Columns 

A column
is a structural member that is subjected to compressive stresses along its
entire 
length,
or axially. In the previous example (Fig. 126) the upright panel acted as a column 
and your
finger pressing down on it acted as a load that was inducing compressive
stresses 
in it.
For a column to remain stable it must bear its load so that it does not
bend to any 
marked
degree or break. The compressive strength of most structural
materials is so high 
that
they will become unstable, or fail, due to other factors before they reach
their limit 
of
compression. Surprisingly, then, the very factor you might think
enables a column to 
resist
being deformed by compressive stresses, its compressive strength, is only
a 
secondary factor in its load bearing capacity (unless it is very
short). In practice the load 
bearing
capacity of a column is mainly dependent on several other factors such as
the 
stiffness of the material it is made of, the geometry of its
crosssectional area, its length, and 
whether
its ends are fixed or not. 

Euler
combined the first three of these four factors into one equation that
computes the 
critical
buckling load, F_{CR}, of a freestanding column (i.e. ends not
fixed): 
where F_{CR} = critical buckling load 
F_{CR} = E
Ι π^{2}
E = modulus of elasticity 
L^{2} I
= moment of inertia 
π
= 3.1416 
L = length 

The
critical buckling load is the maximum weight that a column can bear and
still be stable. 
When the
F_{CR} is reached even a small increase in the load will cause the
column to buckle, 
that is,
bend suddenly and substantially. Therefore columns should not be subjected
to loads 
that
approach the critical buckling load if you do not want the roof to crash
down on you! 

From the
equation you can see that the critical buckling load of a column is
directly 
proportional to the modulus of elasticity, E, of the material the column
is made of and the 
moment
of inertia, Ι,
of its crosssectional area. For example doubling either E or
I
will 
double
the load bearing capacity of the column. Also a column's F_{CR}
is indirectly 
proportional to the square of its length, L. For example doubling
its length will decrease its 
load
bearing capacity by
a factor of four. Let's look at each of these factors in Euler's 
equation
so we can make
some general observations about how columns behave. 

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Knowhere 

Page 85 
Building stability  Columns 

