Interesting kl/r question 1

[Lion06]

AISC suggests limiting kl/r of a compression member to no more than 200, as we're all aware.

My question is this. k has always been assigned from one of the basic cases or the alignment charts. Now with the introduction of the DAM, is it fair to say that you can also use k=1 to satisfy the kl/r<200 criteria (for columns that are part of the lateral system, obviously)? I believe it is, I just wanted some other opinions, because it makes a big difference. If you have cantilevered columns, k=2.1 from the basic case, but with the DAM using k=1, you would potentially have a column with an r of only 48% of the original r and now meet the kl/r<200 criteria. Put another way - it is possible to meet kl/r<200 using the DAM with k=1 and have kl/r=420 based on the principles used just a few years ago. That seems like a big disconnect.

 

[TehMightyEngineer]

I'm not familiar with the acronym DAM. Could you explain?

EIT with BS in Civil/Structural engineering.

 

[ble31980]

This is a very interesting question that I admittedly haven't thought much about. Appendix 7 doesn't explicitly state that K =1 is used to determine the slenderness, but it does state that the columns are to be designed with K =1. Here's the quote:

Section 7.1 - Members shall satisfy the provisions of Section H1 with the nominal column strengths, Pn, determined using K = 1.0.

I take that to mean that K = 1.0 for all aspects of column design, including slenderness. I'm interested to hear others thoughts about this.

 

[delagina]

Interesting.

although all of my kl/r failure, if i recall correctly, are from WT Ver brace, where k is actually 1.

I dont seem to recall I had slenderness issues with columns regardless if i use 2 for moment frame. Maybe my columns have always been oversized.

 

[JAE]

Well, in the 13th Edition specification, the KL/r limit of 200 is now a User Note and is "preferably" <= 200.

So the specification allows you to exceed 200, you just design accordingly. A less stiff (lower r) column will handle less axial load and the PDelta/second order effects will be greater.

Also - read the AISC commentary for Section 7.3. It is apparent to me that the Direct Analysis Method (DAM) in Appendix 7 of the AISC specification allows the use of k=1.0.

 

[ToadJones]

"A less stiff (lower r) column will handle less axial load and the PDelta/second order effects will be greater."

JAE- I'm not totally sure this is true always...
For instance, a W10x12 rx= 3.9 in and a W8x67 rx = 3.72 in.

Assuming columns braced along Y-Y more often, its hard to say.

Just a thought, I really don't know the answer.

 

[JoshPlumSE]

Slendernes is slenderness. The column does not know or care what form of analysis you are using.

You could always have used a KL/r > 200 because it was a suggestion not a requirement. To me that suggestion still applies the same way it has always applied... using an approximate K from the alignment charts.

I suspect that more folks will use the Direct Analysis method (and the K=1.0) to justify a more slender section than they would have used before. That should be okay, though. The DAM should do a better job of capturing 2nd order effects for these slender members. Therefore, the extra slenderness should be okay.

Of course, this is where an experienced engineer will have a better "gut feeling" about the slenderness of his (or her) columns than some newbie using K=1.0 because the code says he can.

 

[steellion]

That is an interesting catch, Lion. I would use K=1.0 for the DAM but still use K=2.1 for individual column designs.

 

[Lion06]

I know it's only a suggestion, but I, and I think most other engineers, try to satisfy it.

Also, there is a difference I'm exceeding it at 250 and exceeding it at 420 - by the old method. That was the basic point of my question. You can have a column that, under the DAM, has kl/r of 200, but under the k-factor method would have kl/r equal to 420 - for the exact same section. It just seemed like a big difference.

 

[JAE]

ToadJones - I guess I may have misused the word "stiff" as I was really referring to the relative r values and not Ix or Iy.

 

[ToadJones]

JAE-
Understood...I almost didn't even say anything.

 

[bootlegend]

I've thought about the same issue concerning the "increased" KL/r too. I reasoned that any difference was offset by the Direct Analysis method requiring the reduction in axial and flexural stiffness that the old K method didn't require.

 

[WillisV]

I do not see the confusion with regard to the code requirements. If you use the Direct Analysis provisions then K=1 for everything; for column design as well as for any KL/r limits you would like to meet. Section E2 clearly states "The effective length factor, K, for calculation of column slenderness, KL/r, shall be determined in accordance with Chapter C." Chapter C indicates the Direct Analysis method as an allowed design method with K=1.

See also 13th Ed. Manual p4-3 and 4-4 (14th Edition is even clearer as to this point).

 

[Ron]

WillisV...exactly.

 

[Lion06]

I wasn't saying there was confusion. I believe k=1 is the right number to use for the check, I was just saying it seemed like a really big difference between the two methods.

 

[firai]

As others mentioned, the kl/r <= 200 has always been a suggestion. As with other engineering judgment rule-of-thumbs, it may essentially be applied however you want to apply it.

With that said, if you're concerned about the slenderness for whatever reason, then the same criteria (including using the alignment charts) should probably apply as before. It's not like columns suddenly gained capacity through the DM method. However, maybe it's time to evaluate whether the criteria is critical and whether columns with kl/r > 200 would perform as intended (which I would probably argue that it's fine).

Structural Design Engineer
New York, NY

 

[csd72]

We must not lose sight of the fact that the formulii we use are all approximations and therefore have inacuracies, particularly at the extremes.

There is a difference between the actual effective length and that used in the analysis.

Not familiar with the DAM but I would expect that the use of k=1 is because these slenderness effects are already catered for in the moment capacity component. This is in line with most other modern codes.

The slenderness check should be based on the actual slenderness as the member does not know how it has been analysed. A very slender member is much less robust and much more susceptable to sudden failure, regardless of how accurate the analysis is. If there was not a slenderness limit then it would be entirely possible to design a column that meets the code but would fail as soon as anyone leant or bumped against it.