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RE: Column Buckling Due to Unifoemly Distributed Load

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Technically the KL/r of 200 is a recommendation and not a hard and fast requirement.


Two methods where you can solve for the Euler buckling loads are the Method Of Successive Approximations (MSA) (Documented by Timoshenko & Gere 1961, Theory of Elastic Stability [based on Newmark’s method] or an Eigenvalue Buckling Analysis… both will return you a load factor which you use to obtain an [Euler] Elastic Buckling Capacity/Strength.  The one caution on the MSA approach from Timoshenko is that he mainly covers a constant axial load as you mentioned so they simplify the internal moment to be M=p*delta, which is only true for a constant axial load.  Using that simplification for a non-constant axial load will give you unpredictable results.  AISC Design Guide 25: Frame Design Using Web-Tapered Members also covers application of the MSA method.


Hope this helps,

Greg Effland


From: h.d.richardson [mailto:h.d.richardson(--nospam--at)]
Sent: Monday, May 07, 2012 12:58 AM
To: seaint(--nospam--at)
Subject: Re: Column Buckling Due to Unifoemly Distributed Load




        Thank you, Harold.  I do have that reference.  It deals with allowable buckling stresses as a function of D/t and has nothing to say about kL/r ratios.. Never-the less, I will look at it again tomorrow when I'm a little wider awake.


        Thank you for your effort.  I do appreciate it.




H. Daryl Richardson

----- Original Message -----

Sent: Sunday, May 06, 2012 8:16 PM

Subject: RE: Column Buckling Due to Unifoemly Distributed Load


The best reference for the fundamentals of stack design is contained in a book published by the Lincoln Electric Company.  It is Design of Tubular Steel Structures (or something like that) and was written by Troitsky. 


I am in DC on business and away from my resources right now, or I could be of more help. 

Regards, Harold Sprague

From: h.d.richardson(--nospam--at)
To: seaint(--nospam--at)
Subject: Column Buckling Due to Unifoemly Distributed Load
Date: Sun, 6 May 2012 13:16:08 -0600

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) = -M




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


M = bending moment

w = 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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