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Cable tension formulas

Cable tension formulas

Cable tension formulas

I'm looking for a formula, calculator or spreadsheet that can calculate the tension in a cable suspended between two points with a concentrated load. Should be simple but my cable is inclined and I need to find the tension in each leg of the cable as a function of the load's position. Example, a guy walking on a slanted tightrope, or a cable zipline.

I came up with a formula that calculates the tension as a function of any x,y position of the load along the cable but my cable length is fixed and the load only travels on a certain path. This path happens to be a portion of an ellipse that is translated and rotated about the origin... basically really really ugly. Any ideas?


RE: Cable tension formulas

I've seeen formulas for the typical cable problem, a catenary. I don't quite see how the loading can be along an ellipse; is the cable made to conform to this shape or is the load path not along the cable?

RE: Cable tension formulas

The cable by itself would form a catenary with no load on it as its not pulled tight to begin with.

I'm assuming the cable's weight to be insignificant compared to the concentrated load that is moving along the cable. The cable forms simple straight lines when under tension. If you have the load moving along the cable so that the cable is always tight then the path the load would trace would be the bottom of an ellipse. The attachment points of the cable are the focci of the ellipse.   

RE: Cable tension formulas

The tension in the cable is (P(1-x/S))/(sin(theta)) where:

P = point load
x = point load distance from left support
S = span from end to end
theta = angle between left end of cable and horizontal

This assumes the cable is straight (weightless), does not stretch, true point load, rigid supports, blah, blah, blah...

If you "heard" it on the internet, it's guilty until proven innocent. - DCS


RE: Cable tension formulas

Thanks for the help but I believe that is only good for a horizontal cable. Mine is inclined. and then I have to somehow define theta as a function of x. This isn't a textbook problem where I'm given that info. Does anyone know of a spreadsheet or calculator program that can numerically solve cable problems? Something you would use for making a rope bridge or zip line? I'm designing an escape slide for guys in oilfield service rigs. The slide and cables are relativly lightweight but two 300 lbs riggers are not and if the slide is rigged up too tight initially they will either pull down the rig or move the anchor at the bottom when they jump on.



RE: Cable tension formulas


You seem to be saying that the locus of the load point as it moves (slowly and gently) down the cable will be an elliptical arc if the cable's weight is insignificant.  It will only be so if the cable's extensibility is also insignificant.

If you are prepared to accept these two simplifications, then you have a relatively simple problem to solve (unless you want to lift up the stone labelled "dynamic effects").  You do, however, have to solve it for multiple assumed positions of the load.

If you wish to allow for cable weight and/or cable extensibility, then you have a much more difficult problem to solve.  I would suggest you find yourself a structural analysis program that has cable elements.  There are plenty out there.

RE: Cable tension formulas

Is the load attached to the cable or allowed to roll along freely?

If you "heard" it on the internet, it's guilty until proven innocent. - DCS


RE: Cable tension formulas

Thanks for the info,

I am assuming the load is moving "slowly" down the cable and that the cable's length doesn't change. When you say I have to solve it for multiple assumed positions of load your saying there's no cable tension as a function of x kind of formula with constants for elevation change, cable length etc.? I know I can solve it in any one position, I was just looking for a less painful method.



RE: Cable tension formulas

Jesse,  Did you ever find the formula, calculator, or spreadsheet that you were looking for?  I am looking for the same.  Any help would be greatly appreciated.  Thanks.

RE: Cable tension formulas

I afraid there is no "less" painful way to handle this analysis, unless there is a black box program claims it can do it, and results were proven true (quite a few structural programs had flunked in this regard - foundamental mechanics, in the past).

Also, I afraid that you can not ignore cable selfweight and elongation characteristics completely, if the applied load is capable of causing cable to deflect to a certain degree (I am not aware of any applicable rule of thumb here). For first you need the selfweight to generate the profile, then it interacts with the applied load to change the profile, thus the reaction and cable tension at any given location.

Painful, yes, but if you formulated correctly in a spreadsheet, it's a woth-while one time deal, if you need to do the analysis thousand times. Wish you luck, and let us know if there exists a simple solution with clarity on all assumptions.   

RE: Cable tension formulas

Add half the self weight to the point load and assume a reasonable deflection to get your initial sizing for the cable.

Add the results into a more rigorous analysis which includes stretch and self weight.

RE: Cable tension formulas

Swearingen gave you the exact formula.  Use it.

RE: Cable tension formulas

Swearingeng's formula is valid, within its limitation of the cable being weightless, for an inclined cable as well as for a horizontal one.  If the cable is not inextensible, then the x and S (and theta) values must incorporate the effects of stretching.

Whether or not the formula could be applicable to Jesse1967's problem depends on how the load - ie the escape capsule - is kept in equilibrium at its various positions down the cable.
»  Is it unrestrained?  If so (except for one theoretical position that might not exist in practice) it will NOT be in equilibrium and will accelerate away?
»  Is it clamped to the cable by some sort of internal braking mechanism?  This is the case to which Swearingeng's formula might apply.  (In the case of your chap on an inclined tightrope, this force is provided by the friction between his shoes and the rope.)
»  Is its "lateral position" controlled by some sort of external force, for example a separate rope that is slowly played out?  If so, then the force in that rope needs to be included in the equilibrium calculation.

RE: Cable tension formulas

Jesse1967, swearingen, and civilperson:

In this equation


theta is the angle of the cable resulting from the load (not an arbitrary angle of inclination of the unloaded cable).

RE: Cable tension formulas

Why do you want a software for this problem?
and why too many assumptions.
You only have a 300 lb concentrated load you say.
besides this is an ordinary Engineering Mechanics problem
you dont need a formula only equilibrium laws and simple
Geometry will give you the reasonable Tensions you need for
your design.
If I were you I will
First, Im going to sketch The loaded cable
second, Take moments with an assumed point
Third, Start the graphical or analytical solution of the problem.
fourth,Draw the Force vectors
Fifth,Check the tension assumption
Six, Continue the construction
seventh:complete the construction
eight: Checked the Lenght of the cable or determine the required Length.
For further Reference Refer to Handbook of Civil Engineering
by Tyler Hicks any Edition...
Hope this helps.

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