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RE: Lateral Restraint for tall column

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There is a paper on Struct Engineering Journal/June 1995, Page 986 by
Prof. Plaut and et of Virginia Polytech "Behavior of three-span braced
columns with
equal or unequal spans." It is the exact model to match your problem.
However, It is difficult to use, too many dimensionless variables. 
Maybe, this is why it was published on Struct engineering journal :-)

A FEA may be worth to try if your program can handle burfication,
because only a couple of columns and springs need study for your case.



> -----Original Message-----
> From:	Rafael Sabelli [SMTP:Sabelli(--nospam--at)]
> Sent:	Wednesday, November 25, 1998 9:40 AM
> To:	'SEAINT'
> Subject:	Re: Lateral Restraint for tall column
> Dear Joseph Grill,
> There are two aspects to the required bracing you described:
> stiffness and strength.
> Timoshenko, in "Theory of Elastic Stability," studied the
> buckling of columns with a spring supports.  The method he
> develops, building on Euler, is to determine the buckling 
> capacity by solving a differential equation of stability.  The column 
> is assumed to be stable and slightly curved by buckling (in neutral 
> equilibrium); internal and external moments must balance, and the 
> corresponding load (the buckling load) is solved for.  If the desired 
> ultimate capacity is known, the required stiffness can be determined 
> (usually by trial and error).  The best reference is Chajes, "Principles 
> of Structural Stability Theory".
> For the buckling of a column with a spring support at its midpoint
> the theoretical stiffness required to preclude first mode 
> buckling is 16pi^2EI/L^3 (sixteen pi squared EI over L cubed, 
> where L is the total length of the column).  I believe this will give
> you a consertative (perhaps very conservative) estimate for the
> case you describe.  
> If this stiffness is provided, there should be no lateral force, in
> theory.  
> Of course, actual columns are not perfectly straight, and there is a 
> resulting lateral force. Moreover, if the stiffness provided is less than 
> that required to preclude first mode buckling, there is an addional force 
> to contend with.  For thecalculation of these lateral forces there is 
> some literature available from AISC (presented at a series of seminars 
> on stability bracing last year).  
> Yours,
> Rafael Sabelli