Local Buckling vs. Global Buckling 5

[MegaStructures]

This thread is not for a specific project, but just a theoretical conversation.

I am trying to better understand the behavior of local buckling in slender elements vs. global buckling in slender columns. I have recently seen a WT brace that is pinned-pinned at its ends and the web appears to be locally buckled (or damaged by construction) near one of the ends, roughly 18" from the gusset plate on a 30' member. I am wondering if it makes sense that this could be a local buckling failure, or if local buckling of the web would occur at midpoint of the member, where the web is the most flexible.

Does the stiffened edge of the plate change the mode shape to something that could buckle at the end, rather than the classic pinned-pinned mode shape with n=1? I don't have a picture of the brace I saw, but I do have another example of local buckling at the end of a member below.

 

[human909]

Insufficient information. But I'll shoot in the dark. The displayed damage could have been cause by LTB of the beams, possibly from uplift on the roof.

With uplift you have the bottom flange in compression and the top flange restrained. A LTB failure of the beam could occur in the centre with the bottom flange elastically deflecting but with the ends restrained you are getting large torsional forces and compression forces on the bottom flange at the end of the beams.

This paper shows similar failures.

http://faculty.uml.edu/tzuyang_yu/Teaching/documents/SS_LN08_0328_Bucklingofbeams-I.pdf

 

[rb1957]

local buckling is (to me at least) crippling of a flange … a localised failure dur to compression.

global buckling is like Euler buckling … to how section has collapsed

now. of course, crippling can lead to a section collapsing (maybe 1 milli-second later) so the difference is analytical.
I can do a crippling calc (b/t etc) for an angle (part of the setion) to show it doesn't buckle, and this should protect the section from global bucking (I've written that quickly, and possibly wrongly ??)

Maybe this is better …
I can do a global buckling check, considering the complete section, and show it good. But global buckling assumes a stable cross-section, so then I do a crippling check (to confirm a stable cross-section). If this latte check fails, I can return to the global check with a reduced section (I think that makes sense).

In your pic maybe it's "multiple local buckling" … as each member has failed locally ?

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

 

[MegaStructures]

I don't think I framed my question correctly. For a pinned-pinned WT shape is it possible to predict where along the member the web could locally buckle given a certain loading i.e. a WT shape in compression with a slender web would always buckle at mid-span, or the ends, or random? Again, this isn't for a project, just interested in understanding the behavior of local buckling better.

 

[JoshPlumSE]

Does the stiffened edge of the plate change the mode shape to something that could buckle at the end, rather than the classic pinned-pinned mode shape with n=1? I don't have a picture of the brace I saw, but I do have another example of local buckling at the end of a member below.

Global euler buckling of an axially loaded member would not be significantly affected by a stiffener plate at the end of the member. That's because the member is going to show buckling deflection at the mid-span of the unbraced length. Not the end.

Local buckling of a flange or web could be affected by a stiffener plate. But, only locally. Since local bucklilng occurs in a web or flange to to axial force in that element (flange or web) you won't see this right at locations where it's stiffened. But, if the element is still overloaded, it may buckle just beyond the stiffened area.

I'm with human909, in that the picture you posted looks more like LTB beam buckling. This will happen at the unbraced compression flange near the location of maximum moment. For a fixed end / moment connected beam this will often be close to the column.... And, a case where a beam with no bottom flange bracing went into uplift could easily result in bottom flange LTB buckling like shown in the picture.... though I will say I'm not sure I can see anything clearly enough to be certain of this diagnosis.

 

[r13]

For a WT with pure axial compression, the buckling will occur in the slender web near the mid-span, where the tendency of instability is the greatest. Note that ironically, the stability at the ends are strengthened by the compression, thus not likely to buckle.

 

[JoshPlumSE]

I don't think I framed my question correctly. For a pinned-pinned WT shape is it possible to predict where along the member the web could locally buckle given a certain loading i.e. a WT shape in compression with a slender web would always buckle at mid-span, or the ends, or random? Again, this isn't for a project, just interested in understanding the behavior of local buckling better.

The web can locally buckle at at point where the compression stress is high enough to cause it to buckle. You can see cases where local buckling occurs at multiple locations along the length of a member. I'm really thinking of Web Buckling in plate girders.

However, in my opinion, the more likely scenario for a WT would be a combined Euler and local buckling. Where the local buckling of the web causes the beginning of an Euler buckling at the midpoint of the member. Why at the mid-point.... Because the axial compression in the member is constant. But, the flexural compression / strain (from buckling) will be maximum at the mid-span of the unbraced length.

 

[canwesteng]

Would be random depending on initial imperfections of the member, but I would guess skewed toward the centre where there may be flexural stresses developing from global buckling modes.

 

[WARose]

Is it me or is that flange of the girder (on the left) look like it's been cut to make [1/4 of] a dogbone? (Maybe it's just bent up/down.)

In any case, to my mind, local buckling is a flange or web buckling (due to it being too thin) before the theoretical buckling capacities (LTB, Euler, etc) can be reached. It's why we check compact vs. non-compact on shapes in the steel manual.

 

[BAretired]

Looks like there are two beams with problems (see arrows). I believe there is a local buckling of the bottom flange in the two grey beams consistent with hanging a load simultaneously from both beams. Who knows? We are just guessing.

In the case of the WT brace, we don't have a picture, but the connection at the damaged end may not be pinned. What passes for a pin may be a shear tab or similar which puts too much load in the web, resulting in a compression failure near the connection. It is also possible that the web was bent prior to the application of load.

BA

 

[MegaStructures]

I think I'm hearing exactly what I expected. The local buckling of a web in a WT shape with pinned-pinned ends would buckle towards the middle, since deflection will be the greatest at that point. For moment connected members buckling could occur near the end, because moment is greater near the connections. It is highly likely that the WT member I saw was damaged during construction.

 

[JoshPlumSE]

BARetired -

I don't think these beams have moment connections. So, under gravity load, it should be the top flange in compression. Bottom flange should be in tension. Under uplift load, however, you'd see them in compression.

 

[oldestguy]

I'm suspecting this column area is built from material salvaged from another building that was torn down, etc leaving reasonably good material. The labels suggest that.

 

[BAretired]

I don't think these beams have moment connections. So, under gravity load, it should be the top flange in compression. Bottom flange should be in tension. Under uplift load, however, you'd see them in compression.

Well, I can't see the connection well enough to tell. They may not have full moment connections, but if the bottom flange is butting up to the column, there may be enough connecting material above to generate a negative moment. That is my best guess.

Under uplift, the bottom flange goes into compression in the span, but it should not produce compression at the column. LTB may be at play, but who knows?

BA

 

[KootK]

The local buckling of a web in a WT shape with pinned-pinned ends would buckle towards the middle, since deflection will be the greatest at that point.

1) I'd expect it to buckle, mathematically at least, near mid-span because that is where the compressive stresses would be the highest as JP intimated earlier. Like canwesteng said, where it really buckles will be largely influenced by the random-ish distribution of imperfections that would tend to initiate local buckling.

2) I don't believe that it would have anything to do with the location of greatest deflection except, in a roundabout way, that the location with the maximum cross section curvature is also likely to be the location of maximum compressive stress. And that'll usually be at mid-span for a uniformly loaded, pin-ended member.

3) Note that the expected wavelength of a local bucking incident will, in general, be much shorter than the overall length of the member. While one might intuitively think that the longer the wavelength of the local buckling, the lower the capacity, at some point the torsional resistance of the cross section as a whole kicks in and creates enough torsional resistance to restrain such a large scale local buckling mode and, instead, force a higher mode buckling mechanism.

 

[MegaStructures]

KootK

1. I don’t follow how compressive stresses are higher near mid-span. I would think compressive stresses are constant throughout the entire section if it remained perfectly straight.

3. This here might be the answer! This challenges my understanding of buckling in general and is something I need to look into more. I’ve seen elastic Euler buckling described before as a force that would cause instability of a member from an infitecimal eccentricity of load or curvature in the member, basically any small increase in moment to go with the compressive force. A pinned-pinned columns lowest energy mode is a half sin wave and the buckled shape will resemble this. I suppose a stiffened WT web will buckle with a mode shape that resembles multiple periods of a sin wave and could buckle at any of the peaks. How wrong am I here?

 

[human909]

I think I'm hearing exactly what I expected. The local buckling of a web in a WT shape with pinned-pinned ends would buckle towards the middle, since deflection will be the greatest at that point.

Yes for Euler buckling of LTB buckling the memeber will likely buckle between restraints.

However the observed damage can occur at the END of a member where the stress may exceed the yield capacity and you have local yielding and buckling towards the end of the member.
Eg like the example I posted earlier:

It is highly likely that the WT member I saw was damaged during construction.

If it looks anything like the image you posted then I would suggest that this conclusion would be incorrect.

 

[MegaStructures]

However the observed damage can occur at the END of a member where the stress may exceed the yield capacity and you have local yielding and buckling towards the end of the member.
Eg like the example I posted earlier:

Your claim that local buckling will occur towards the end is because torsional forces may be higher at the end and combine with compressive forces, yes?

 

[KootK]

1. I don’t follow how compressive stresses are higher near mid-span. I would think compressive stresses are constant throughout the entire section if it remained perfectly straight.

I had thought that we were talking about a simple span, uniformly loaded flexural member oriented as an upside down Tee. Were that the case, obviously the compression stresses in the tee stem, at the top of the member, would be at a maximum at mid-span. Let's not get hung up on this part though. So long as we all agree that local buckling will happen at locations where the combination of cross section compression stress and plate slenderness is most critical, we're all good.

I’ve seen elastic Euler buckling described before as a force that would cause instability of a member from an infitecimal eccentricity of load or curvature in the member, basically any small increase in moment to go with the compressive force.

That is certainly one valid description of the Euler buckling phenomenon which is a subset of bifurcation buckling (go / no go rather than gradual onset typical of real life). Another, interesting way to think of it which is rarely grasped is this:

1. General: buckling is when some aspect of stiffness tends to zero as a result of increasing load.

2. Specific: column, elastic, Euler buckling is when a compressive load is reached at which the effective flexural stiffness of the column goes to zero as a result of P-Delta effects. This is especially interesting with respect to the programming of FEM elements as it means that, at sufficiently levels of axial load in the system, some members go from being restrained at their ends to being, effectively, pinned at their ends. Tell me that isn't cool?

A pinned-pinned columns lowest energy mode is a half sin wave and the buckled shape will resemble this.

Yes. Looked at another way, a half sine wave is the buckling mode shape that that would take flexural stiffness to zero under the minimum axial load. This is because structures find their lowest energy states by assuming deflected shapes that minimize internal strain energy. The half sine wave, for example, embodies less internal strain energy than the full sine wave. Or triple, octuple wave mode shape etc.

I suppose a stiffened WT web will buckle with a mode shape that resembles multiple periods of a sin wave and could buckle at any of the peaks. How wrong am I here?

Uhhh... it becomes difficult to discuss this stuff with any precision without having a very specific case in mind with which to focus the discussion. Does the sketch below help at all? I hope so.

 

[KootK]

To really understand local buckling as we envision it in steel design, you really have to go back to the fundamentals and understand general, elastic plate buckling. Our code limits on slenderness etc are all derived from greatly simplified plate buckling models that:

1) Generally do not consider moment gradient in the member and;

2) Greatly approximate plate boundary conditions.

It has to be simplified because, frankly, it's insanely complex for any real world situation.

You can learn plate bucking any number of places but I learned it from the book below which I highly recommend. It's one of the few stability texts for which I've actually been able to follow the math start to finish. It's a killer presentation of some meaty stuff. A read of that and you'll be heads and tails above most engineers' understanding of local buckling phenomenon. It's not even 300 pages. Kind of like "Stability for Dummies" to the extent that there could ever be such a thing.

That said, we're happy to keep helping you with this in the here and now for as long as you continue to have questions and feel as though we're offering value.