How does adding weight affect Sag/Tension Calcs?

[epena]

I am a relatively new engineer working for an electrical utility. I am interested in sag and tension calculations for aerial cable designs. I have done extensive research and have found numerous information regarding performing the calculations, e.g catenary eqs, parabolic eqs, weight spans, etc. One concept that is not explained in the material is how does the sag and tension change when weight (in the form of a cable) is added to an existing wire. Assuming a piece of messenger wire is installed between two poles and I wish to lash a cable to the messenger, how much more does the messenger sag and how is it calculated? I had someone in engineering run simulations using Sag10 software but I'm interested in the hand calculations. Since I don't have the program, I am looking to manually calculate a particular "what-if". Thanks in advance.

 

[rollingburnout]

Calculate the same way you calculate the original sag, only add the weight of the additional cable?

 

[wareagle]

Check here

http://www.acasolutions.com/resource_center/white_papers/index.html

 

[bacon4life]

Googling "centenary equations" has worked better for me than looking up anything related to "transmission" or "sag".

rollingburnout is correct that you just change the weight per foot to the sum of the messenger and the cable.

http://www.spaceagecontrol.com/calccabl.htm

has an example calculator.

Another form of the equations is in 1724E-152 The Mechanics of Overhead Distribution Line Conductors available at

http://www.usda.gov/rus/electric/bulletins.htm.

 

[jghrist]

When you add weight, the tension increases according to the approximate parabolic equation H=w·S²/(8·D) where w is weight per unit length, S is span length, and D is sag. With more tension, however, the conductor stretches, so the length increases according to the equation
L2 = L1·[1+(H2-H1)/(Ec·A)] where L2 is the new length, L1 is the old length, H2 & H1 are the tensions, and Ec is the modulus of elasticity.
The length is related to the sag by
D=sqrt[3·S·(L-S)/8]
With more length, there is more sag and less tension. You can solve these equations iteratively for a change in weight. This is shown in Standard Handbook for Electrical Engineers by Fink and Beaty, and was originally worked out by J.S. Martin in 1922, forming the basis for "Martin Tables" that were republished by Copperweld Corporation in 1931.