## Cable tension formulas

## Cable tension formulas

(OP)

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?

Thanks

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?

Thanks

## RE: Cable tension formulas

## RE: Cable tension formulas

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

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

http://www.eng-tips.com/supportus.cfm

## RE: Cable tension formulas

Thanks!

Jesse

## RE: Cable tension formulas

http://www.slideruleera.net/miscellaneous.html

www.SlideRuleEra.net

www.VacuumTubeEra.net

## 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

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

http://www.eng-tips.com/supportus.cfm

## RE: Cable tension formulas

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.

Jesse

## RE: Cable tension formulas

## RE: Cable tension formulas

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 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

xandS(andtheta) 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

In this equation

(P(1-x/S))/(sin(theta))

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.