Unbraced Length of a Cantilever 1

[Soundwallguy]

Hi All:

Been a long time since I had to calculate Unbraced Length of a Cantilever in bending. Some literature says to multiple the length of the cantilever by two, others say just use the length of the cantilever. Any concensus?

 

[ishvaaag]

The info is from Galambos IV. Galambos V I think to remember was the same or alike, and Ziemian in 6th guide has more modern appraisals for the critical moment at cantilevers.

 

[JAE]

I asuume your are talking about steel cantilevers?
AISC design or some other specification?
And unbraced length in regards to strength correct?

If so - the length of the cantilever is the unbraced length. Recommendations are to brace the tension side of the cantilever end to avoid twisting. Cb = 1.0 (for AISC specification).

 

[ishvaaag]

As long you have the compression flange effectively braced, you can take Cb=1 for Lb as JAE says. The values in the figure I gave just apply to the conditions therein to give a critical moment.

 

[ishvaaag]

Attached Critical Moment of Cantilever for the conditions in the Galambos IV Guide, a Mathcad 2000 Professional worksheet.

 

[hokie66]

There does seem to be a bit of difference of opinion about this issue, even as the opinions relate just to the US code. For other codes, I don't believe there is agreement either.

http://www.modernsteel.com/steelinterchange_details.php?id=197

 

[Sufjan]

I just did a steel blade canopy with no bracing. Unbraced length = 2x cantilever span.

I believe this came out of AISC commentary.

 

[JAE]

I can't find any reference in AISC to use 2x the length of the cantilever. If anyone has a reference to that I'd like to know.

hokie66, that was an interesting link to the MSC article.

 

[ishvaaag]

I started to read (and port) procedures in Ziemian's led 6th guide ... unfortunately I stopped (for now) at chapter 6 or so. However the case we are talking about is dealt with in a non comprehensive way but hopefully (for the case) more accurate than Galambos' in chapter 5.

I attach the Mathcad 2000 Professional worksheet.

By the way and what read I seem to have found 6th guide better as a collection of references than as a collection of procedures, at least comparatively with previous guides. This quite likely will render the book less useful to get direct results for those not having the resources to delve in the references themselves.

 

[FoxSE14]

When checking deflection limits, IBC says L shall be taken as twice the length of the cantilever. Table 1604.3 footnote "i".

 

[msquared48]

As for the deflection ratio of the beam, I double the length of the cantilever to get the "realistic" simple beam length for comparison.

However, for the unsupported length, it depends on the lateral support mechanism spacing, if any, for both flanges, not just the compression flange, for the tension side can roll over too, even if the compression flange is braced.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[JAE]

ssmr14 - yes - the deflection limits are really a measure of curvature so the 2L distance for a cantilever makes sense to equate L/360 etc. for simple span beams.

But for strength I've never heard of using 2L for Lb.

 

[BAretired]

If a cantilever beam has a moment applied at the free end, the moment is constant over the length of the beam. In that case, 2L should be used for strength.

If the moment varies from zero at the end to a maximum at the support, L may be used because the average moment is less than or equal to half the maximum moment.

If the support is not completely fixed about both axes, this simplification is not justifiable and the equivalent length should be greater than L.

BA

 

[hokie66]

This seems to be treated typically as a buckling controlled strength issue, when really it is in some cases a question of stability. If we take the case of a simple beam which is unrestrained at the supports in the weak direction, we consider it unstable. A cantilever unrestrained at the end depends totally on weak axis bending and torsion for stability.

 

[Soundwallguy]

Thanks all. This has been very helpful.

 

[JAE]

BAretired - I'm not trying to argue with you but if the end of the cantilever is braced against rotation (which it usually is for my structures) I still can't see using 2L.

The length of beam between cantilever support and end doesn't "know" that it is a cantilever but rather just a segment of beam with braces at each end.

I still don't see using 2L. It is not in the AISC specification that I can see and I've never seen it in journals or texts.

 

[Sufjan]

I like to conceptualize the compression flange as a column. If completely unbraced (as mine was), K = 2.0 from table C-C2.2 page 16.1-240 in AISC. I think this makes sense. The buckling shape is 1/2 a sine wave for an unbraced cantilevered beam, whereas for a simple beam, the buckling shape is a full sine wave. So unbraced length of the cantilever should be taken as 2x span to make it equivalent in the lateral torsional buckeling equation.

Also, there is some discussion about this relating Cb on page 16.1-271 at the top (black book).

 

[JAE]

Yet I'm not sure the buckling shape & K value for sway columns is the same effect as LTB in beams. Different mechanisms completely.

 

[JAE]

I did a few calculations for a cantilever using, and then not using, the Kc value method that hokie66 posted above.

These are based upon a W10x26 beam with 8, 12, and 16 ft. spans.

Using the Kc method from Modern Steel Construction, the values of Mn for the beam were determined based upon the method given with Cb = 1.0 per the article.

For the Mn values derived strictly from the AISC specification (without the Kc method) I used Lb = span of cantilever and the Cb values were calculated and included (the spec says to use Cb = 1.0 for cantilevers where the free end is unbraced.

I only looked at conditions where the support was laterally braced as well as the tip as most all cases we brace members that way.

From this, the values are about the same except when the span gets a longer (12 - 16 ft). A 16 ft. cantilever is quite long for a W10 but could happen I guess.

For the other cases where the support is not totally braced or the tip is not totally braced, the Kc method really punishes you.

I also don't think this Kc method includes the fact that in many cases the top flange of the cantilever is tied into the slab system and thus the connection helps resist - to a point - rotational twisting of the beam. We usually don't consider that anyway but it does help.

 

[JAE]

OK - ignore that attachment - made a mistake - will update shortly.