This paper presents an analysis and sample results of the lateral buckling and vibration of a compressively loaded column whose cross section is piecewise constant along its length. The column is symmetric about its midspan and consists of three sections, with the center section having a stiffer cross section than the two identical outboard sections. Buckling and vibration characteristics of the column are determined from a 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 outboard sections based on both buckling load and vibration frequency requirements. In these analyses two relationships between cross-sectional mass and bending stiffness are considered; one is a low-efficiency method for increasing the bending stiffness of the cross section, and the other is a high-efficiency method. The effect of axial load on vibration frequency is also examined and compared with that of a uniform column. Introductio
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