Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

CHAPTER16
Columns
16.1 Introduction
In their simplest form, columns are long, straight, prismatic bars subjected to compressive,
axial loads. As long as a column remains straight, it can be analyzed by the methods of
Chapter 1; however, if a column begins to deform laterally, the deflection may become
large and lead to catastrophic failure. This situation, called buckling, can be defined as the
sudden large deformation of a structure due to a slight increase of an existing load under
which the structure had exhibited little, if any, deformation before the load was increased.
A simple buckling “experiment” can be performed to illustrate this phenomenon, with
a thin ruler, yardstick, or meterstick used to represent a column. A small compressive axial
force applied to the ends of the column will cause no discernible effect. Gradually increase
the magnitude of the compressive force applied to the ends of the column, however, and at
some critical load, the column will suddenly bend laterally, or “bow out.” The column has
buckled. Once buckling occurs, a relatively small increase in compressive force will produce
a relatively large lateral deflection, creating additional bending in the column. However,
if the compressive force is removed, the column returns to its original straight shape.
The buckling failure illustrated by this experiment is not a failure of the material. The fact
that the column becomes straight again after the compressive force is removed demonstrates
that the material remains elastic; that is, the stresses in the column have not exceeded
the proportional limit of the material. Rather, the buckling failure is a stability failure: The
column has transitioned from a stable equilibrium to an unstable one.
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