Buckling of viscoelastic beam columns

Abstract

The paper presents a theoretical study of the creep buckling behaviour of viscoelastic beam-columns under general loading conditions. A detailed analysis is given for three particular cases, axially compressed columns with initial curvatures, laterally loaded beam-columns and beam-columns in bending. The creep buckling problem is formulated in terms of the constitutive equations of the linear hereditary viscoelasticity. It includes two types of viscoelastic materials, those with limited and unlimited creep. The general solution is derived by means of the quasi-elastic method and is examined in detail for two simple rheological material models. It is shown that the creep buckling behaviour of linearly viscoelastic beam-columns under various loading conditions is typically governed by the magnitude of the axial compressive force. For viscoelastic materials of the limited creep type there is a safe load limit below which the creep buckling characteristics of the structure are limited in time. The magnitude of the safe load limit as related to the Euler's elastic critical load solely depends upon the asymptotic value of the creep function of the material. Quasi-elastic approximations and the corresponding exact analytical solutions are compared in two simple problems. It is observed that the quasi-elastic technique is adequate for applications to the linear creep buckling analysis.