The catenary is a classical problem concerning the shape of a uniform cable hang

Question

The catenary is a classical problem concerning the shape of a uniform cable hanging under its own weight. Figure 12.20 shows a drawing of the cable and its associated coordinate system. Notice that the horizontal distance x is measured from the lowest point (so that x_a is negative and x_b is positive), and that the lowest point is a distance v above the vertical datum. Based upon this coordinate system, the length of the cable is calculated as L = nu [sin h(x_b/nu) - sin h(x_a/nu)] and the difference in height between the end points is calculated as h = nu [cos h (x_b/nu) - cos h (x_a/nu)] Also, the width spanned by the cable is given by w = x_b - x_b Suppose a 100-ft cable is suspended is such a manner that x_a -30 ft and h = 20 ft. Solve for the corresponding values of x_b, w, and nu in Excel using Solver.

Explanation / Answer

The Answer for this problem is as follows :

xb = 62.8 ft

W = 92.8 ft

v = 80.9 ft

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