whose cross sections have unequal dimensions, such as the one modeled in Fig. 134, the

SR of the narrower face, e.g. 2 inches, is the determining factor.


Building codes specify the maximum permissible SR of load bearing columns for common

structural materials.  This is to establish minimum uniform building standards for structures.

The SR for three common structural materials are listed here:



Slenderness ratio

structural steel

> 150


> 55


< 50


Finally, regardless of a column's geometry or the material it is


made of, another factor affecting its load bearing capacity is its


end condition.  That is, whether its ends are fixed or whether it


is freestanding.  Euler's equation for the critical buckling load


of column's presented earlier presumes they are freestanding.


However the ends of most structural columns are fixed in place


to the foundation they rest on and to the load they support.


Thus Euler's equation needs to be modified by adjusting the


Fig. 135 - Column with

length factor, L, with an "effective length" factor, Leff, for those


fixed ends

columns with fixed ends.  Basically the effective length of such

  columns is one-half the length of a freestanding column of the  

same length.  Since the critical buckling load of a column is indirectly proportional to its

length squared, fixing the ends of a column increases its strength by a factor of four.




Beams are called by different names, such as beam, girder,

strut, brace, or joist, depending on their function or location

in the structure. However they all share similar characteristics.

A beam is one of the simplest structures in design but one of

the most complex to analyze in terms of the external and


internal forces acting on it.  The complexity of its behavior under load depends on how it

is supported - at one or both ends - and how its ends are attached to the supports - fixed,

hinged, or roller.  Three basic beam types are the hinged cantilever beam, the fixed

cantilever beam, and the simply supported beam.


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Page 89 - Building stability - Beams

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