Cable support reactions (or cable tension) given a "ruling span", "wind span" an 2

[brTCP]

Is it possible to calculate the cable support reactions (or the cable tension) given only:
- the weight of the cable per unit length;
- the ruling span;
- the wind span;
- the weight span?

My understanding is that there is an infinite number of solutions for this problem depending on the height difference of the supports and the horizontal tension, but my client insists that the information they provided is sufficient. Could you shine some light to this problem?

If it helps, here are some values:

weight of the cable = 0.01597 kN/m;
ruling span = 300 m
wind span = 350 m
weight span = 500 m.
​

Thanks!

 

[jghrist]

You also need the sag, or the location of the conductor in three places along the span. If you want tension with wind and/or ice, you also need the conductor diameter.

 

[Sparweb]

It's easiest if you have the sag, then curve-fit to a parabola.
Technically, it's a catenary, not a parabola, and there's an analytical method for that in Roark, I think.
If you don't know the sag, then you need the Young's Modulus of the cable. Doing it that way is harder (iterative?)

 

[brTCP]

Thank you for your answers. @Sparweb, I can't see how the Modulus of Elasticity can be used in this case. Could you please elaborate a bit more?

 

[Sparweb]

The answer above came off the top of my head. I could tell you were missing important input values, and named the one that seemed most obvious.

The sag in a steel cable is probably greater than the sag in a rubber cable, just obviously, I'd say. The critical difference between steel and rubber (in this narrow-minded problem) is their elasticity. More sag means greater component of the end-reaction in the vertical reaction - which is proportional to the angle the cable makes at the reaction point, too. For that reason, I am sure a high-stiffness cable will have different end reactions than a stretchy one.

I wouldn't go any farther with my musings than this - I'd go to the books instead. Roark. Pilkey. Mark's Handbook. I am sure any of these can help you solve this better than me.