Static and dynamic stability of sloped columns : a matrix approach

Abstract

The purpose of this thesis is to investigate the static stability characteristics and the free vibration phenomena of a beam-column inclined from the vertical alignment. A modern compact matrix approach is utilized to formulate the mathematical solutions. A variety of end support conditions are considered, including fixed ends, simple supports, and a combination of those.

For the static stability problem, critical buckling loads are determined for various angles of inclination of the beam-column. For each end support condition, nonlinear load-deflection curves are plotted and critical buckling loads are determined from the maximum point of those curves.

For the free vibration problem, the natural frequencies of free vibration of the sloped beam-column are determined for various values of the inclination angle. For each end support condition, axial force-natural frequency curves are constructed using an approximate linearized condition.

In general, it is found that the critical buckling load decreases as the angle of inclination (measured from the horizontal) decreases. For the free vibration problem it is found that, as the induced axial force increases, the resonant frequency decreases. When the induced axial force reaches the critical buckling load, the resonant frequency is zero.