Deformation of Uniformly Loaded Beams Obeying Complex Creep Laws

Abstract

The deformations of uniformly loaded, simply supported beams are derived for a simple creep law of the type where is the secondary creep rate, ρ is the applied stress and n is the creep index. The solution is extended to include a yielding behaviour such that ρ ≥ Y where Y is a yield stress. The deformations are found to be relatively insensitive to the value of n so long as the strain rate is known at a ‘representative stress’ in the beam and the representative stress is less than about 95 per cent of the yield stress. The concept of representative stress is used to estimate useful upper and lower bounds for the deformations of a simply supported beam composed of a material with a complex creep law in which the stress index n is continually increasing with increasing stress. Similar results for cantilevers and clamped beams suggest that the representative stress concept is useful for the solution of many problems involving deformations under complex creep laws or for problems in which a minimum of creep information can be obtained.