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RE: seaint Digest for 6 May 2012

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Daryl - 

Timoshenko and Gere use something called the "Method of Successive
Approximations" in their 1961 book "Theory of Elastic Stability".  This can
be used for developing the theoretical buckling values for variable axial
load or variable cross section (or both).  The AISC Design guide for tapered
members (DG-25) has an example or two in their appendix if you cannot find a
copy of that old book. It's takes a bit of work to set up, but with Excel
it's not all that difficult.  


Josh Plummer, SE
RISA Technologies

-----Original Message-----
Subject: seaint Digest for 6 May 2012
From: "h.d.richardson" <h.d.richardson(--nospam--at)>
To: <seaint(--nospam--at)>
Subject: Column Buckling Due to Unifoemly Distributed Load

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Fellow engineers,

        I am working on two free-standing stacks.  A question has come = up
regarding maximum permissible slenderness ratio, KL/r.  AISC, CISC, = and
other structural codes traditionally limit KL/r to being less than = 200.
ASME SST-1-2000 doesn't cover the subject.  For KL/r AISC permits = stress
of 3.73 ksi whereas a stack axial stress will be about 10% of = this value.

        I submit that limiting KL/r to a maximum of 200 is much too =
conservative since the loading assumptions for AISC and others are not =
applicable to stacks.  Structural load cases assume ALL loading in the =
form of a point load at the top and NO uniformly distributed load while =
stacks have NO point load at the top and ALL of the load is distributed =
along the height.  Guyed stacks are a different matter, of course, = because
most of the load comes from the force of the guys or from the = weight of
other sections of the stack above the guys; I would always = restrict KL/r
to being less than 200 got guyed stacks.

        My thought was to solve the Euler equation and use a safety = factor
of 2.5 or 3 but my skill with differential equations is not what = it used
to be.  The equation I am trying to solve for UDL only is

EI(d2y/dx^2) =3D -M


M=3D m* Integral (from x to L) of w*y*dx

M =3D bending moment
w =3D weight/foot

        Any other thoughts, references, or help in solving the equation =
would be welcome.  Also, since I'm never sure if I'm connected to the = list
or not any more, a direct response would also be welcome.

Thanks in advance.

H. Daryl Richardson

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