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


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

Travel:


* Points :math:`B` and :math:`E`

:math:`f=\frac{{\mathrm{Pl}}^{3}}{96{\mathrm{EI}}_{1}}+\frac{{\mathrm{Pl}}^{3}}{96{\mathrm{EI}}_{2}}` with :math:`{I}_{i}=\frac{b\times {e}_{i}^{3}}{12}`


* Points :math:`G` and :math:`H`

:math:`f=-\frac{{\mathrm{Pl}}^{3}}{192{\mathrm{EI}}_{1}}(\frac{{I}_{1}}{{I}_{2}}+\frac{7}{2})`


* Bending moment:

:math:`M(x)=\frac{\mathrm{P.x}}{2}`


Reference quantity
---------------------


* :math:`\mathrm{DZ}` move from :math:`z` to points :math:`B` and :math:`G`.


* :math:`\mathrm{MXX}` soft moment for :math:`x=\frac{L}{2}` and :math:`x=\frac{L}{4}`


Reference quantity and result
---------------------------------


+---------+--------------------+---------------------------------------+
|Point    |Component           |Reference                              |
+---------+--------------------+---------------------------------------+
|:math:`B`|:math:`\mathrm{DZ}` |:math:`0.3515625m`                     |
+         +--------------------+---------------------------------------+
|         |:math:`\mathrm{DRZ}`|:math:`0.`                             |
+         +--------------------+---------------------------------------+
|         |:math:`\mathrm{MXX}`|:math:`-50\times {10}^{4}\mathrm{m.N}` |
+---------+--------------------+---------------------------------------+
|:math:`G`|:math:`\mathrm{DZ}` |:math:`-0.2629743m`                    |
+         +--------------------+---------------------------------------+
|         |:math:`\mathrm{DRZ}`|:math:`0.`                             |
+         +--------------------+---------------------------------------+
|         |:math:`\mathrm{MXX}`|:math:`-25.\times {10}^{4}\mathrm{m.N}`|
+---------+--------------------+---------------------------------------+