dynamic stability of an axially loaded elastically restrained column
abstract
the dynamic stability of axially loaded columns is a key problem in structural analysis, and in
earthquake engineering particularly. experience has shown that columns occasionally buckle
when subject to dynamic axial loads that are only a small fraction of the load-carrying capacity predicted by static methods. while the mechanism behind these failures has been
identified, theoretical studies have focused almost exclusively on pin-pin (and, to a lesser
extent, fixed-fixed) connections. in practice, however, most columns have fixities between
these two extremes and are described as having semi-rigid or elastically restrained supports.
very few studies have been conducted on this condition, and of the studies performed, none
have included experimental verification. additionally, calculation of the stability based on
existing methods is very computationally expensive, as they calculate the response of the
column, rather than the stability behavior. as a result, dynamic stability theory is not
yet directly applicable to most design situations. to apply this theory to key problems in
earthquake and structural engineering, a more practical approach to computing the stability
behavior of more complex support conditions is required. this research studies the dynamic
stability of axially loaded columns with elastically restrained supports theoretically, numerically, and experimentally. the equation of motion of an elastically restrained column is
first derived and converted to a mathieu equation, from which the stability regions can be
obtained using bolotin’s method. second, a numerical method is developed to compute the
state transition matrix for a particular excitation, giving the stability condition and response
simultaneously. this numerical method is compared to the analytical results to determine
the relative error associated with both the analytical and numerical solutions. third, a novel
experimental apparatus capable of simulating an axially loaded column with elastically restrained supports is designed in the laboratory. the experimental apparatus is capable of
providing experimental verification for the matrix-based numerical method and is fully automated to allow the collection of large quantities of data. due to unforeseen equipment
damage, the experimental data could not be collected, but the automation was sufficiently
advanced at the time of damage to be proven in principle.