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
cross-sectional 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, FCR, of a freestanding column (i.e. ends not
fixed): |
where FCR = critical buckling load |
FCR = E
Ι π2
E = modulus of elasticity |
L2 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
FCR 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 cross-sectional area. For example doubling either E or
I
will |
double
the load bearing capacity of the column. Also a column's FCR
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. |
|
Back to
Knowhere |
 |
Page 85 -
Building stability - Columns |
 |
|