Use of Engineering Strain and Trefftz Theory in Buckling of Columns

Abstract

The elastic buckling of columns with allowance for prebuckling axial shortening is analyzed using Trefftz's initial stress theory of 1933 and the engineering strain definition; the results are compared with earlier results based on the Green strain definition. When the latter definition is used, the buckling load can be obtained using the Euler solution after scaling the flexural rigidity by the ratio of the original column length to the prebuckling shortened length. It is found that when the engineering strain is used instead, the corresponding factor is equal to the square of the aforementioned ratio.