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, F_CR, of a freestanding column (i.e. ends not fixed):

                                                                      where  F_CR = critical buckling load

                                  F_CR = 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 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 cross-sectional 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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