Chain catenary vertical reaction help 11

[Carcajou]

For dead load chain catenary with different y-axis end support positions, it's clear that as more chain is hanging from upper support A) both vertical attachment end reactions cannot be identical, and B) upper support vertical end reaction will be higher than lower support vertical end reaction. How are vertical end support reactions determined - losing my sanity a bit. I think chain horizontal component will be equal across chain length, and a cable would react identical to a chain. S.O.S.

Carcajou

 

[Celt83]

Denial

I had not used the formulas myself but made use of another section in the book several years ago.

Made a quick spreadsheet this morning and there is certainly something amiss in the formulas. The formula for S'' does not check out simply doing the case of Z=0 where S' should equal S'' shows an inconsistency in the formula, for a known Z rearranging equation (2-11) seems to provide the correct result for S''. T'' seems to check out when Z=0 will need to do some additional checks on this. Equation 2-10 for X seems to give the wrong sign. I have the first printing of the book from 1978 , ISBN 0-07-035504-5 but I have not had any success locating any errata. A description on the new version in the amazon link I posted seems to indicate that there were some errors corrected from earlier printings.

Edit: Got some contact information for McGraw-Hill and have reached out to them about any errata or any correction to the catenary formulas, if I get a response from them will post back.

Edit2:I'm no longer able to edit my initial post if a forum moderator could edit it to note that there seem to be some errors associated with the formulas and to use with caution that would be appreciated.

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[IRstuff]

@Celt83 You should red flag the post to ask the moderator to add the caveat

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[Celt83]

Thanks IRstuff didn't think to do that, have reported my earlier post.





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[Celt83]

Denial:

Screenshot from my spreadsheet this morning which confirms what you posted. I checked against your spreadsheet as well as IDS's spreadsheet which give consistent results for a sample problem of unity for each of the various inputs.

My Personal Open Source Structural Applications:

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Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[Denial]

A follow-up to my floated correction to Krishna's formula (2.12) for elastic stretch in my 03Feb20@05:57 post above.

I now believe that this correction does apply.[ ] It is the same formula as one given in the paper "Precise Sags and Tensions in Multiple Span Transmission Lines", by J. Barrien, Electrical Engineering Transactions, 1975, published by The Institution of Engineers, Australia.[ ] On its second page this paper gives the formula, introducing it with the traditional and uninformative "It can also be shown that...".

Barrien's formula was what I initially used in my cable spreadsheet.[ ] However its accuracy declines as the cable's slackness increases, whilst still remaining adequate for most engineering purposes.