Buckling of Beams and Columns with Defects

Beams and columns subjected to the axial pressure are studied. Critical buckling loads are established for stepped beams clamped at one end and elastically fixed at the other end. The beams under consideration are of piecewise constant thickness and are weakened by cracks emanating from re-entrant corners of steps. The cracks are assumed to be stable part-through surface cracks. The influence of a crack on the stability of the beam is modeled by the method of distributed line spring known in the elastic fracture mechanics. Numerical results are presented for beams with a single step making use of different stress correction functions.