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Re: Lateral Restraint for tall column

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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