Over the years I've contemplated posting something like this, but have never gotten around to it. Some recent discussions prompted me to bite the bullet and post it.
This is my take on a pier design spreadsheet that should be fairly simple for the lay person to use. You enter your desired pier height, what it's supporting (mount, scope, camera weights totalled), what kind of pier you want to use (eg circular hollow section, square hollow section, square concrete, circular concrete), set some movement limits, and it will output the minimum sized pier to meet those criteria.
The input cells are the orange ones. All other cells and worksheets are protected so the formulae and section properties don't get changed/corrupted by accident. Hopefully it's all pretty self-explanatory.
Quick summary of assumptions:
- It does not model vibrations. Having read around, asked a few questions, and chatted to a few experienced pier/observatory builders, we agreed that for appropriately sized piers based on the other criteria in the spreadsheet, vibrations should not be a critical factor. There are too may sources of vibrations; the frequency, magnitude of them is impossible to model simply, and it's not worth pursuing that when they're not going to increase the size of the pier anyway.
- The sizing of the pier is based on a horizontal/lateral load being applied on the top of the pier, causing a deflection. This is the same model as proposed on the often referred to Cloudy Nights post on Pier Design Fundamentals.
- Similarly, the default minimum load applied (2kg) is in the same order as the 5lb load suggested in the above CN post, but can be overridden.
- I've included a function for the weight the pier is supporting, and use a fraction of that load to be applied horizontally. This is to deal with mounts carrying quite large loads where the above-mentioned 2kg arbitrary load may start becoming a bit light on.
- The deflection limits of 0.5arcsecs and 0.1-0.5pixels (whichever is worst) were also borrowed from the CN post and discussions with other IIS members.
The steel section sizes are based on Australian Tube Mills availability. There's probably other section sizes available, and they can easily be added to the spreadsheet later.
Edit: I've now added a "rat cage" section to check the impact of it on stiffness/deflection. To use it, though, you must use the "custom section" bottom part of spreadsheet.
I'm happy to open discussion about what are acceptable deflection limits, and any other improvements within reason.
Future additions/improvements I am thinking of are:
- suggest reinforcement for the concrete options
The results of all formulae in my spreadsheet (running on MS Excel on Mac) for the .xlfn and all dependents are #NAME?
ie I think its either not recognising your custom function for the cantilevered calcs or one or more of the parameters needed isnt available.
So not sure if the function is embedded or mv version of Excel simply isnt reading it properly
Its not a problem as I have my own spreadsheet as you know, but others might have this same problem.
Thanks for taking the time to work out the engineering aspects, this will be very useful
Geoff
No worries mate. Hope it’s useful.
Quote:
Originally Posted by RickS
Nice work, Troy. Does it make a correction for Kobe Steel?
imagine if they supplied to VW. You’d drive a car that falls apart and breaks emission targets
Quote:
Originally Posted by rally
Hi Troy
The results of all formulae in my spreadsheet (running on MS Excel on Mac) for the .xlfn and all dependents are #NAME?
ie I think its either not recognising your custom function for the cantilevered calcs or one or more of the parameters needed isnt available.
So not sure if the function is embedded or mv version of Excel simply isnt reading it properly
Its not a problem as I have my own spreadsheet as you know, but others might have this same problem.
Rally
Thanks for the feedback. The only thing I can think of is for the section selection it uses data validation list as a dropdown, and that may not work on all spreadsheet apps. The other on is a function that may only be avail in Office 365 and not earlier versions. I’ll try rewriting to make it only use basic functions for broader compatibility.
Hi Troy, thanks for doing that. I'm in the middle of pier design at the moment using mostly wild plucks for dimensions (well, actually based on what appear to be other people's successful examples).
Similar to Rally, I get #NAME? in the output fields ... that's using Excel 2010 in Windows.
I assume the section size given is for "plain" CHS welded to a base plate. How would this change for a pier that includes full-height, fully-welded fins?
Hi Troy, thanks for doing that. I'm in the middle of pier design at the moment using mostly wild plucks for dimensions (well, actually based on what appear to be other people's successful examples).
Similar to Rally, I get #NAME? in the output fields ... that's using Excel 2010 in Windows.
I assume the section size given is for "plain" CHS welded to a base plate. How would this change for a pier that includes full-height, fully-welded fins?
I just re-did much of the way it was calculating section sizes so it's using more standard functions. Hopefully no compatibility issues, although I have no way of testing myself. Will rely on feedback.
You're correct - they're just tubes, no stiffeners/fins. No need if you use these section sizes. The stiffeners/fins are probably only necessary if the tube you're using is undersized and needs stiffening.
I may do an exercise to see the effect of smaller sections, but add stiffeners, and see if actually ends up being heavier (ie more expensive, because steel usually $/kg, and also more welding with fins).
Ok, I've updated the spreadsheet to use simpler functions. Hopefully those with older or Mac versions of Excel, or even maybe Google Sheets or Libre etc, may be able to use? Please feel free to let me know.
...
I assume the section size given is for "plain" CHS welded to a base plate. How would this change for a pier that includes full-height, fully-welded fins?
So I just did a quick exercise to see what benefit there would be to add stiffeners. Assumption was a circular tube with 4 equally sized stiffeners (at 12, 3, 6, and 9 o'clock) full height. Stiffener plate thickness was set to 10mm.
With no stiffeners, you'd need a 219X6.4CHS.
With the same design parameters, and assuming the reason you want the stiffeners to reduce the CHS size, I dropped the CHS size to the lightest (thinnest wall) of the next diameter down - 168x4.8CHS. To get the same stiffness as teh 219x6.4, the stiffener plates need to be 57mm long (in reality you'd use the next off-the-shelf flat available, which is 65x10).
Thing is, 168x4.8CHS with 4 stiffeners 57mmx10mm weighs 37kg per metre. A 219x6.4CHS with no stiffeners weighs 33.6kg/m. So for the same stiffness, no plate stiffeners is lighter (ie more efficient). Usually cost is measured in kg/m too - so it's cheaper. And that's ignoring the fact that plate stiffeners require more welding too.
I did an earlier comparison of 100x100 Square Hollow with and without ribs against 150x150 Square Hollow on an equal added mass basis, handraulically...
100x100x6 Square Hollow Section:
Second Moment of Area = 3.04 x 10^6 mm^4
100x100x6 Square Hollow Section PLUS 50x6 Full length Ribs at 12, 3, 6 and 9 o'clock:
Second Moment of Area = 6.54 x 10^6 mm^4
There are four 50x6mm ribs used above. Instead of using them as ribs imagine adding each of these (distributing their mass) to each 100mm side of the 100mmx100mm SHS, whilst still maintaing the 6mm wall thickness. Well each side wall is now 150mm - You now have 150x150mm SHS. Now look at the Second Moment of Area of the 150x150mm SHS:
150x150x6 Square Hollow Section:
Second Moment of Area = 11.3 x 10^6 mm^4
So all other things being equal, the 150x150 SHS should have 6.54/11.3 = 58% of the deflection / slope / bending stress of the 100x100mm SHS reinforced with full length ribs. A 42% reduction.
In short, whatever gets the mass out furthest from the neutral axis in bending, will always win the deflection/rotation/bending stress battle (without changing the material of course)
You're exactly right, JA. It's much more structurally efficient to use the larger section and no stiffeners than it is to use smaller section with stiffeners.
I've just uploaded a new version. It now puts in brackets the weight of the pier in kg after the section size.
Also added a section at bottom where you can put in a section size that may not be in the list - assumes steel and a circular or square hollow section. You'll need to know the section's outside diameter/length, it's second moment of area Ix, and it's weight in kg/m.
In that custom section you can also add stiffeners, so compare a smaller section size with stiffeners vs plain sections no stiffeners appropriately sized. It assumes 4 equally sized stiffeners at 12, 3, 6, and 9 o'clock (hope/assume that description is obvious). If you don't want stiffeners but still use custom section, just use a thickness or length of zero.
Now you can prove to yourself that for the same design parameters, it's lighter/easier/cheaper to go plain section with no stiffeners than smaller section with stiffeners.
I just uploaded another new version, not with "rat cage" feature. Hopefully it's self-explanatory with the notes in the spreadsheet itself. You can play with bolt diameters and spacings to see what stiffness and impact on deflections.