Buckling of circular arches and rings: a general question. 7

[WARose]

Recently I had a couple of projects that involved lifting rings [that were part of equipment] and a couple of arches that were loaded with both in-plane and out-of-plane forces. (By in-plane, I mean forces that are applied radially to an arch or something like a vertical load that can cause snap through buckling. By out-of-plane forces I mean forces coming in from a perpendicular direction to that…..something like wind load.)

I pulled all available resources off my shelf……but was still left with a very important question: almost all the formulas that dealt with arch/ring buckling typically gave buckling values that we caused by in-plane forces. I really couldn’t find anything for out-of-plane loads. Now, one reference I have [i.e. ‘Guide to Stability Design Criteria for Metal Structures’ by: B.G. Johnson, 3rd Edition, p.476-477] had this to say on the subject: “Out-of-plane buckling of rings, arches, and other curved planar members is in every way analogous to lateral-torsional buckling [LTB] of beams and beam-columns.” They proceed to give a number of buckling formulas, but I’m not sure they are applicable to the out-of-plane forces I discuss here.

So I guess what my question is: where can you find allowable for such a situation? Is it just a matter of calculating LTB as per an applicable code? If so, what would you call your unbraced length? For example, in that ring lift scenario I mentioned earlier, we just basically lifted a ring with attached lugs (8 of them around the circumference; it had a 30’ radius). The self-weight of the ring is causing the out-of-plane moment. Obviously the lifting point isn’t restrained torsionally…….but laterally, I would think the arch [think of the ring in pieces] would be stiff enough to prevent lateral translation (but obviously that would require calcs). [What I did there for unbraced length was subdivide the circumference of the ring into 4 pieces; because I reasoned that it would buckle into at least 4 parts.] Same deal with an circular arch (receiving out-of -plane load): at the least, I would think the highest unbraced length would be ¼ of the circumference (if it was a complete circle). Only thing about those approaches is: you kind of counting on the structure to brace itself…..and I always thought that was big no-no.

Anyway, any insight is appreciated…..and be sure to have a good 4th.

 

[ishvaaag]

errata, Xanthakos, the 3d time I hope I write it right.

 

[SAIL3]

interesting problem.....here is how I would approach the out-of-plane buckling...
1. visualize various buckled shapes and determine which is more likely to happen...
2. intuitively due to the curvature of the ring the tendency to buckle out of plane is less than a straight member..so I put that info in my hip pocket to use in later assumptions..
3. now, how to apply a pracical analysis to this problem?..to me it reduces down to what effective unbraced length to use?.
4. counting on the structure to brace itself is one way to describe a symmetrical buckled mode....
5. 1st mode of buckling to me would be two-halves of the ring buckling out of plane in opposite directions....and I would use an effective length somewhere between half the circumference and and the diameter of the ring.
I would back-off from using half the circumference by taking into account that it is a 4-point lift...the inherent stability of a curved member when comparing actual lengths versus a straight member etc....conclusion..I would take 75% of half the cicumference...one note of caution..computer programs can give a misleading interpretation of the buckling load unless you carefully check the results..