Stability of the Compressed Rod by the Scheme of Two-Module Material beyond the Limit of Elasticity

Abstract

It is shown that at an infinitesimal bending of a compressed rod beyond the elastic limit, the secant modulus of its longitudinal fibers both in the zones of additional loading and unloading moves along an infinitely small section of the tangent to the critical point on the compression diagram . Each of the longitudinal fibers of a compressed rod under conditions of infinitesimal bending has its own secant modulus, which linearly depends on the vertical coordinate z; in the zone of additional loading it decreases, and in the zone of unloading it increases.