Application example
=====================

This example is that of the installation of a cable with two spans and with imposed adjustment tension.

On [:ref:`Figure 7-a <Figure 7-a>`], :math:`O` is the cable anchor on the left stop bracket. :math:`{P}_{1}` is a first pulley placed at the foot of the :math:`{P}_{1}C` suspension chain, fixed in :math:`C` to the alignment support. :math:`{P}_{2}` is a second pulley placed on the right stop support. :math:`O`, :math:`{P}_{1}` and :math:`{P}_{2}` are, for simplicity, located on a horizontal.


.. image:: images/10002D9C000030FD00000BFD694B147970A15849.svg
    :width: 497
    :height: 107


.. _RefImage_10002D9C000030FD00000BFD694B147970A15849.svg:

**Figure 7-a: Balance of a cable with two ranges, subject to a given adjustment tension.** :math:`{\text{OP}}_{1}={\text{P}}_{1}{\text{P}}_{2}=100m` ****; **:math:`w=30N/m`**; **:math:`E´A=5x{10}^{7}N`** **** **;** :math:`{N}_{p}=\mathrm{5 000}N`

In the initial position, the cable at rest, assumed to be weightless, is straight: the line at the centre line of [:ref:`Figure7-a <Figure7-a>`]. For finite element modeling, this line is divided into:


* ten cable elements with two nodes between :math:`O` and :math:`{Q}_{1}`;


* a cable-pulley element :math:`{Q}_{1}` :math:`{R}_{1}` :math:`{P}_{1}`;


* nine cable elements between :math:`{R}_{1}` and :math:`{Q}_{2}`;


* a :math:`{Q}_{2}` :math:`{R}_{2}` :math:`{P}_{2}` cable-pulley element.

The cable is simultaneously subjected to gravity and to the adjustment tension :math:`{N}_{p}` exerted in :math:`{R}_{2}`. The equilibrium position (solid line of [:ref:`Figure 7-a <Figure 7-a>`]) is reached in 11 iterations by the STAT_NON_LINE operator of*Code_Aster*. The arrows are :math:`7.955m` and :math:`7.867m`, in the left and right ranges respectively.

For a **inextensible** cable with a range of :math:`100m`, with a linear weight of :math:`30N/m` and subject to an end tension of :math:`\mathrm{5 000}N`, the theoretical deflection is :math:`7.941m` [:ref:`§An2 <§An2>`].

By adjusting the adjustment voltage, one of the two arrows can be adjusted to a value fixed in advance.