Deflection in cable 1

[Plainsboro]

I have a 1/8" dia cable fixed at two ends (same level). A point load is applied in middle. What equation can be used to find how much cable will deflect. I saw some ref but they want two of these three quantities be known 1) Horz comp of tension in cable , 2) load 3) deflection. What If I know only applied load and span and than parameters of cable. Thx a lot.

 

[PSlem]

Iteration will get you there. Pick a small deflection. Calculate the load in the cable from geometry. Check it against the increased length of the cable and its known strain for that stress. Adjust whichever way helps and keep plugging.

 

[JStephen]

If I remember right, you can assume small angle relations and simplify the problem considerably. Assuming you have small angles, of course.

Also, check on the modulus of elasticity for cable- it's different than for, say, a solid bar.

 

[MikeDB]

You have more unknowns than equations. You have to determine the initial tension in the cable or the initial sag and you will need to know the cable properties. I have not seen an equation to solve this directly. I think you will have to determine the elongation of the cable due to the point load and use that to determine the change in sag of the cable.
Option 2, you can find a computer program that handles cables.
Option 3, you can experiment with a piece of the cable.

 

[SAMO]

I think the difference between a cable and any other section is the flexural stiffness (EI), in the case of a cable, it is very small. if you know the flexural stiffness, then you can model the cable using any software such as SAP2000 and assign the appropriate stiffness and analyse it.
Please correct me if I am wrong.

Cheers

 

[marisse]

I think you can apply the PL/AE to find the cable deflection, taking in consideration the angle formed by the deflection. You also have to use the actual area of the cable. Hope this will help.

 

[flamby]

If the load is considerable and cables bend in triagular form instead of looking like circular arc, you can just use laws of simple statics assuming a symmetrical traingle of cable.

Ciao.

 

[yack]

1st) If you know the length of cable and span and cable self weight, calculate the tension in the cable without the point load.

2nd) Calculate the tension in a cable with an additonal free hanging length in the middle whose self weight equals that of the point load. Where, your span is the horizontal distance of the outer two portions.

Felt like a million bucks, when I figured this out--on my own.
Take that "Structurals"

 

[dbuzz]

Roarks Formulas has relevant equations.