G. Vadillo

First order solutions for the buckling loads of weakened Timoshenko columns

In this work, closed-form expressions for the buckling loads of weakened Timoshenko columns with different boundary conditions and shear force approaches (proportional to the bending rotation or to the total slope) are presented. The crack model used promotes discontinuities in both transversal displacements and rotation due to bending. To solve the buckling problem, the perturbation method is used, considering that the solutions for both the cracked and the uncracked columns are slightly different. This procedure leads to first-order closed-form expressions for the buckling loads of the Timoshenko cracked column, which were compared with those found by directly solving the corresponding eigenvalue problem, establishing validity limits for these solutions.

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

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.