Buckling of columns: Allowance for axial shortening
Abstract
The paper investigates the effect of axial shortening on the following: (1) the elastic buckling of columns with a continuous elastic restraint; (2) the elastic buckling of rotating columns; and (3) the free vibration of columns under a static axial load. These column problems may be solved in a unified approach because the resulting energy functional is similar. The field differential equation is derived by minimizing the energy functional with respect to the lateral displacement function via calculus of variations. The buckling load or fundamental frequency may be obtained by solving analytically the twopoint boundary value problem. It was found that the boundary conditions and the restraint parameter or angular velocity parameter affect the influence of axial shortening on the buckling load. In vibrating columns, tensile forces enhance the effect of axial stretching on the fundamental frequency.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1990
 Bibcode:
 1990STIN...9321234W
 Keywords:

 Angular Velocity;
 Axial Loads;
 Boundary Value Problems;
 Displacement;
 Elastic Buckling;
 Free Vibration;
 Static Loads;
 Stretching;
 Boundary Conditions;
 Differential Equations;
 Structural Mechanics