Sag Tension Calculations, Temperature Changes

[TechEagle]

I need to know the worst-case sag for a wire when it is strung at a known design tension/% breaking strength. Anyone know where I could find the article from Harvey and Larson published in 1977?

 

[wareagle]

If you are a member of IEEE they have it here

http://ieeexplore.ieee.org/Xplore/l...arnumber=1412645&arSt=+0_1&ared=+28&arAuthor=

 

[TechEagle]

The article was informative, but not quite what I was looking for. It works great as an example of what I am looking for though; On page 25 of the PDF of the document above how did they calculate Table C.1? I have talked to numerous people that have zero clue how to calculate this by hand. Frustrating.

It seems so simple, I specify that my controlling design condition is 25% of RBS at 60 degrees F. This gives me a known sag according to that tension. Then I want to create a similar table to C.1 showing what the sag and tension will be for any given combination of weather conditions. But this is apparently only calculated by computers because people have given up on knowing how to do it.

 

[jmmee97]

TechEagle,
If you can find the "Mechanical Design for Overhead Distribution Lines" manual from RUS it has catenary and parabolic sag equations in it I believe. It is bulletin 160-2 (may have changed?). Check their web site. Also, Alcoa's Sag10 program may get you what you want. Not sure if it is available for download.

 

[bacon4life]

The new bulletin is 1724E-152, "The Mechanics of Overhead Distribution Line Conductors."

People have not given up on knowing how to do it, but rather choose to have computers do it because calculating it exactly can be very time consuming, especially for anything beyond a single level span. I would be a bit scared if the people you asked were line designers. Although SAG10 and PLS-CADD give you lots of nice numbers, unless you have a feel for doing the basics by hand, how will you check that it is doing what you think you have it doing?

If you really want to go to basics, get a Statics or Physics text book and go through the derivation of the catenary equations. It should be fairly straight forward to calculate sags based on different temperatures (conductor length)/ice(conductor weight) for a single level span. Alcoa has a demo version of SAG10 with a few example conductors you can use to check your answers.

 

[stevenal]

When it comes to real conductors changing in length, RUS points to the computer programs. There is a non-computer example of in the McGraw Hill Electrical Engineering Handbook, using Thomas and Martin methods. I wouldn't call it straight forward, though, eyeballing the graphs and looking up the tables.

 

[tommom]

Okay, I have the formula - But you have to send me your Christmas bonus to get it.

This formula assumes a parabolic shape instead of catenary, but since the span length is usually greater than 10 times the sag, this is a pretty good approximation.
(** = squared)

(f2**2)*[f2 – (K – a*t*E)] = (l**2)*(d**2)(q2**2)*E/
24

K = f1 - (l**2)*(d**2)*(q2**2)*E/
24*(f1**2)

f2 = Stress in conductor in lb./sq. in. at temp t2

a = Coefficient of expansion per degree F

E = modulus of elasticity in lb./sq. in

t = difference in temp between two sets of loading conditions

q2 = Loading factor (weight multiplier of ice- or wind-loaded conductor to bare conductor) in still air (can include ice loading - without ice or wind loading, q is 1.)

A = area of conductor in sq. in.

d = weight of conductor per ft. run per sq. in cross-section

Then sag S is

S = (l**2)*(d)*(q2)/
8*f2

and the tension in the conductor T = f2A

The problem is to solve the cubic equation. You can plug this all in, run it four or five times, or do what I did: plug all this, including the modulus of elasticities for steel, aluminum and a means to calculate it for ACSR (you might be able to get that from the mfr.) into a spreadsheet.

If you want the spreadsheet, contact me with your email info. Only problem, it's in Quattro Pro 7, and may not have converted cleanly to Excel.

 

[jghrist]

For a composite conductor like ACSR, the calculation is not so simple. There is an interaction between the steel and the aluminum that needs to be considered. Hand calculations to accurately take this into account involve graphically interposing the stress-strain curves of the two materials. There was a thread about a year ago on this subject and someone posted a link to a program that gave a good approxite solution. Try searching this forum.

 

[tinfoil]

Adding further complication to this is wire creep - old ACSR has been permanently 'stretched' to be longer than new ACSR, which is why all the sag tables have initial sags and tensions (for unstretched wire) and final sags and tensions (for older wires).

Of course, if ANY conductor has too much strain applied (i.e. outside of its elastic range) it will ne permanemtly damaged/stretched/deformed. The 'creep' I am describing above is considered 'normal usage'.

There's some good reference stuff at

http://www.geocities.com/ieee_tpc/ieee_tutorials/IEEETPCTutorial_Sag-tensionCalcs.pdf

 

[tommom]

The calculation that I use takes the "short-term stretchiness" of ACSR into account - ACSR has a composite modulus of elasticity which can be calculated. I did not include that calculation in my post.

I did not include the effects of long-term creep - I'm not sure exactly how to do that based on the calculation I gave - there is no additional information on how to do that in the book I "quoted."

The point is that it's not a simple calculation, it can be done and estimated but if you need precision a program is probably better. SAG10 can be used, a demo version is free from Alcoa but you need to pay for the full version - I forget the limitations on the demo.