you know the shear stress, right? (T/(2*[A]*t), [A] is the enclosed area (pi*r^2 for you)

then Bruhn, eqn C8.5, had Fcr = 0.6*E*(t/r) (Bruhn, Analysis of Flight Vehicle Structures, for monocoque cylinders) ... should be in other texts as well (Flavbel, Niu, etc)
presumably limited by Fsy.

another day in paradise, or is paradise one day closer ?

Timoshenko's book 'Theory of Elastic Stability' has a section on this. (Page 500-509 in the second edition.)

I was thinking I had seen that in a place or two- try Roark's Formulas for Stress and Strain, maybe Timoshenko.

H3 of the AISC spec provides torsion design info and they specifically mention the limit states of torsional yielding and torsional buckling. That section also continues on to provide combination formula for torsion, shear, flexure & axial forces.

Years ago I built a spreadsheet around these formuale when I was doing a lot of work w/ monopole signs. And since then I've found that Risa3d does a good job matching my spreadsheet.

Regarding neglecting the torsion:


Out of curiosity, what range of diameters and wall thicknesses are we talking about?

Excellent, the Timoshenko reference was what I was looking for. Couldn't find it in roarks,

Wow, can't believe I didn't check the AISC spec first...

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Wow, can't believe I didn't check the AISC spec first...

I don't know what your pipe diameter (and wall thickness) is.....but if it is outside of the scope of AISC's shapes: be careful. (You said your pipes are "fairly large".)

Of course you have to be careful with anything out of Timoshenko's book as well because there are no safety factors [SFs] suggested. And for a large, thin walled shell.....the initial imperfections and so forth can drive these to be quite high. We are use to SFs on the order of 2-3 to eliminate the possibility of things like LTB, Euler buckling and so on for structural steel......different ball game for thin walled structures. I fall back on ASME code in many cases (including pressure vessel handbooks).

For that matter, be careful with Timoshenko, especially if he doesn't address relationship of theoretical buckling to actual- which can be considerable in some cases.

This is on the order of 1.2m diameter for 30mm wall at the thinnest. I'm trying to keep everything within what is called "class 2" in Canada. Essentially, ratio of wall thickness to diameter should allow the plastic moment to develop before local buckling. Alternatively, I would have looked at an elastic model, checked the buckling ratio and tossed on a FS of perhaps 5. In any case, I'll keep things within the realm of being governed by material shear stress (0.6Fy) instead of the buckling capacity from AISC. I'm certainly looking to be quite safe here

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For that matter, be careful with Timoshenko, especially if he doesn't address relationship of theoretical buckling to actual- which can be considerable in some cases.

Hey that's what I just said.....(albeit differently ).

At a D/t ratio where you are, the 0.6Fy controls in AISC anyway.

You have to get pretty thin walled for those other Fcr formulas to get below the 0.6Fy ceiling.