Post-Buckling Analysis of Edge Cracked Columns Under Axial Compression Loads

Abstract

In this paper, post-buckling analysis of an edge cracked cantilever column subjected to non-follower axial compression loads are studied by using the total Lagrangian Timoshenko column element approximation. The cross-section of the column is circular. The cracked column is modeled as an assembly of two sub-column connected through a massless elastic rotational spring. In the case of columns subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric nonlinearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain-displacement relations of the column. The columns considered in numerical examples are made of lower-carbon steel. In the study, the effect of the cracks on the deflections, rotational angles, postbuckling configuration and Cauchy stresses of the columns are illustrated in detail in post-buckling case. The difference between cracked case and intact case is investigated in detail.