How do cables bend and curve when fixed at two points?

[dazzler77]

Hi I have a cable that is fixed at 2 points, and I would like to model the curve that it bends as the two points move together and further away.

In one scenario, the cable is fixed at both ends (one above the other) like a "C".
In the other scenario, both ends are also fixed in clamps, but it is like an "S"

Is there a formula to show what the curves might look like ({x,y} = z), given some stiffness or minimum bend radius? Is the "C" curve like a cosh

or is there some software that might simulate this? do I need finite element analysis? or is there a simplified estimate?

 

[Simon Bridge]

You can try working it out for yourself by modelling the cable as a large number of small masses connected by springs ... fbd for each mass and solve the system of equations.
http://calculuslab.deltacollege.edu/ODE/7-A-1/7-A-1-h.html

The curve is called a "catenary".
http://en.wikipedia.org/wiki/Catenary

 

[Vadar2012]

That brings back bad memories. Solved those equations for an assignment at uni. Although we had to derive the second order non linear equation for the rope, wish I knew the equation beforehand.

 

[dazzler77]

Thanks for the replies.
The website http://calculuslab.deltacollege.edu/...1/7-A-1-h.html was very helpful.

However I would like to have it start off horizontal rather than hanging, and curve around and be clamped below horizontal as well, like a "C" shape.

maybe in some ways it's more like compression than hanging.

 

[Simon Bridge]

Thanks for the replies.
The website http://calculuslab.deltacollege.edu/...1/7-A-1-h.html was very helpful.

However I would like to have it start off horizontal rather than hanging, and curve around and be clamped below horizontal as well, like a "C" shape.

maybe in some ways it's more like compression than hanging.

Well yes - cables don't generally hang like that... except if they are very stiff indeed. The approach is the same - the "C" would sag a little depending on the stiffness.