Cruciform LTB 2

[cal91]

I have an unbraced column length of 40'-0". The column is a cruciform made up of (2) W24x55 sections (one is split and then welded). How would you calculate the LTB of this section? CB = 2.24.

My co worker thinks that we can use the AISC 360 provisions for W sections, calculating Lp and Lr from rx and ry for the entire composite shape. My worry is it will overestimate the LTB capacity. Capacity comes out to be governed by the plastic section (which he gets from adding Zx from one and Zy from another W24x55) so 552 k-ft

I would think to use the LTB capacity of a single W24x55, so 135 k-ft.

Intuitively, my idea is a lower bound and my co workers is an upper bound. The gap is wide. How would you do this?

 

[Lomarandil]

I've looked at this in the past -- can't seem to find those old calcs or references though... sorry.

I recall trying the method mentioned above -- using the "weak axis" W24 to brace the "strong axis" W24 about the axis of rotation (per AISC brace provisions). As I recall, it was a lot of work without much payoff.

I also recently had a project where the flange tips of a built-up cruciform column were battened together as relative bracing. I wasn't able to justify those as providing restraint for LTB, only traditional weak axis buckling.

Sorry to not be more help.

----
The name is a long story -- just call me Lo.

 

[KootK]

I don't believe that this shape can laterally torsionally buckle (LTB). Ix = Iy, which means that rotation of the beam does not produce added deflection and, therefore, does not result in a lowering of the system potential energy (mathy definition of buckling). In fact, under uniaxial bending, I believe that your effective Ix would actually increase when this particular section rotates. Super stable.

I think that even your coworker's proposal is conservative.

As described in your article, it's important to note that LTB and torsional column buckling are different animals. That said, torsional buckling's off the table here too. It's a non-issue for normally braced wide flange columns and, by inspection, therefore even less of an issue for a flanged cruciform section which is really quite great at resisting torsion. Not HSS great. But nowhere near angle/tee/plate cruciform bad.

I also think that the article's proposal to interconnect the flanges with stiffeners intermittently is junk. It's the same misguided logic that lead folks to erroneously stiffen the crap out of wide flange beams in the hope that will meaningfully increase torsional strength or torsional stiffness. Boo I say. Stiffen 'til you're blue in gills, all the action will just take place between stiffeners.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Lomarandil]

Ix=Iy, but are those the minimum I values for any rotation?

I don't have access to a shape property calculator at the moment. But my gut feel is that there is probably a less stiff orientation somewhere in between there.

Could be wrong!

----
The name is a long story -- just call me Lo.

 

[thaidavid40]

Even though this is made up of open sections (wide-flanged beams), the composite section is doubly symmetrical. Similar to a closed tube, wouldn't that mostly remove lateral-torsional buckling from consideration? And the more lacing bars you provide, the closer that would approximate a closed tube? Instead of bars, maybe use plates with extended length - that would really approximate a tube.
Dave

Thaidavid

 

[bearjew]

I've looked at this in the past -- can't seem to find those old calcs or references though... sorry.

I recall trying the method mentioned above -- using the "weak axis" W24 to brace the "strong axis" W24 about the axis of rotation (per AISC brace provisions). As I recall, it was a lot of work without much payoff.

I also recently had a project where the flange tips of a built-up cruciform column were battened together as relative bracing. I wasn't able to justify those as providing restraint for LTB, only traditional weak axis buckling.

Sorry to not be more help.

I'm sorry, I don't follow. How would battening together the flange tips not provide LTB restraint in this case? It may be old school, but I've always been told that only 2% of the compression flange force is required to classify as lateral bracing. You must've had some incredible loads to not be able to get the battening to check out.

Just so we are on the same page, when you say battening I am imagining a section similar to the cruciform shown as Figure 7 from page 3 of the document that cal91 linked to above.

edit: I guess if the battening was made of thin plate only, I could see it not working out. I was imagining angles as the shape at first.

 

[cal91]

Ix=Iy, but are those the minimum I values for any rotation?

I don't have access to a shape property calculator at the moment. But my gut feel is that there is probably a less stiff orientation somewhere in between there.

Could be wrong!

No matter how you rotate it, the I value is the same. Ix1 + Iy1 = Ix + Iy. For any shape where Ix = Iy, no matter how you look at it I is always the same. Because of this I agree with KootK on the first half. LTB won't happen here. However, column torsional buckling will. I wasn't asking about it because I feel I already had a good handling on it. But if KootK disagrees maybe we'll open that discussion up

As described in your article, it's important to note that LTB and torsional column buckling are different animals. That said, torsional buckling's off the table here too. It's a non-issue for normally braced wide flange columns and, by inspection, therefore even less of an issue for a flanged cruciform section which is really quite great at resisting torsion. Not HSS great. But nowhere near angle/tee/plate cruciform bad.

Here I disagree with you. Yes, they are different animals but, It's NORMALLY a non-issue for braced wide flange columns because usually their weak-axis bracing points will also brace torsionally. However we can think of this cruciform section as two W-sections, each strong axis is bracing the other's weak axis along the entire length. However, they do not brace each other from torsion because they will rotate about the same axis. So the unbraced length for weak axis bending is basically 0, while the unbraced length for torsion and strong axis bending is 40'-0".

I've already ran the calculations for this shape's capacity as a column. KL/rx = 52.7, flexural buckling capacity is 539 kips. Torsional Buckling is 167 kips.

Having said that, I do agree with you about providing intermittent stiffeners does not help with torsion. But they do help with Flexural buckling. If the cruciform were bending about a 45 degree axis, the flanges would want to flatten out to the neutral axis. Providing these intermittent stiffeners prevents that.

 

[cal91]

KootK, you have me thinking now about the columns torsional buckling in terms of minimizing energy in the system. With flexural, and even flexural torsional buckling, this is made apparent because as the column buckles the load on top of the system is lowered and thus lowering the potential energy.

However with purely torsional buckling such as in angles and as I would expect in this cruciform shape, I do not see how torsion lowers the potential energy of the load... I'm starting to wonder if there is even such thing as purely torsional buckling. I always thought angles did purely torsional buckling, but now I'm thinking it's actually torsional flexural buckling. But then AISC 360 Section E4 distinguishes between torsional and flexural-torsional buckling... Any thoughts?

 

[WARose]

[blue](cal91)[/blue]

I'm starting to wonder if there is even such thing as purely torsional buckling.

There is....but it is precluded for most of the shapes in the manual (at lengths that would be used in construction) where the limiting width to thickness ratios of flanges and so forth (in the code) are followed. It can become critical in singly symmetric shapes or plate girders (forgetting those limiting ratios for a moment).

That's the danger of getting away from the code in this: you are inviting in buckling modes that are not easy to quantify. (Which goes back to my reasoning in my original post.)

You aren't getting a great deal more by figuring this (and risking a great deal) in my experience. For example, I was looking at the AISC article I mentioned in a previous post on this thread......and in one case: the buckling stress went from about 5 to 9 ksi (going from the I shape to the built up one). Doesn't justify that time and risk to me.

 

[KootK]

Any thoughts?

I hear 'ya on this. I find torsional buckling harder to "feel" somehow. Try telling yourself this story for your particular column: it's effectively four tee shaped columns buckling in unison and each deflecting much as a normal column does when it buckles. I think the logical hangup there is still the center of the column where it's hard to visualize anything moving vertically downwards. In the wild, I would assume that buckling of the four tees would be followed shortly by ordinary lateral buckling possibly combined with yielding of the central bits.

Any chance you'd want to share your calcs on this? I'm surprised by your results obviously. I suspect this could be a learning opportunity for me.

Without running any numbers I have the following, anecdotal doubts about torsional buckling governing:

1) This shape is a popular shape for mega high-rises. Hard to see that working out if there's a glaring torsional buckling issue.

2) I feel that each column in the set should be capable of dealing with its own torsional stiffness needs independently. If one column would be good for P, then two columns ought to be good for at least 2P I'd think.

I'm curious, if you looked at a single w245x55 here, would torsional capacity govern over strong axis? If so, maybe things are shaking out as they have because this simply isn't a good column section, regardless of whether it's used alone or built up. Perhaps this is part of the reason that we consider certain sections to be column appropriate in the steel manual and others not.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[cal91]

hear 'ya on this. I find torsional buckling harder to "feel" somehow. Try telling yourself this story for your particular column: it's effectively four tee shaped columns buckling in unison and each deflecting much as a normal column does when it buckles. I think the logical hangup there is still the center of the column where it's hard to visualize anything moving vertically downwards. In the wild, I would assume that buckling of the four tees would be followed shortly by ordinary lateral buckling possibly combined with yielding of the central bits.

I see it now. At first it's purely torsional. The four WT's all buckle clockwise about their intersection point. Their flanges move vertically downwards but the center does not. As this happens the effective column section is reduced to just the intersection point, which will then yield/flexurally buckle and thus move vertically down (thereby lowering potential energy).

Any chance you'd want to share your calcs on this? I'm surprised by your results obviously. I suspect this could be a learning opportunity for me.

No problem. The numbers I gave you before was for a single W24x55 braced in weak axis but not braced flexurally or torsionally for 480 ft, and then multiplied the capacity by 2. I realize that this isn't entirely accurate so I reran it based on the cruciform shape. The torsional buckling capacity exactly doubled, but what I didn't expect is for the flexural buckling capacity to increase by 70%.

Without running any numbers I have the following, anecdotal doubts about torsional buckling governing:

1) This shape is a popular shape for mega high-rises. Hard to see that working out if there's a glaring torsional buckling issue.

Yes, I think that is most likely because we have a beam shape instead of a column shape. W24x55 has the largest Ix to Iy ratio in the steel manual haha. But we have much larger moment demands than axial demands so that is why.

2) I feel that each column in the set should be capable of dealing with its own torsional stiffness needs independently. If one column would be good for P, then two columns ought to be good for at least 2P I'd think.

I'm curious, if you looked at a single w245x55 here, would torsional capacity govern over strong axis? If so, maybe things are shaking out as they have because this simply isn't a good column section, regardless of whether it's used alone or built up. Perhaps this is part of the reason that we consider certain sections to be column appropriate in the steel manual and others not.

Agreed! It's just that in both scenarios it's torsional buckling that governs.

Thanks all! It's been fun diving into the nitty gritty for cruciform columns, column torsional buckling, and lateral torsional buckling.

 

[Deker]

I've only used box sections at columns shared by orthogonal frames, and I suspect that most would approach this problem by ignoring the weak-axis components of the cruciform. That said, I think I mostly agree with your coworker. Drawing from some notes I have from the recent AISC Night School course on stability, the user note equation in AISC 360 F2.2 can be rewritten in a way that helps elucidate the behavior and makes me feel more comfortable using the composite section properties:

M[sub]cr[/sub][sup]2[/sup] = (π[sup]2[/sup] E I[sub]y[/sub] / L[sub]b[/sub][sup]2[/sup])(G J + E C[sub]w[/sub] π[sup]2[/sup] / L[sub]b[/sub][sup]2[/sup])

The first term represents the compression flange trying to produce minor axis buckling of the entire cross-section. The second term represents the effect of the tension flange resisting this buckling by creating a resisting torque, which includes St. Venant (G J) and warping components (E C[sub]w[/sub]). For your flanged cruciform section, I[sub]y[/sub] is the minor axis moment of inertia of the composite section, and J and C[sub]w[/sub] are twice the values of those used for a single beam.

L[sub]r[/sub] can be found by using equation F2-6, which sets M[sub]cr[/sub] equal to 0.7 F[sub]y [/sub]S[sub]x[/sub] and solves for L[sub]b[/sub]. I don't have any insight into how L[sub]p[/sub] is determined so I would be hesitant to apply it to your section, but it would be conservative to use L[sub]p[/sub] for a single beam.

 

[KootK]

Thanks for the calc. It suggests a possible reinforcement strategy:

- Weld some batten plates between the flanges for 2' at the bottom of the column and 2' at the top.

- Now call your column thing torsionally fixed at the bottom and the top. K = 0.5 theoretically but we'll roll with 0.65 for good measure.

- This should increase your torsional capacity by about 2.36 and get you within about 15% of your flexural capacity.

Not bad for a buckling mechanism we barely even believe in.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[cal91]

Excellent. Thanks Deker and KootK.