Nonlinear Creep Deformations of Columns of Rectangular Cross Section

Abstract

Abstract Creep deformations of columns of rectangular cross section are studied for the case of materials following the nonlinear law ϵ̇ = (1/E) σ̇ + λσk. The essential point of the paper is the following: The time rate of the curvature κ̇ of an element of a bar loaded by a constant force P and an increasing bending moment M(t) has bounds, which depend on P and on the instantaneous values of M and Ṁ, but not on the history of M. In combination with the collocation method, this permits the formulation of ordinary differential equations for upper and lower bounds on the deformations. Closed solutions for the critical time are obtained for one bound, while the other requires numerical integration. The bounds which are a function of the initial eccentricity are reasonably close and are presented in tables and graphs. By qualitative reasoning it is further shown that the location of the actual critical time with respect to the two bounds is governed by the ratio of the column load P and the nominal Euler buckling load PE of the column if it were elastic.