Buckling and vibration analysis of a simply supported column with a piecewise constant cross section

An analysis and sample results for the lateral buckling and vibration of a compressively loaded column is presented whose cross section is piecewise constant along its length. The column is symmetric about its mid-span and consists of three sections, the center section having a stiffer cross section than the two identical end sections. Buckling and vibration characteristics of the column are determined from numerical solution of the exact eigenvalue problems. Parametric structural efficiency analyses are performed using a nondimensionalized set of governing equations to determine the optimum ratio between the lengths of the center section and the outer sections based on both buckling load and vibration frequency requirements. In these analyses, two relationships exist. One is between cross-sectional mass and the cross section, and the other is a high-efficiency scheme. The effect of axial load on vibration frequency is also examined and compared with that of a uniform column.