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Unbraced Length, Lb, of bottom flange in compression....

ichibansan (Structural)
16 Aug 01 12:10
Say I have a cantilevered W-section beam with a backspan of 25 feet and the cantilever extending 8 feet out over a column support.  There is uniform loading (due to concrete slab, etc.) along the entire length of the beam, and there is a substantial concentrated load at the end of the cantilever.  Obviously the top flange of the beam is continuously laterally braced by the metal deck/concrete slab (Lb=0), but what is the unbraced length of the bottom flange if it is in compression due to negative moment over the column?  Is it the distance from the column support (which braces the bottom flange through the cap plate connection and beams framing in perpendicular at this location) to the inflection point in the backspan, where moment changes from negative back to positive?

Thanks for any feedback.
engcomp (Structural)
16 Aug 01 22:45
Dear AUB,

If the bottom flange is unbraced for the whole cantilever length then Lb could be twice the cantilever, i.e. 16 ft.

However, any stiffening running from the slab connection to the bottom flange would cut this down to the distance between stiffeners.

Good luck, Helmut
http://www.engs-comp.com/
haynewp (Structural)
17 Aug 01 10:39
Depending how "substantial" your concentrated load is, this inflection point distance can vary a lot, even more than twice your cantilever distance. I don't think I would take an inflection point to be a point of lateral bracing anyway. I would check the max (-) moment in each segment length, Lb=25' and Lb=8'.
JAE (Structural)
17 Aug 01 12:29
You should absolutely have lateral X bridging at the cantilever support.  Once this is included, you have two designs:  the cantilever and its maximum moment, unbraced length = cantilever length and Cb = 1.0

The second design is in the span:  check the negative moment at the support with unbraced length = the span (25 feet) and Cb calculated per AISC method.  Also check positive moment (if applicable) with Lb = 0 and Cb = either calculated or 1.0.
ishvaaag (Structural)
17 Aug 01 14:26
The case is covered in Fig. 5.11 of

Guide to Stability Design Criteria for Metal Structures, Vth ed., Theodore V. Galambos, John Wiley and SOns, New York, 1998, at page 207.

If
the root of the cantilever is continuous

and

the tip of the cantilever is torsionaly restrained by bracing both top and bottom flanges

then the effetive length to be considered for the cantilever is

1.5·L if the load falls in top flange

0.8·L if the load falls in bottom flange.

So there being explicit precision in one competent technical reference like this I would go for this approach, in spite of my feeling it being clearly overconservative, at least for most cases.

For my entertainment I once did a Quattro sheet covering the lateral bracing of the bottom flange by the mere vertical stiffness of the part of the web protruding from one partly embedding floor assumed to deliver full fixity at the base of the protruding part, but I don't locate it now. When found I might made it available to you for comment. Hope I will post something about this.
ishvaaag (Structural)
17 Aug 01 16:39
I  have located the quattro pro sheet on bracing of a compressed flange, both discrete and continuous (by the against lateral displacement stiffness of the web). This file is read at least by Excel 97, but is in spanish. It should be if well done a port of procedures suggested by Yura. Maybe I will remake it in the more clear presentation of Mathcad, then for whatever the unit system.

I will send it free to whomever asks it via e-mail, for whatever the use, study, comment or whatever you may want do with it.

er, as long you are not many in which case would devise a site for download.

Write me to

mom@arrakis.es

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