Optimization and Stability of Columns under Opposing Distributed and Concentrated Loads

Publisher Website
Google Scholar
Abstract
A bar subjected to simultaneous compressive and tensile axial loads behaves like either a column or tie, depending on the relative magnitudes of these loads. The result of this double structural behavior is a stability boundary which separates a conditionally stable region (column action) from an unconditionally stable region (tie action). In this paper the optimal design of such a structure is presented when it is in the conditionally stable region; in addition, the stability boundaries of uniform and optimal columns are given for various problem parameters. The columns under consideration are elastically clamped at one end and free at the other, and subjected to nonuniformly distributed and concentrated loads which act in opposite directions. The best possible distribution of the cross-sectional area is determined, such as to maximize the load-carrying capacity of the column subject to volume and thickness constraints. Furthermore, dual variational bounds are given which provide upper and lower estimates on the buckling loads of optimal columns. Similar stability problems are formulated which arise in connection with columns attached to the rim or hub of a rotating wheel.

This publication has 13 references indexed in Scilit: