Correct way to define a cable sag 1

[Costin Ruja]

Good evening,

I have to work myself through some electrical line sag calculations and the norm states that it shouldn't have more than 6% sag.

In this particular case where the supports at different levels, how is the sag defined? S1 and S2 are pretty self explanatory and S4 comes into mind from simply supported beams.



Regards,
Costin

 

[JAE]

Not sure if this helps: https://resources.wolframcloud.com/FormulaRepository/resources/Inclined-Span-Catenary-Sag

 

[JAE]

Or this: https://www.fhwa.dot.gov/publications/research/infrastructure/bridge/05083/appendg.cfm

 

[JAE]

Sorry - one more: https://www.southwire.com/medias/sys_master/related-pdfs/related-pdfs/hf2/h66/8874318168094/AppJ.pdf

 

[BAretired]

6% of what? horizontal span? I would think it should be (S1+S2)/2, but the norm is not clear.

 

[Costin Ruja]

Tons of material for calculations, thank for the links @JAE.

Also one from my side:

https://www.researchgate.net/public...rhead_Line_Based_on_a_Given_Catenary_Constant

The issue, as @BAretired pointed out is that the norm does not state exactly how to measure the sag. Ah, yes, and the 6% are related to the total length of the wire. Guess I'll have to ping pong some emails to the code body that oversees these calculations.

 

[BAretired]

If 6% relates to the length of wire, then I would say the sag to be used is S4.

 

[Denial]

I have no idea how various Codes of Practice express themselves. However I have read a lot of academic and semi-academic papers on the subject of cables, and they pretty much universally define sag as the VERTICAL distance from the MIDPOINT of the straight line between the cable's end points to the appropriate point on the cable. So unless the cable's endpoints are at the same height the cable's actual lowest point is irrelevant in this context.

This is an irresistible opportunity to refer you to a spreadsheet I have developed over quite a long period, which calculates the forces and displacements for a single cable with (or without) a single point load applied anywhere along it. The spreadsheet can be downloaded from my website, https://rmniall.com.

 

[BridgeSmith]

To be consistent with the typical analysis of a catenary span, I think the 6% should be measured as S3. Could use S1.

That said, in a typical analysis, the dead load is a small component of the total, with the design wind load being 80% or more. Given the very approximate nature of estimating projected areas and wind pressures, getting picky about where to measure the sag doesn't seem warranted.

 

[EnzoAus]

Australian standard AS7000:2016 for Overhead Line Design defines the vertical sag as "The maximum vertical departure of the catenary from a chord joining the support points (approximately mid span)". Whilst this will be at the midpoint of the span if both ends are terminated at the same vertical height, it will be displaced from the centre point if one end of the line is elevated above the other. There is also horizontal sag or "blow out" due to wind but I assume the OP's question is in relation to vertical sag.

I would expect European and US standards to have a similar definition given Australia's tendencies to align to international standards. The excerpt below is from the standard.

 

[EnzoAus]

Costin, please note that the Australian Standard does NOT quote a 6% maximum, so it would be useful to get the source document for your quoted 6%. It is always possible that your source (be it a company policy or other standard) may have a different definition of sag.

 

[BridgeSmith]

Costin, please note that the Australian Standard does NOT quote a 6% maximum, so it would be useful to get the source document for your quoted 6%. It is always possible that your source (be it a company policy or other standard) may have a different definition of sag.

How the sag is measured does not change regardless of the percentage. It's a function of how the analysis is performed.

The percentage of sag is a design parameter chosen to meet the limitations and goals of the installation (clearances required vs. capacities of the components).