8. Application example

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

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

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

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

• ten cable elements with two nodes between \(O\) and \({Q}_{1}\);

• a cable-pulley element \({Q}_{1}\) \({R}_{1}\) \({P}_{1}\);

• nine cable elements between \({R}_{1}\) and \({Q}_{2}\);

• a \({Q}_{2}\) \({R}_{2}\) \({P}_{2}\) cable-pulley element.

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

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

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