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LTB of cantilevers to AISC codes 1

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Ussuri

Ussuri

Civil/Environmental
May 7, 2004
1,582
We are currently looking at a design in our office which has been completed using AISC WSD codes (March 2005). We have a query which I was hoping some of the US based 'tippers' might be able to help with. The topic was discussed briefly in 2007 but the links provided no longer work.

thread507-180478

We have a single cantilever effectively built in at one end providing both lateral and torsional restraint. The section is a 305UC137 (section classification plastic UK/compact US). The other end is completely free. The load is applied to the tension flange (destabilizing).

The UK codes provide effective length factors for use when calculating LTB resistance, depending on end fixity. These range from 1.4 up to 7.5. In our case the effective length Le = 1.4L.

We were looking for something similar in the AISC code but couldn't see anything. LTB capacity seems to be based on Lb, the distance between two braced points, so not applicable for a completely free cantilever (Section F2). The only other reference seems to be Section J10 part 7 which dicusses unframed ends.

How does the AISC address lateral torsional buckling of free cantilevers? What are we missing in the code?
 
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Should the 2.1 K factor for cantilever columns per Table C-C2.1 (ASD 9th ed) be used?
 
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I don't think AISC addresses this. My S&J text references the SSRC Guide, 5th ed. for K factors, but also says it is conservative to use the actual unbraced length with a Cb=1.0 (It goes on to say that this assumption requires that loading be applied at the shear center OR at the bottom flange).
 
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If I rember correctly, when checking allowable compressive stress for cantilever, k = 2.0 (or 2.1?).
 
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When designing purely flexural members per the 9th Edition of AISC (Allowable Stress Design), there is no "k" (or, to put it another way, "k" = 1). As noted above, Cb = 1.

DaveAtkins
 
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StructuralEIT & DaveAtkins are both correct.

Per "Steel Structures - Design and Behavior", 2nd Ed. P.483, by Charles G. Salmon & John E. Johnson: "...the lateral buckling of a cantilever beam is not even sever as the unbraced segment under uniform moment. Since the moment at the end of the cantilever is zero, the compression force in the flange decreses from a maximum at one end to zero at the free end".
It concluded with: "The authors suggest that the actual cantilever length be used...taking KL = L is recommended".
 
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WillisV - that gives the answer straight from the AISC folks - use Cb = 1.0 and Lb = cantilever length.

 
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JAE,

I do not believe you have a very convincing argument. There are several variables...first, the magnitude of bending moment over the length of the cantilever...second, the bracing of the top and bottom flanges and third, the point of application of the applied load above or below the neutral axis of the beam. All of these factors affect the stability of a cantilever beam. It is a complicated elastic stability problem, not readily solved by uttering simple rules from the code.

If you are designing a new structure, why would you not brace the compression flange at or near the tip of the cantilever to eliminate all this uncertainty? And you must admit, there is a lot of uncertainty.


Best regards,

BA
 
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I thought there was a body of opinion that you need to brace the tension flange of cantilevers rather than the compression flange.
 
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Also remember to look into vibration for cantilevered steel floor beams. I got burned on this one a few years back that was part of a large balcony system. It acted more like a diving board than I ever would have expected with the damping I thought it had. I ended up having to add a truss system between the ends of all the existing cantilevers to dampen it.






 
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BAretaired:

Please check the reference WillisV provided, I think that's where JAE's comment came from.

Hokie:

I think for real world applications, the cantilever beams are most likely braced by roof/floor elements, though more practical than stability concerns (also, it is more likely than not to have free ends framed - answer to BAretired). For single, un-roofed cantilevers, use of torsion friendly tube section is common place. Anything you think is missing?

haynewp: good point.
 
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BAretired, I was just repeating what the AISC rep had stated. I was not attempting to put forward "a convincing argument."

If you disagree, check out the link from AISC's response and pose a better solution or refutation of their statement.

Thanks.



 
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I back up JAE, the effective length and the moment factor tend to cancel each other out. The common practice is to assume they result in unity.

The code commentary gives a reference to look up if you wish to do a more detailed analysis.
 
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This is interesting. In the UK code you determine both the effective length factor and the equivalent uniform moment factor (mlt) as part of the process for determining LTB resistance.

For a cantilever mlt=0.6 for a stabilizing load, or 1.0 for a destabilizing load. Effective length factor ranges from 0.8 to 3.0 under a stabilizing load or 1.4 to 7.5 for a destabilizing load. So in some cases they do more or less cancel out, but not always and only for a stabilizing load condition.
 
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I tend to agree with the UK code that the effective length should be considered separately from the moment envelope on the unbraced length.

The Canadian Code states that for cantilever beams, a rational method of analysis taking into account the lateral support conditions at the support and tip of the cantilever should be used. I'm not sure what that means.

I find no mention in CISC about the point of application of the load above or below the neutral axis of the beam, yet the Kirby-Nethercot research indicates that this is an extremely important variable. "Theory of Elastic Stability" by Timoshenko and Gere recognizes the diminishing of the critical load as the point of application moves up from the neutral axis.

My inclination, whenever theory gets too complicated, is to be conservative. Thus, I would ensure that the tip of the cantilever is thoroughly braced both top and bottom, then use a K value of 2.0. So call me old fashioned.






Best regards,

BA
 
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AISC (US), 9th Ed, Sect F1.3:

Fb = f(Fy, L, rt, Cb...)

L = ......For cantilevers braced against twist only at the support, L may conservatively be taken as the actual length.

Cb = ....Cb may conservatively be taken as unity for cantilever beams. **

** For the use of larger Cb values, see Galambos (1988).


 
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