Buckling of shear deformable beams with singularities

Singularities occurring in shear deformable beams due to the presence of cracks cracks are considered and modelled as Dirac’s deltas. The latter model is exploited to account for the shear deformability of the beam with multiple cracks and in presence of an axial load. The governing stability equations are proposed, under the hypothesis that cracks do not undergo the closure phenomenon, and they are integrated to obtain the explicit closed form expression of the buckling load equation and the relevant buckling modes. The presented solution is able to capture, besides compressive, also buckling under tensile load.