Calculate Length of Wire with Elasticity & Tension - Young's Modulus 56kN/mm2

[Creini]

Hi,

I'm trying to figure out how long a wire will be when I hang it up between two supports.

I have:
The Young's modulus for the wire (E): 56kN/mm2
The length of the span (L): 55m
The weight of the wire (w): 0.73kg/m
The tension of the wire (T): 11kN
The cross sectional area (A): 266mm2

I know how to calculate the length of an inelastic wire:

L'= L + (w^2*L^3) / (24T^2)

But that I assume the Elasticity of the material must matter?

So, what I'm after is some formula for calculating this, not an answer
(although an answer could be good to compare to I guess)

Regards,
Mattias

 

[Bob S]

Hi Creini-
I think your equation is for a cable between two points supporting a uniform horizontal weight, like a roadway (suspension bridge). What you want is the equation for a cable supporting its own weight, which is a catenary.
Bob S

 

[ully]

You may also like to consider running a support in accompany with the wire, depending on the wire length and size some simple stainless steel safety wire may suffice (snap it by bending with two pliers, do not cut it, it will ruin your tools (unless you have very expensive cutters designed for stainless steel)) with a turnbuckle and hook to tension it- if the cord (elec wire) is not specifically designed for outdoor free air use it will not have adequate ozone protection and strain in the insulation will cause cracks quickly- and even if it is, it will last a lot longer and safer with support. But it is more labor intensive. Unless you have a cherry picker I would suggest using black zip ties (black ones are UV/Ozone protected) to attach the wire/cable, to the cord on the ground- providing a bit of slack and appropriate drip loops. I would also bond the the wire/cable to your electrical ground, not a Earth ground, simply continuing the safety wire to the nearest junction box with the cord- and mechanically attach it to either the box enclosure with a screw, or wire nutted/crimped to the green wire.

Unless you are doing this on a steel building (the building would bond it) you should bond it (bond means ground but explicitly to the electrical ground, not Earth ground)- if this is like for your kids treehouse, bond the wire and you have a much safer and reliable system then no support at all.

 

[FredGarvin]

I don't think it will follow the catenary because of the probable end supports (fixed in the x and y directions). I would suspect that the max deflection would be less than that.

 

[nvn]

Creini: I only have time to give you the answer, so I hope that will help you, as you mentioned. The answer is << answer deleted by berkeman >>

Hey, wait. Is this school work?