Question

A uniform flexible but inextensible cable is 120ft long and total weight 60lb is hung at each end by supports of equal height. If the sag in the middle of the cable is to be 8ft below the supports what is the required horizontal distance between the supports, the minimum tension in the cable, the maximum tension in the cable and the angle the cable makes with horizontal at each support?

Answer 1

DATA:

Solution:

First. we calculate the value of c :

or

In this problem is calculated (see figure) as:

The value of in this problem is:

Replacing (3), (2) into equation (1.1) we have:

or

Isolating we have:

Therefore:

The minimum tension in the cable is defined as:

Here, is:

Replacing this result in equation (4) we have:

Therefore:

The maximum tension is defined as:

or

Replacing values we have:

The angle can be calculated starting of:

Isolating we have:

Replacing values:

Therefore:

Finally, the required horizontal distance between the supports is defined as:

and is calculated using:

Isolating we have:

Replacing values given in DATA:

Therefore:

Finally,