Optimization and Stability of Columns under Opposing Distributed and Concentrated Loads

摘要

A bar subjected to simultaneous compressive and tensile axial loads, which behaves like either a column or tie, depending on the relative magnitudes of these loads is examined along with the resulting stability boundary which separates a conditionally stable region (column action) from an unconditionally stable region (tie action). The optimal design of the structure, when in the conditionally stable region is presented. The stability boundaries of uniform and optimal columns are given for various problem parameters. The columns 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 cross sectional area is determined, such as to maximize the load carrying capacity of the column subject to volume and thickness constraints. That variational bounds are given which provide upper and lower estimates on the buckling loads of optimal columns. Stability problems are formulated which arise in connection with columns attached to the rim or hub of a rotating wheel.