States of Equilibrium and Secondary Loss of Stability of a Straight Rod Loaded by an Axial Force

A general analytical solution of the problem of postcritical deformation of a straight incompressible rod loaded by an axial force is given. The bending of the rod is studied under various boundary conditions, and new states of equilibrium the occurrence of which is due to the secondary loss of stability are found. It is shown that, for simply supported and clamped rods, the solution bifurcates when the ends meet.