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


Calculation method
-----------------

A first calculation was carried out with*Code_Aster*.

For this calculation, the reference axis is the elastic center of the straight section, combined with the barycenter G since the section is homogeneous:

:math:`\vec{\mathit{OG}}={y}_{G}\vec{y}+{z}_{G}\vec{z}`

with:

:math:`{y}_{G}=0`

:math:`{z}_{G}=1/S\sum {z}_{\mathit{Gi}}{S}_{i}=1/0.27\times 0.05\times (0.125\times 3+0-0.125\times 2)=0.023148148m`

The reference solution is therefore obtained with:

COOR_AXE_POUTRE = (0., 0.023148148)

The values of the natural frequencies and modal displacements are used as a reference. Indeed, these values should not depend on the position chosen for the calculation reference axis (keyword COOR_AXE_POUTRE of the DEFI_GEOM_FIBRE operator).

**Note:**

*Because of the non-symmetry of the straight section, the point O is not the center of gravity of the straight section.*