Dynamic stability of an axially loaded elastically restrained column
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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.