straight beam subjected to forces and moments at one end and embedded at the other end:

**Traction**:

.. image:: images/Object_2.svg
    :width: 114
    :height: 41


.. _RefImage_Object_2.svg:

**Twist**:

.. image:: images/Object_3.svg
    :width: 114
    :height: 41


.. _RefImage_Object_3.svg:

**Bending around**

.. image:: images/Object_4.svg
    :width: 114
    :height: 41


.. _RefImage_Object_4.svg:

:

.. image:: images/Object_5.svg
    :width: 114
    :height: 41


.. _RefImage_Object_5.svg:

**Bending around**

.. image:: images/Object_6.svg
    :width: 114
    :height: 41


.. _RefImage_Object_6.svg:

:

.. image:: images/Object_7.svg
    :width: 114
    :height: 41


.. _RefImage_Object_7.svg:


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

**Traction:**


.. image:: images/Object_8.svg
    :width: 114
    :height: 41


.. _RefImage_Object_8.svg:

**Twist:**


.. image:: images/Object_9.svg
    :width: 114
    :height: 41


.. _RefImage_Object_9.svg:

**Bending around:**

.. image:: images/Object_10.svg
    :width: 114
    :height: 41


.. _RefImage_Object_10.svg:


.. image:: images/Object_11.svg
    :width: 114
    :height: 41


.. _RefImage_Object_11.svg:

**Bending around:**

.. image:: images/Object_12.svg
    :width: 114
    :height: 41


.. _RefImage_Object_12.svg:


.. image:: images/Object_13.svg
    :width: 114
    :height: 41


.. _RefImage_Object_13.svg:

**Note:**

The use of the shell-beam connection for embedding and for loads makes it possible to remain within the framework of the Euler-Bernouilli hypothesis (cf. [:ref:`R3.03.06 <R3.03.06>`]). The previous analytical solution is therefore the reference solution to the problem.


Uncertainty about the solution
---------------------------

Analytical solution.