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: 
. 
Material 
Slenderness ratio 
structural steel 
> 150 
aluminum 
> 55 
wood 
< 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, L_{eff},
for those 

fixed ends 
columns with fixed ends. Basically the effective length of such 


columns is onehalf 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 


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. 

Back to
Knowhere 

Page 89 
Building stability  Beams 

