Buckling of a Laminated Column with Transverse Crack

Transverse cracks can emerge in composite materials in form of matrix cracking or fiber breaking. Apart from the stress concentration in the vicinity of crack, stability consideration of a cracked beam is incumbent upon any designer. Buckling behavior of an open cracked beam is studied in this paper employing an analytical approach and several numerical examples have been implemented and verified. The conventional analytical approach for cracked beam is to separate beam into two virgin beams and specify two differential equations for the left and right side of the beam, but in this study, one differential equation for the whole beam is assumed which has discontinuity in flexural stiffness, which consequently saves a lot of time and calculation. To investigate the behavior of a cracked beam, the crack is replaced with the linear massless rotational spring joining the two uncracked parts of the structure. In addition, the formulation is extended for the case of composite materials. Moreover, cross-ply laminates with different lay-up are used to monitor the influence of stacking sequence on critical loads of a cracked beam.