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

Calculation method used for the reference solution
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A loading path (increasing and discharging) is reproduced on an element in each of the 2 mechanisms for assembling the bi-directional behavior relationship (effort in direction :math:`x` and moment around the axis :math:`y`). It expresses the reduced movements compared to the reduced efforts. The mechanisms and the law of assembly behavior are described in figures [:ref:`Figure1.2-a <Figure1.2-a>`] and [:ref:`Figure 1.2-b <Figure 1.2-b>`].

The charge path expressed in :math:`({p}_{\mathrm{1,}}R({p}_{1}))` comprises 12 steps defined as follows:


.. image:: images/100038E6000069D50000599BE56D172045737EF7.svg
    :width: 431
    :height: 364


.. _RefImage_100038E6000069D50000599BE56D172045737EF7.svg:


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

Find the variable-criterion correspondence of the boundary curve of the behavioral relationship.


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

Numerical solution for the reversal of a non-linear relationship. There is one unknown at the same time: the internal variable of the mechanism. The other values are deduced from this. The calculation is direct for the first mechanism, incremental for the second (discussion in the summary in [:ref:`§5 <§5>`]).


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

P. PENSERINI: "Modeling bolted connections in truss towers". Note HM-77/93/287