Temperature effects on conductors

[atrizzy]

I'm trying to assess forces from a lightning shielding wire.

Wind, ice, self weight are fairly straightforward using the cantenary equations, however, I'd like to assess the force differences under different temperatures.

Does anyone have a resource or spreadsheet that considers these temperature effects?

 

[IRstuff]

Force on what, the supports? The weight doesn't change

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[atrizzy]

Typically the supports consist of towers. The weight doesn't change but the lateral tension, sag, etc, changes quite dramatically with temperature.

 

[IRstuff]

So, are you concerned about the force on the support or the tension in the cable?

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[atrizzy]

@IRstuff, both, the support needs to resist both vertical and lateral loads.

 

[dik]

Wouldn't that only have an impact on the dead end structure? or drastically different spans?

Dik

 

[atrizzy]

@dik, these are for lightning masts within a substation. Technically all 'dead end', with loads applied from one side or orthogonal sides only.

 

[IRstuff]

Seems to me that you can use the expansion coefficient to figure out a different length for the catenary and come up with new values for the forces.

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[dhengr]

Atrizzy:
The horiz. reaction forces caused by a catenary can be astronomically high, and so can the forces caused by extension and contraction due to temp. changes. I am not that familiar with the design and construction of electrical substations, but I would bet that your lightning shielding wires are not stretched too tightly, in the first place, exactly for these types of reasons. You just can not design for the forces which can occur. Thus, the real design problem is picking a catenary shape (geometry vs. forces/stresses) which tolerates these loads, movements and forces, mostly by a reasonable length and geometry change, which does not drastically alter the reaction forces on the towers. Temp. changes on the wire, and its length change and how that changes the length/shape of the catenary should not be that hard to start to get a good approx. value to work with. Then how does that change the horiz. catenary reaction? Solid wire will be one thing and any cable wound type wire will be another due to the mechanical action within the cable.

 

[BridgeSmith]

For a rough estimate, you should just be able to adjust the sag used for design based on the shortening of the cable due to temperature change. That will give you a conservative estimate of the increase in tension. Attempting to get closer to that seems like a fool's errand to me. As the temperature drops and the sag decreases, but the tension stress increases, increasing the strain, lengthening the cable, which increases the sag. You could be chasing convergence for a long time.

I've done dozens of span wire spans for traffic signals, and the wind load is the dominant contributor to the total loading. Estimating the wind pressure is subject to a substantial amount of variation, with drag coefficients, etc. By far the largest and most unpredictable source of variation is the wind speed. Make a slightly different assumption of the maximum wind speed and the small changes due to temperature suddenly don't matter.

It seems the level of refinement you're attempting is not really warranted, or achievable, in a real-world environment. I suspect that's why it's not addressed in the equations you referred to.

 

[CANPRO]

I’ve gone through this calculation before when designing fall arrest cables...I took the approach that IRstuff mentioned...just used the change in temperature to get the change in length. It’s an iterative solution, but excel handles it easily.

It’s been a while since I’ve gone through the numbers, but I remember the change in temperature not being a huge factor unless you start off with a very high tension/low sag condition.

 

[atrizzy]

Thanks all,

The reason I'm so interested in the temperature effects is that odds are pretty high that I'll need to add some more of these conductors, for which I'll need to provide a sag/tension table for different installation temperatures.

Appreciate the responses and looking forward to any other comments.

 

[TLHS]

You're doing a substation. Can you get the utility's distribution standards? They'll have a bunch of standard sag install charts and design tensions that you can use.

Manually making sag charts on your own is a pain in the ass. It's only a single span, so it's not terrible. You mentally seem to be approaching this right. Pick a trial sag or tension. Calculate the length of the line. Decide on the design temperature difference. Apply that and determine the new reduced length of the line and, from that, the sag geometry. Apply the weight of the cable, plus any other design conditions (wind, ice, birds). For tension purposes you can conservatively just pretend the wind is a downward force on the same catenary. Calculate the resulting tension with your various load cases at the reduced temperature geometry. You can either use the first solution, which should be conservative, or you can incorporate tension elongation of the cable into it and iterate. The loaded condition will give you your design tension. If you don't like the answer, pick a different trial sag or tension and do it again.

Now you get to make an install sag chart. Take your initial cable length and recalculate at some regular temperature interval (every 10 degrees, say). Calculate the sag, cable length and tension at each of those values and chart them so that the design conditions for any given temperature are known.

 

[Denial]

Over the years I have developed a spreadsheet that rigorously analyses a cable allowing for the cable's elastic elongation.[ ] It does not directly accommodate thermal expansion, but since it takes "unstretched length" as one of its input parameters any such expansion/contraction is very easily handled.

The spreadsheet can be downloaded from my web site

http://rmniall.com