First-Order Solutions for the Buckling Loads of Euler-Bernoulli Weakened Columns

Abstract

In this work, closed-form expressions for the buckling loads of a weakened column with different boundary conditions are presented. The cracked-column model is based on the well-known method consisting of dividing the column into two segments connected by a rotational linear spring whose flexibility is related to the crack size and the geometry of the cross section. For the formulation of closed-form expressions, the perturbation method is used and the results are compared with those found by directly solving the eigenvalue problem.