Determining the Elastic Buckling Stress of a Section

[ToadJones]

This is a very general question and I suspect I'll be lambasted here, but, no risk, no reward....

The commentary of section F.12 of AISC 360-05 mentions that a designer can determine the elastic buckling stress for an unsymmetrical shape by using finite element analysis.

Is there anyone out there that explain how one might go about doing this...even very generally?

 

[BAretired]

One very simple way to do it, Toad is with the Newmark Numerical Prodedures which is a hand method but could easily be adapted to a computer spread sheet.

BA

 

[PicoStruc]

If I had describe the procedure simply I would say this :

With FEA software, you do a eigenvalue analysis with the stiffness matrix. It's like doing modal analysis without any mass. The mode shape will correspond to buckling shape and eigenvalue correspond to force factor !

 

[PicoStruc]

Just to be clear, You need to model the whole studied structure, apply the loads, do you bucking analysis, not just cross-section analysis.

 

[BAretired]

Toad, here is a thread describing the Newmark Method:

thread507-267603

BA

 

[JStephen]

BA, if I'm not mistaken, the methods discussed there would be adequate for variable loading on a symmetrical beam, but wouldn't help much for an asymmetrical member.

Toad, somewhere on these forums are Finite Element forums and perhaps also some devoted to different FEM software, you might check there.

 

[BAretired]

JStephen,

I think you have a good point. The Newmark Method would not be able to detect torsional buckling.



BA

 

[JoshPlumSE]

For local buckling of the cross section, you might refer to the AISI cold formed code. Specifically section B2.1 and B5.1.... Though I can't say that these are truly.

For LTB buckling, I don't know of any formulas for critical buckling strength of unsymmetric sections. Though I would think the SSRC Guide might have something....

 

[BAretired]

Actually JoshPlum, CSA S16-01 has an expression for (a) doubly symmetric, (b) singly symmetric and (c) asymmetric sections. Does the AISC have similar expressions?

BA

 

[ishvaaag]

What SAP2000 v.15 can do from CSI website. That I remember, you make a model and constraint it, and place some loading. You do linear buckling analysis, and for any modeshape found, you find a buckling factor, i.e., the times the structure can stand your applied loading when buckling in such mode shape. So the elastic buckling load is got by multiplying the loading factor by your applied loading at input. Derived from such buckling load, you may find some stresses of interest.

... never to forget that this is ELASTIC buckling load.

 

[JoshPlumSE]

BA -

Where are those formulas? I'm looking at CSA S16-01 and I can't find it. Keep in mind that I was referring to Lateral Torsional Buckling.... i.e. Bending of laterally unsupported members. So, I looked in clause 13.6. All I see there is a reference to the SSRC guide.

 

[BAretired]

Josh, I may not have the latest issue (December 2004). I am looking at 13.3.2 Torsional or Torsional Flexural Buckling.

BA

 

[JoshPlumSE]

AISC has the same provisiong for Torsional Flexural Buckling. But, that's a limit state for AXIAL loading. I believe the OP was referring to AISC chapter F which is related to beam Lateral-Torsional buckling. i.e. beam compression flange buckling which can occur under pure flexural moment.

Don't you just love how Lateral-Torsional buckling is a limit state related to FLEXURAL loading. But, FLEXURAL-Torsional Buckling is a limit state related to axial loading. How easy is it to get those two flipped around in your head?

 

[ToadJones]

Even better yet, doesn't AISC 360-10 have provisions for "pure torsional buckling" because it can theoretically occur even though it has never been observed in testing or in any structure!?

 

[TLHS]

Yeah, there's no code or easy calculation way to do this with beams as far as I know. It's definitely not in CSA S16 and as far as I'm aware it's not in the AISC. S16 goes as far as singly symmetric, but doesn't attempt to do asymmetric sections.

The sixth edition of the Guide to Stability Design Criteria for Metal Structures, doesn't even try to talk about LTB of arbitrary sections. It has things for standard types of shapes, but that's about it. Buckling is a complicated process and coming up with arbitrary formulas isn't realistic, unfortunately. If it's an issue regarding member stability and it's not in that book then there probably isn't a proven consensus method of analysis.

I haven't done it, but I'd likely model the entire beam as plate elements, load it, place nominal horizontal loads or a deformation at the point of load application and then iterate a p delta analysis. Alternately, you could see if your software has a built in buckling analysis and whether it's appropriate for this situation.

I'd just avoid the situation as much as possible, personally. I'd go as far as ignoring portions of the cross sectional area if that's what's necessary to make the section at least singly symmetric.

 

[BAretired]

Josh,
Sorry about that. I thought the OP was talking about column buckling. I am not familiar with Chapter F. I agree with you that the terminology is a bit confusing.

Toad,

Even better yet, doesn't AISC 360-10 have provisions for "pure torsional buckling" because it can theoretically occur even though it has never been observed in testing or in any structure!?

Are you talking here about columns or beams? I would think pure torsional buckling is possible with a cruciform shaped column.

TLHS,

I'd just avoid the situation as much as possible, personally. I'd go as far as ignoring portions of the cross sectional area if that's what's necessary to make the section at least singly symmetric.

I agree with avoiding the situation as much as possible, but ignoring portions of the cross section may not always be a safe method.

For example, a laterally unsupported WF could have a long vertical plate welded on top. The WF may be adequate on its own but the plate attached to the compression flange can make it unstable.

BA

 

[TLHS]

That's an interesting point, BA. I would have assumed that the section would be able to carry at least the amount of load that a reduced section could carry, but by moving the line or action off such that the centroid of the resisting moment shifts it may not be so, I guess. My intuition would be that if the plate would increase the torsional strength of the section then it should increase the lateral torsional buckling capacity of the section, therefore ignoring it would be conservative. If I have some time I might run some numbers for my own knowledge. One set on a doubly symmetric W section and a another set on a singly symmetric section comprised of a W section plus a plate welded far off the centroid and see what happens.

 

[TLHS]

Reading this again, I was picturing a different situation in my head than you intended. Yes, obviously the plate on the compression flange could buckle, which would be a failure. From an ultimate load standpoint, your section would continue to take load, however, while that area buckled out. A plate that buckled locally in that fashion also wouldn't be strong enough to force the rest of the section into buckling. Your welded plate along the top would fail, but in my mind the combined shape of the top portion of the beam is still strong enough to prevent lateral torsional buckling of the entire resisting shape to at least the level it had previously resisted.

So yes, it's a buckling failure. Fair point. I believe it does, however, still maintain the ultimate strength of the original section.

I will amend my above comment to say that I would feel comfortable ignoring parts of the section for the purpose of lateral torsional buckling if I could satisfy myself that the elements would not individually buckle under the stresses they would see when loaded as a section.