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RE: Unbraced Length of Cantilever

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Another good place for information regarding this issue is "Steel
Structures: Design and Behavior" by Salmon and Johnson... My version is the
3rd Edition but I would assume others, particularly the earlier editions
would have a good commentary on the ASD procedures.  The 3rd or newer
editions should also have LRFD commentary...  

Assuming that you are using ASD here is my interpretation (LRFD should be

For the cantilever beam Kx should be 2.10 per table C-C2.1 in the Chapter C
Commentary ASD 9th Ed. (Recommended design value when ideal conditions are
approximated)... Assume free end is free to rotate.

For Ky use 1.2... this depends on the restraint of the beam and assumes that
it is not free to rotate at the free end (laterally)... could possibly be
2.1 or 1.0 also (depends on bracing conditions, etc.)

Kx and Ky only affect the axial allowables and since you mentioned no axial
load then these won't matter.

As far as flexural bending or lateral-torsional buckling, members whose
unbraced length exceed Lc are those subject to lateral-torsional buckling
problems.  ASD Section F1.3 considers the lateral-torsional buckling when
determining the bending allowables from equations F1-6, F1-7, and F1-8.
Something else that might be of interest is that if the cantilever section
(or any flexural section) is doubly symmetric then you are allowed to use
rt(equiv) versus rt.  Refer to ASD Commentary Section F1 page 5-146 for
further information regarding rt(equiv).

For your case, for gravity loads I would use a Lb = maximum distance of
torsional restraint on the bottom flange; for uplift I would use Lb =
maximum distance between torsional restraints of the top flange (purlins,
etc.). Dr. Joseph Yura, Dr. James Fisher, and Dr. LeRoy Lutz each have
several good papers on what is a good restraint for these conditions.

For Ly I would also conside only points which restrain both flanges or at
least a large part of the beam as a whole, but again with no axial this
won't make a difference.

Hope this helps,

Greg Effland, P.E.

-----Original Message-----
From: Rick.Drake(--nospam--at) [mailto:Rick.Drake(--nospam--at)]
Sent: Thursday, December 07, 2000 8:42 AM
To: seaint(--nospam--at)
Subject: Re: Unbraced Length of Cantilever

For a good discussion on effective-length factors for cantilever steel
beams see the SSRC's Stability Design Criteria For Metal Structures, 5th
Edition, Section 5.2.4 and Figure 5.11.  The effective length factor for
cantilevers is a function of the lateral bracing at the support, the
lateral bracing at the end, and which flange is loaded.  Most of the
effective length factors are greater than one.

For the condition you described, full lateral bracing at support, top
flange bracing at the end, and top flange loading, the effective length is
1.4 times the cantilever length.

Rick Drake, SE
Fluor Daniel, Aliso Viejo


Ricky Leblanc <Rick.Leblanc(--nospam--at)> on 12/07/2000 05:36:43 AM

Please respond to seaint(--nospam--at)

To:   "'seaint(--nospam--at)'" <seaint(--nospam--at)>

Subject:  Unbraced Length of Cantilever

Here is the situation.  Cantilever beam (W36 shape) laterally braced at two
points on the top flange (free end and midspan).  These two points offer
bracing against lateral displacement only (no torsional restraint).  At the
fixed end there is full restraint about all bending axes (including
torsional).  Full shear restraint as well.  Under gravity load the top
flange is the tension flange and bottom flange is compression flange (i.e,
the lateral restraint is at tension flange only).  Major axis bending only,
no axial load.  Is the unbraced length of the compression flange the full
cantilevered span, or is it something more?


Rick LeBlanc, PE
Kellog, Brown & Root
Houston, TX

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