New AISC Code: compressive capacity

[chichuck]

I've been watching this group for posts about the new AISC code, and I've not seen any. May I be the first?

This post is long, and I apologize for that, but I couldn't condense it and still have something that makes sense. Here goes.

My confusion is about compressive capacity, in Section E of the new code.

An example is: an element (beam-column, if you will) with some compressive load on it.

Shape: W12X45
Material: A992
Lx = 12’ Ly = 12’ span = 12’

What is the compressive capacity of this member? Hint: this member has flanges that are not slender and the web is not slender.

I went to code section E1. It says I need to figure the limit state for flexural buckling, torsional buckling and flexural torsional buckling, and then find the smallest one. That smallest one is the nominal compressive strength.

The section continues: a) for doubly symmetric and single symmetric members the limit state of flexural buckling is applicable. So okay I need to go to section E3 to figure out the limit for flexural buckling.

Then it goes on: b) for singly symmetric and unsymmetric members and certain doubly symmetric members, such as cruciform or built-up columns the limit states of torsional or flexural –torsional buckling are also applicable. I would go to section E4 to figure out the limit on torsional and flexural-torsional buckling. But, does this also apply to rolled W shapes, are rolled W shapes other “certain doubly symmetric members?” I can, of course just calculate it and see. But is that paragraph b) saying it just does not apply to rolled W shapes? How about plate girder members which are H shaped but not rolled, are they different from rolled?

If Section E4 does apply to rolled W shapes, I need to use part (b) (i), which is Eq. E4-4 to figure out the limit state for torsional or flexural-torsional buckling.

I read the commentary and got no help. On pp 258-259, commentary on Sec. E3, it says:


“….Equation 3-4 presents the familiar Euler for for Fe. However, Fe can be determined by other means also, including a direct frame buckling analysis, as permitted in Chapter C, or from a torsional or flexural-torsional buckling analysis addressed in Section E4. “

So, E4 is an alternate to E3, and it apparently does apply to doubly symmetrical shapes like a rolled W shape.

Further, on page 260, commentary on section E4, it says the same thing about “certain doubly symmetric members. Then it goes on.

“ The equations in Section E4 for determining the torsional and flexural-torsional elastic buckling loads of columns are derived in texts on structural stability, for example, ….”

“Since these equations apply only to elastic buckling , they must be modified for inelastic buckling by using the torsional and flexural-torsional critical stress Fcr, in the column equations of Section E3.”

Next comes the interesting part:

“Torsional buckling of symmetric and flexural-torsional buckling of unsymmetrical shapes are failure modes usually not considered in the design of hot-rolled columns. They generally do not govern, or the critical load differs very little from the weak-axis planar buckling load. Torsional and flexural-torsional buckling modes may, however, control the strength of symmetrical columns manufactured from relatively thin plate elements and unsymmetrical columns and symmetric columns having torsional unbraced lengths significantly larger than the weak-axis flexural unbraced lengths…”

So, apparently there are some conditions where Section E4 would apply to hot rolled W shapes.

My question is: apparently, even though Section E1 paragraphs (a) and (b) make it sound like you do not apply Section E4 to rolled W shapes, that is what is required. Am I correct?

Sorry for the long post, but I couldn’t cover it all by being brief. BTW, this is the simple example because the shape does not have slender elements in it.

 

[UcfSE]

I think the best thing to do is to calculate all the limit states and see for yourself which one controls. You will need to do some investigation on your own to figure out which are the "certain" doubly-symmetric members. Notice it reads cruciform. Columns shaped like a plus sign (+) are more prone to torsional buckling for instance.

I myself would read the paragraphs as though all the limit staes may apply but certain ones tend to control for certain shapes. Plate girders are different from hot-rolled shapes in that the residual stresses across the section are different. This will directly affect the critical buckling stress.

This might be a good question to submit to the steel solutions center on the AISC website.

 

[chichuck]

UcfSE,

I have to make some assumptions to calculate critical stress/load for torsional buckling of W shapes. Section Ef.(b) directs me to use Eq. E3-2 or E3-3, using the torsional elastic buckling stress, Fe. I don't know what KL/r to use in order to choose which of those two equations to use; I know K from the commentary, L is definied by my frame geometry, but what r should be used? Is it an r based on Ix+Iy? I can of course calculate Fe from both Equ. E3-2 and E3-3 and use the minimum, that would be conservative. But if that ever gave me a governing case, I would still be left with this question: maybe there is a different "correct" KL/r to use here, which would give a higher Fe for torsional buckling, that maybe wouldn't govern. I realize that the conservative assumption is probably acceptable and would give me a "safe" number, but I'd like to understand how to get it correct.

I have not taken this up with AISC as yet, I think I will do that next.

Regards,


chichuck

 

[UcfSE]

It looks to me like everything is defined as needed. If you are checking a wide flange for torsional or flexural-torsional buckling, use E4, more specifically E4-4. E4-4 is for doubly symmetric members. Use the Fe then in equations E3-2 or E3-3 as applicable. It doesn't look like there is even an "r" term involved in that case. You're using Fe > or < 0.44Fy to determine whether you use E3-2 or E3-3, as I read it of course.

 

[chichuck]

UcfSE,

Yes, I can use Eq. E4-4 to calculate Fe. There is no r in that equation. I see what you are saying: I don't need to check the value of KL/r to be able to choose between Eq. E3-2 and E3-3, I can just choose based on the value of Fe. I missed that.


Thank you for pointing that out.


Now go and check out what happens if you want to figure out the compressive capacity of a W14X34, which has slender web. I have a lot of questions about that. But that is for a new thread.

I'll post on that soon.

Regards,


chichuck

 

[UcfSE]

I'm sure we can figure something out.

 

[14159]

I took this up with some steel experts recently. The answer was something like:

Torsional buckling is a possible limit state for a doubly-symmetric I-shaped member. Flexural-torsional buckling is not. Only lateral buckling needs to be checked for rolled shapes as I think is fairly clear from E1.(b). My question was what's the difference between a W-shape and a compact built-up shape with respect to the applicable compressive limit states? The answer was that torsional buckling can control even for rolled shapes but the check is extremely dependent on boundary conditions, so doesn't happen in reality. For built-up I-shapes with weirder proportions, torsional buckling is more realistic, hence E1.(b) inclusion of "...such as cruciform or built-up columns,..." Therefore, it's my understanding that lateral buckling is all that needs to be checked for hot-rolled shapes but the torsional buckling check must be included for built-up I-shapes, even symmetrical ones.

The only real significant difference between the 3rd Edition phiPn and the 2005 phiPn is that the 2005 allows phi=0.9 rather than 0.85.

I hope this helps.

DBD

 

[chichuck]

DBD,

I had figured out that flexural torsional buckling does not apply to doubly symmetric shapes, like wide flanges. As for the difference between rolled shape & built up shapes, in addition to different proportionis, I also thought different residual stresses come into play.

About the difference between a W-shape and a compact built-up shape; I offer this: if the built up shape is compact, it doesn't have weirder proportions, and so for that particular built up shape, flexural torsional buckling probably will not govern. But since I cannot tell the difference between that compact built up shape and one with "weirder proportions" just by looking at the dimensions, I'd have to go with the spec provisiona and just check it. I bet it takes a deep plate girder web for that to come into play.

I suspected that for rolled shapes, the torsional buckling would rarely if ever would govern, but again, I can't prove that so I was prepared to make that check anyway just to be sure.

Thank you for your input, it does indeed help.

My next problem is slender compressive elements in the new code. As I said earlier this is a much more complex problem and will generate a very long post. I'll figure out how to minimize it and start a new thread on that.


regards,

chichuck

 

[14159]

Flexural-torsional buckling is a distinctive mode compared to torsional buckling. A doubly-symmetric section can have torsional buckling but not flexural-torsional.

As for the slender elements stuff, I've looked at that in nauseating detail lately and it's not any worse than the 3rd Edition Spec, IMO.

DBD