## Local buckling of thin-wall tubes in bending

## Local buckling of thin-wall tubes in bending

(OP)

For thin-walled square and rectangular tubes, I'm trying to find a formula for the loss in bending strength due to local buckling in the compression 'flange' and side walls.

I've heard of heuristics like keeping (width/t) < 50 to avoid dimpling of the walls; I'm looking for something more specific.

For torsion of thin-walled round tubes (steel & aluminum), I found an approximate formula in Roark and Young:

'Loss Factor' = 1600 /(( (OD/t) - 2)^2 + 1600)

(p 318 of 5th ed... formula is from 1935)

but they don't have the equivalent for square & rectangular tubes in bending. According to that formula, there is a 20% loss in torsion strength when OD/t = 22. And 50% loss when OD/t = 42. Quite a lot for some common tubing.

Thanks for any leads.

I've heard of heuristics like keeping (width/t) < 50 to avoid dimpling of the walls; I'm looking for something more specific.

For torsion of thin-walled round tubes (steel & aluminum), I found an approximate formula in Roark and Young:

'Loss Factor' = 1600 /(( (OD/t) - 2)^2 + 1600)

(p 318 of 5th ed... formula is from 1935)

but they don't have the equivalent for square & rectangular tubes in bending. According to that formula, there is a 20% loss in torsion strength when OD/t = 22. And 50% loss when OD/t = 42. Quite a lot for some common tubing.

Thanks for any leads.

## RE: Local buckling of thin-wall tubes in bending

BA

## RE: Local buckling of thin-wall tubes in bending

See the front of the book where there give HSS geometric properties. At the end of that section they tell you how do determine in the shape compact, non-compact, or slender.

## RE: Local buckling of thin-wall tubes in bending

The question is not whether the shape is compact, non-compact or slender. The question is about local buckling of thin walled HSS members. I do not believe local buckling is a problem with commonly available HSS sections, but if anyone has any more info on this, please let us know.

BA

## RE: Local buckling of thin-wall tubes in bending

## RE: Local buckling of thin-wall tubes in bending

In the particular case of HSS members:

Class 1 b/t <= 420/√Fy

Class 2 b/t <= 525/√Fy

Class 3 b/t <= 670/√Fy

In Canada, we use the SI system, so Fy is expressed in MPa. For HSS, Fy would normally be 350 MPa, so a Class 3 HSS requires a b/t ratio less than or equal to 35.8.

BA

## RE: Local buckling of thin-wall tubes in bending

AISC defines flange local buckling and web local buckling as applicable limit states for hollow structural sections (HSS) in bending. However, you need to the classification of the shape (compact, non-compact, or slender) to determine in the limit states are applicable.

I forget how it is precisely defined, but I know that if it is a compact section, then local buckling isn't an issue.

## RE: Local buckling of thin-wall tubes in bending

I apologize...you are correct about compact and non-compact sections. If by slender you mean slenderness of the wall then that would be correct too. I took it to mean slenderness of the column. You can give me a big fat raspberry.

BA

## RE: Local buckling of thin-wall tubes in bending

Haha. No problem.

Cheers.

## RE: Local buckling of thin-wall tubes in bending

If we could weed through all the machinations the code writers have gone through, what with all the factoring up and down for a bunch of probabilistic considerations, etc. (I hesitate to use the term 'bunch of Junk,' although that's about what I really think, because some of those people are my friends, when I'm not out buying new editions of their latest work) and including accounting for the differences btwn. SI and US units; I suspect that the Canadian classes 1, 2 & 3 and their b/t's, and the AISC's compact, non-compact, and slender; would lead to BA's explanation and terminology 'fully plastic moment and redistribution, attain plastic moment, and attain yielding moment.' I further suspect that they would both lead back to the same testing and theoretical work if any of us could follow the math any more. Our (AISC's) compact, non-compact and slender are all mixed together in beam/column stability and buckling theory, lateral torsional buckling theory, unsupported lengths, and if you finally account for and protect against the former possibilities, you are working at a stress level were localized plate buckling can still be an issue. But, this has now become a cookbook recipe exercise over last fifteen years or so, rather than an engineering understanding of the whole problem and concept. And, I'm certainly not suggesting that I can really understand it all any longer.

Hokie>> Look back at BA's excellent post on Newmark's Methods, since your last post there. We have to improve our applications and interviewing methods, re: old dogs.

## RE: Local buckling of thin-wall tubes in bending

I'm glad I learned something about this. Thanks again!

## RE: Local buckling of thin-wall tubes in bending

As long as the section meets the wall slenderness limits stated in the code then those formulii can be used but for more slender walls you will need to use more stringent formulii.

Blodgetts would probably be a very good referenece for this, I am sure I saw a formula in there. Unfortunately I do not have access to my notes on this at the moment.

## RE: Local buckling of thin-wall tubes in bending

And later:

So it would appear that the buckling of very thin cylindrical shells is not well understood, even by the experts.

BA

## RE: Local buckling of thin-wall tubes in bending

A thin-walled member is loaded in bending, and, if overloaded, will fail somehow.

Isn't the OP asking whether a HSS will fail by local buckling first, rather than some other mode of failure? If so, how would invoking the steel design codes tell you (me!) how it will fail if overloaded?

Robert

## RE: Local buckling of thin-wall tubes in bending

unlike stretching, for example, when a member will simply keep stretching under additional load; once something has kinked at a single point, the whole member has zero strength against bending.

The rest of the tube may be still straight and capable of carrying a load, but the structure has failed - will continue to fail - as soon as the first point on the wall of the tube kinks. It (the structural member) will keep bending at that location.

## RE: Local buckling of thin-wall tubes in bending

The steel design codes give equations for the nominal bending strength (prior to applying a factor of safety) of rectangular HSS based on different limit states (yielding, flange local buckling, web local buckling). Guidance is given based on the geometric properties the HSS in question as to whether or not each limit state is applicable. So, based on the code criteria, you can determine what the controlling failure mechanism will be.

One caveat being that the equations for local buckling are most likely somewhat conservative and those sections that are barely slender enough to be governed by local buckling per the code may actually reach yield in an experimental investigation. I can't attest to the accuracy or level of conservatism in the steel code expressions for local buckling in HSS, but they usually err of the side of safety for failure mechanisms that aren't precisely defined by theory, particular for non-ductile failure mechanisms like buckling. I have seen this in the American steel code for other types of local buckling failures in beams.

## RE: Local buckling of thin-wall tubes in bending

Well, it has been well established that the elastic buckling strength for any structural application is a dream when it comes to the real world behavior. The elastic buckling strength is based on the critical assumptions of a pure axial load acting a member with no imperfections. In many instances, it is difficult to come close to achieving this even under the most idealized lab settings. Any initial imperfections are immediately exacerbated once loading begins. I would imagine these effects are particularly significant for a thin cylindrical shells.

Researchers at the time of Timoshenko and Gere's book did not have the tool of finite element analysis to account for these effects. I'd imagine that by now, someone has investigated these features for thin cylindrical shells through finite elements analysis and been able match their analysis more closely with experimental results.

## RE: Local buckling of thin-wall tubes in bending

_{cr}for a simply supported plate of thickness h and width b. The factor k varies with a/b ratio (a is length of plate) and may be taken as 4.0 when a/b is very large.The ratio b/h can be calculated from Eq. (9-7) for σ

_{cr}= Fy (see highlighted text).BA

## RE: Local buckling of thin-wall tubes in bending