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


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

The reference solution consists of the results of tensile tests carried out on corroded bars (the initial diameter is :math:`6\mathrm{mm}`). Following these tests, a decrease in plastic deformation at break with an increase in the degree of corrosion is observed.


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

Evolution of the plastic deformation at break of corroded bars as a function of the degree of corrosion (the reduction in the diameter of bars or the thickness of flat reinforcement compared to non-corroded ones) is presented on the [:ref:`Figure 2.2-a <Figure 2.2-a>`] and the [:ref:`Figure 2.2-b <Figure 2.2-b>`].


.. image:: images/10000000000001D00000015453D6DB7E07C0471D.jpg
    :width: 4.2335in
    :height: 2.9728in


.. _RefImage_10000000000001D00000015453D6DB7E07C0471D.jpg:

**Figure 2.2.a Influence of corrosion on the behavior of steel as a function of the corrosion rate**


.. image:: images/1000000000000270000001E1D40C8CF3A568EEF7.png
    :width: 3.6028in
    :height: 2.6827in


.. _RefImage_1000000000000270000001E1D40C8CF3A568EEF7.png:

**Figure 2.2.b Evolution of plastic deformation at break as a function of corrosion rate**


Flexural modeling with thermal expansion
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

By placing itself at the elastic limit, the reference solution is analytical.

At point :math:`B` we have:

:math:`{u}_{x}=\alpha ({T}_{\mathit{final}}-{T}_{\mathit{ini}})L`,

:math:`{u}_{y}=\frac{{F}_{y}{L}^{3}(4+{\phi }_{y})}{12E{I}_{z}}`,

:math:`{\theta }_{z}=\frac{{L}^{2}{F}_{y}}{2E{I}_{z}}`,



with :math:`{\varphi }_{y}=0` and :math:`{I}_{z}=4{e}_{y}^{2}\pi \frac{{\varphi }^{2}}{4}`.

At point :math:`A` we have:

:math:`{V}_{y}={F}_{y}`,

:math:`{M}_{z}={F}_{y}L`


Uncertainties about the solution
----------------------------

Code accuracy.


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


1. A.A. ALMUSALLAM: "Effect of degree of corrosion on the properties of reinforcing steel bars", Construction and Building Materials 15, 2001.


2. A. OUGLOVA, Y. BERTHAUD, I. PETRE - LAZAR: "Experimental characterization of the corrosion of steels in concrete on ancient analogs. First modeling approach", HT-25/02/030/A, EDF, 2002.