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

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

We ask:

:math:`{k}_{\mathrm{An}}=\frac{{\mathrm{EI}}_{\mathrm{An}}}{{l}_{\mathrm{An}}}`

with :math:`n=B,C,D` or :math:`E`

:math:`\begin{array}{}K={k}_{\mathrm{AB}}+{k}_{\mathrm{AD}}+{k}_{\mathrm{AE}}+\frac{3}{4}{k}_{\mathrm{AC}}\\ {r}_{\mathrm{An}}=\frac{{k}_{\mathrm{An}}}{K}\end{array}`

with :math:`n=B,C,D` or :math:`E`

:math:`{C}_{1}=+\frac{{\mathrm{Fl}}_{\mathrm{AD}}}{8}-\frac{{\mathrm{pl}}_{\mathrm{AB}}^{2}}{12}`

• Rotation to :math:`A`:

:math:`\theta =\frac{{C}_{1}}{\mathrm{4K}}`

• Moment in :math:`A`:

:math:`\begin{array}{}{M}_{\mathrm{AB}}=+\frac{{\mathrm{pl}}_{\mathrm{AB}}^{2}}{12}+{r}_{\mathrm{AB}}\mathrm{.}{C}_{1}\\ {M}_{\mathrm{AD}}=-\frac{{\mathrm{Fl}}_{\mathrm{AD}}}{8}+{r}_{\mathrm{AD}}\mathrm{.}{C}_{1}\\ {M}_{\mathrm{AE}}={r}_{\mathrm{AE}}\mathrm{.}{C}_{1}\\ {M}_{\mathrm{AC}}={r}_{\mathrm{AC}}\mathrm{.}{C}_{1}\end{array}`


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

Value of rotation and moments in :math:`A`.


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


1. Guide VPCS - 1990 edition.