Limiting Slenderness Ratio 1

[nrguades]

From Aisc (Ninth Edition) Section B7, it is stated that for members whose design is based on compressive force, the slenderness ratio kl/r preferably shoud not exceed 200 and for members whose design is based on tensile force, kl/r preferably shoud not exceed 300.

I am designing a frame with cross bracing, primarily intented for lateral forces having beams that span up to 31 ft. due to architectural requirements.The Kl/r value governs in the beam design.

Is it ok to disregard the kl/r limit considering that the code uses the term preferably? What exactly is its effect to the member designed and the entire structure?
thanks...

 

[DaveAtkins]

Yes, I have on occasion ignored the kl/r = 200 (compression) and 300 (tension) slenderness limits. But this has been the exception, not the rule. I'm not sure what the theoretical basis for kl/r = 200 is, but I believe the kl/r = 300 limit exists because a tension member COULD see compression from time to time.

DaveAtkins

 

[GregLocock]

I'm a little concerned you have had no response. I am not a PE, but I did study structures at uni.

These limits seem a litle odd to me, particularly the compressive case, which seems to be well into pure elastic buckling.

200:1 is /far/ beyond what is normally seen, and any slight errors in eccentricity of loading will render such a simple analysis optimistic.

The tensile case is interesting, again far outside what I would expect to see, but I can't see much harm in that so long as we are talking about rods, rather than sections.

If anyone out there wants to correct this , be my guest.

Cheers

Greg Locock

 

[jec67]

According to the AISC commentary:

The recommended limit of kl/r for tension members is intended to give a size of member that will have a minimum level of stiffness to avoid unwanted "slapping" or vibration of the member.

 

[jec67]

Follow-up:

The AISC LRFD 3rd edition commentary states that the Kl/r ratios for compression are based on Engineering Judgement and Economics. One should look at this commentary for further information.

 

[flamby]

nrguades,

In our Indian code, the conditions of l/r are binding and so I would expect from other codes too. Ignore such limits at your own risk because if the structure fails due to fall of a meteor on it, you will be held liable for crossing the line. It is preferable to ignore the word "preferably", as you cite, just to be on the defendable side.

 

[3dboy]

Kl/r of 200 is used to account for accidental eccentricity due to the tolerances of hot rolling steel, the fundamental slop of the the connections, out of plumbness of columns, etc. If you are going to ignore the KL/r limits you had better take into account the actual bending stresses due to these factors and use a combined stress formula. You also need to use the Euler buckling formula for Kl/r > Cc.

Have fun!

 

[EngineerofSteel]

In response to GregLocock and DaveAtkins above:

AISC 9th Edition: B7, Sect. 5-37

"...The above limitation does not apply to rods in tension. Members which have been designed to perform as tension members in a structural system, but experience some compression loading, need not satisfy the compression slenderness ratio."

In context, the paragraph says above described members need satisfy KL/r<300, but not KL/r<200.

 

[theonlynamenottaken]

If I were to ignore the kL/r less than equal to 200 I would certainly perform a second order analysis of the member. Once kL/r reaches that magnitude the dead load deflection of the member at midspan will cause a considerable moment due to the compression eccentricity (P-delta effect). Factor that in and your section will need to be stiffer which would most likely put it back under 200 anyway.

Stouter member or second order analysis? Easy decision in my book.

As far as the tension member case? I've used swaged & turnbuckled wire rope for tension-only bracing... where does that fit in?

 

[JAE]

theonlynamenottaken -

I think that the preferable for compression is more important than the preferable for tension.

 

[archeng59]

the first question that comes to my mind is this: what is your KL/r ratio and how much larger is it than 200? what size member are you trying to use and what size member will give you a KL/r ratio less than 200? Also, if this is a beam, you can add kickers (diagonal braces) to reduce the KL/r ratio to less than 200 with the L being equal to the spacing between the kickers. typically, the top flange of a beam is essentially continuously braced by the floor joists or roof joists. The bottom flange is the unbraced member. If you can add the kickers, say at third points along the beam, between the bottom flange and the floor/roof deck you may see your slenderness problem disappear.

 

[J1D]

To check the column elastic buckling strength curve (Pr/A vs kL/r, Pr=column elastic buckling strength; kL/r is the slenderness ratio), I can see kL/r=200 is in a range where the slope changes from steep to shallow.

It is interesting to notice that from kL/r=100 to 200 (kL/r=100 is somehow corresponding to the 0.5Fy point, which is the elastic limit of AISC) Pr decreases substantially, whereas from 200 to 300 the decrease is not very significant at all. As stated by 3dboy, I guess the 200 limit is not solely from the concern of pure axial strength, it is for dealing with the additional bending moment, construction imperfection, etc

 

[DesignIntegrity]

Your quote, "I am designing a frame with cross bracing, primarily intented for lateral forces having beams that span up to 31 ft."

If your "lateral forces" include earthquake forces you had better pick up a copy of AISC Seismic Provisions because you have a completely different set of kl/r provisions depending on your type of lateral system.

If your braces are "tension only", check the building height restrictions of the ASCE 7. In many cases you are required to take some degree of compression. In addition your kl/r is sprecifically restricted for the bracing members. No preferably less than language.

Do your lateral forces include earthquake?

 

[14159]

I agree with "theonlynamenottaken" and 3dboy.

For your second-order analysis, make sure you add a bunch of nodes along your beam. Some programs are not smart enough to capture P-(little delta) effects.

You should read the 2005 AISC Spec. I think there might be some changes to the KL/r limitation wording.

14159