Ruling span calculation for transmission cables. 1

[mtroche]

Help strongly desired!!

I am working in calculating the sag and tension of transmission cables, and I have this doubt: if I have a ruling span, shall I use the difference in elevation at the beginning and end of the ruling span or shall I use the maximum difference in elevation in the ruling span to calculate the horizontal tension? Please, don't tell me about any program to calculate it. I want to know how to work with the ruling span in calculating the horizontal tension.


ATT.
MTroche

 

[ishvaaag]

The answer is that for a cable you will get a profile in equilibrium with the loads.

It is easy to understand with the parabolic cable as an approximation of the profile (reasonably accurate when the sagitta is small). Then, the uniform per length load is reasonably approximated by one uniform load.

Be L/2 the projected distance along abscissas between lower point in parabola and highest support, and h be the sagitta between such points.

Horizontal forces H are opposed at support and center of span (lower point); uniform load q acts on half span. Support is a hinge. There is not vertical shear at the lower point of the cable. Then, a mere equilibrium of moments gives the force:

M=H·h
M=q·(L/2)·(L/4)=q·L^2/8

H=(q·L^2/8)/h

The idea is the same for any other cable and load, you have to solve for the funicular of the load, in this case for the uniform load parabolic.

 

[mtroche]

ishvaaag:

I have a ruling span composed of three poles whose elevetions are 46m, 46.75m, and 46m. As you can see, if I take the difference in elevation for the ruling span as the diferrence in elevation between the first and the last pole, the ruling span would be horizontal, but if I take the highest and lower elevation in the ruling span there would be a difference in elevation, so the horizontal tension should be calculated with an inclined ruling span. I know I can tie the cables to the lower and upper poles so there will be no problem with which difference in elevation to use, but I want to know how to deal with this situation without changing the case.

I just want to know if I have to try this case as horizontal or inclined. I have no problem with the formulas to use.

Att.
MTroche

 

[ishvaaag]

Taking the inclined case won't do harm, since such is the setup.

 

[mtroche]

The question continues to be unanswered: HOW DO I CALCULATE THE DIFFERENCE IN ELEVATION FOR THE RULING SPAN CASE JUST MENTIONED IN THE LAST COMMUNICATION?

Att.
MTroche

 

[ishvaaag]

mtroche,

I don't really yet see what exactly is your problem... "ruling span case"..."calculate difference in elevation". Gepmetrical constraints -such where the top of the cables are- use to be a chosen given. So happens with if sliding or clamped at support. So I assume you have some problem in determining something, say, the tension or stress at any given point of the cable for the load case you well know but I am unable from your explanations to fully understand (english is not my own language).

If you can explain in more simple structural terms what you pretend to calculate or determine maybe I will be able to be of help.

Best regards.

 

[Polecat]

Mtroche:

Ruling spans are defined as being between deadends in a line, and are for the purpose of establishing the span from which to caculate the sag-tension properties for stringing the line.

Mathematically, the ruling span is:
sqrt((spana^3+spanb^3+spanc^3....+spann^3/(spana+spanb+spanc...+spann))

If you are talking about three poles, you don't really have a "ruling" span per se, but merely two adajacent spans. As such, you need to treat it just that way. You have two spans (which may or may not be the same length) with a slight difference in elevation; hence, two inclined spans.

http://www.spiraleng.com

 

[mtroche]

PoleCat:

You are right!! But, I have this problem that I have to calculate the horizontal tension in the ruling span composed by three (3) poles where the cables are tied only in the first and third pole; so, what difference in elevation do I have to take to calculate the horizontal tension in the cables? Check out my second message for details. I will appreciate your help.

Att.
MTroche

 

[ishvaaag]

Out of equilibrium, the adjacent spans need have the same horizontal reaction at the central support. This gives an equation. The other is given by the length in the 2 spans summing the input length of the cable. It is only a matter os stating these two equations. With this one should be able to solve for the geometry and horizontal force. A mathcad sheet can do it, I think.

 

[dlew]

mtroche

Some utilities and engineers approch non-level span in different ways. I have not designed a transmission line in 15 years, but my recollection is as follows:

To calculate the ruling span we used what was called an "imaginary" span (I preferred to call it effective span) on all the non-level spans. The effective span was longer than the actual distance between the two poles. It was twice the horizontal distance from the high end to the point of maximum sag, and was given by the following formula:

S(eff) = X + 2*Y*Th/(X*wt)

where
X = actual span (horizontal distance between the two poles)
Y = sag (vertical distance from the high end to the point of maximum sag)
Th = horizontal component of the cable tension
wt = weight of cable (#/ft)

Since Y and Th were unknown at the time, we needed to guess these values and recalculate S(eff) if the difference was considerable. Since ruling spans are normally rounded upward, most of the time we got it right the first time.

Hope this could be of some help.

AEF

 

[JanLCA]

I have a question and deem this thread may be more proper to ask since we all dealing with pole and wires. This is my first time on this site.
My question is the following:
Did I misinterpreted 1997 National Electrical Safety Codes by not applying extreme wind (80 mph for this site)on cables below 60 feet (18m)under Loading 250C for Extreme Wind Loading? While Rule 250B specified 40mph wind to be applied to supported facilities and supports.
I am evaluating capacity of existing H-Column erected back in 1926 for proposed installation of additional 3 groups of cables electrification project.
Thanks.