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

The analytical reference solution is determined by the theory of beams.

We consider a freestanding embedded beam. The geometric characteristics are those defined in paragraph [:ref:`§2.1 <§2.1>`]. The prestressed cable applies a normal compression force :math:`(\mathrm{-}F;\mathrm{0 };0)` and a bending moment :math:`(\mathrm{0 };–\mathit{eF};0)` to the free end.

The solution to this problem is as follows:

**Stress tensor**:

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    :height: 80


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with

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    :height: 80


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**Travel:**

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    :height: 80


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with the **boundary conditions**:

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    :height: 80


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When the effects of Poisson are overlooked (

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), the travel solution is simplified as follows:


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    :height: 80


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The numerical reference values are calculated using the analytical expressions above, using for :math:`F` the overall equilibrium value of the normal force in the cable:


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    :width: 125
    :height: 80


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