Reference problem
=====================

Geometry
---------


.. image:: images/1000000000000322000000A981A3ED590E00FCFE.png
    :width: 5.7701in
    :height: 1.1736in


.. _RefImage_1000000000000322000000A981A3ED590E00FCFE.png:


.. csv-table::

    "", ":math:`O` "," :math:`{P}_{1}` "," :math:`{P}_{2}` "," "," :math:`{R}_{2}` "," :math:`C`"
    ":math:`x` ", "0. ", "100. ", "200. ", "20. ", "100."
    ":math:`z` ", "0. ", "0. ", "0. ", "0. ", "10."


**Table** 1.1-a **: Coordinates of points (en** :math:`m` **)**

Names and positions of the nodes (middle of range before installation):

• left hand range: :math:`\mathrm{N6}` and :math:`x=48.50m`

• right-hand range: :math:`\mathrm{N19}` and :math:`x=160.50m`


Material properties
-----------------------

Cable linear weight: :math:`30N/m`

Axial stiffness of the cable (product of Young's modulus by the area of the straight section): :math:`5\mathrm{.}{10}^{7}N`


Boundary conditions and loads
-------------------------------------

Points :math:`O`, :math:`C`, and :math:`{P}_{2}` are fixed.

The cable, fixed in :math:`O`, is supported by two pulleys. The first is attached to the lower end :math:`{P}_{1}` of the suspension attached in :math:`C`. The second is set to :math:`{P}_{2}`.

The cable is subjected to its weight and is given an arrow by moving its right end from :math:`\mathrm{10 }m` from :math:`{R}_{2}` to :math:`{R}_{2}\text{'}`.

The position of points :math:`{Q}_{1}`, :math:`{R}_{1}` and :math:`{Q}_{2}` is not imposed, but care must be taken to ensure that during installation the pulley :math:`{P}_{1}` stays on the cable section :math:`{Q}_{1}{R}_{1}`.