An analytical model for elasto-plastic buckling of columns

Abstract

The theory of buckling strength of compression members in the plastic range has been extensively studied, and numerical methods already exist which deal with such behaviour. However, there is significant research interest in developing analytical models for elasto-plastic buckling, largely driven by the need for simplified mechanics-based design tools, but also by the desire for enhanced understanding of this complex phenomenon. This paper is intended to illustrate the mechanics of the elasto-plastic buckling response of stocky columns by means of a simplified analytical model, starting from the point of buckling initiation and considering the post-buckling response. In this model, the Rotational Spring Analogy is used for formulating the geometric stiffness matrix, whereas the material stiffness matrix is obtained with due consideration for the spread of material plasticity. In addition to establishing some key features of elasto-plastic buckling, the imperfection sensitivity in the plastic range is also studied and as a result a threshold level of imperfection is identified.