Stability of columns subjected to earthquake support motion

The problem of stability of an initially straight, simple column which is subjected to dynamic overload due to the vertical component of ground acceleration during an earthquake is considered. The time history of this component of earthquake, its maximum absolute amplitude and a Liapunov's function are used to define a sufficient condition under which the column will always be stable. It is shown for the case of a simple column that this condition implies that the column will be stable as long as the maximum load which the column is subjected to is less than the Euler buckling load during an earthquake.