Equation Stress on Aluminum Portion of Conductor

[lookintomyeyes]

Hello,

Can anyone provide a reference document that would contain the equation for calculating the Aluminum Stress on a combo Steel-Aluminum Conductor?

I'm reviewing an old report and it uses an equation in MS Excel that appears something as follows, but I would like to know what the source for this equation was.

Sigma_a = T1 - (B_a-B_s)*(T_a-20)* E_sI * (A_t - A_a) * E_aI / (Es_I * (A_t - A_a) + E_aI * A_a)

where:
Sigma_a = Aluminum Stress
T1 = initial tension at -35C
B_a = ??? (I'm guessing its a coefficient of expansion for aluminum, units were noted as K-1)
B_s = ??? (I'm guessing this is coefficient of thermal expansion for steel, units noted as K-1)
T_a = temperature of ???
E_sI = ??? (Guessing initial modulus of elasticity for steel)
E_aI = ??? (Guessing initial modulus of elasticity for aluminum)
A_t = total conductor cross-sectional area
A_a = cross-sectional area of aluminum


If any of you can help out, thanks!

 

[MikeDB]

I don't know if the Aluminum Association conductor manual or Southwire's conductor manual covers this subject. Most folks don't use the stress-strain curve method of by-gone years. I can't comment on the equation shown, but it appears to have the proper elements in place. However due to creep, the stress in the aluminum changes over time and is a function of how far it has been streched in the past. The equation seems to only address an initial condition.

If you don't have access to ALCOA's sag and tension program or Powerline System's CADD program which has sag and tension capability, I suggest you contact one of the conductor manufacturer's and ask them for the info for your particular application.

 

[lookintomyeyes]

Hi MikeDB,

I do have access to both Alcoa's SAG10 and PLSCASS, but the report I am reviewing did not use it. The equation does not appear to be in the Southwire manual either, as that was the first source I checked.

The report back-calculates aluminum stress based on a specified required RTS (used to calculate T1), so it doesn't actually use a span length, as PLS-CADD and Sag10 require.

I'll see if I can track down an Aluminum Assoc. conductor manual and see if the equation is in there.
Thanks!

 

[jghrist]

Maybe this will help. From the Standard Handbook for Elecdtrical Engineers, Fink & Beaty, 14th Ed.,

[α]_AS = [α]_Al·(E_Al/E_AS)·(A_Al/A_total) + [α]_St·(E_St/E_AS)·(A_St/A_total)

E_AS = E_Al·(A_Al/A_total) + E_St·(A_St/A_total)

E_Al = modulus of elasticity of aluminum, lb/in²
A_Al = Area of aluminum strands, square units
[α]_Al = aluminum coefficient of linear thermal expansion, °F^-1

AS for aluminum-steel composite
St for Steel