SOME CONCEPTUAL ISSUES IN THE MODELLING OF CRACKED BEAMS FOR LATERAL-TORSIONAL BUCKLING ANALYSIS

This paper is focused on the lateral-torsional buckling of cracked or weakened elastic beams. The crack is modelled with a generalized elastic connection law, whose equivalent stiffness parameters can be derived from fracture mechanics considerations. The same type of generalised spring model can be used for beams with semi-rigid connections, typically in the field of steel or timber engineering. As the basis for the present investigation, we consider a strip beam with fork end supports and exhibiting a single vertical edge crack, subjected to uniform bending in the plane of greatest flexural rigidity. The effect of prebuckling deformation is taken into consideration within the framework of the Kirchhoff-Clebsch theory. First, the three-dimensional elastic connection law adopted is a direct extension of the planar case, but this leads to a paradoxical conclusion: the critical moment is not affected by the presence of the crack, regardless of its location. It is shown that the above paradox is due to the non-conservative nature of the connection model adopted. Simple alternatives to this cracked-section constitutive law are proposed, based on conservative moment-rotation laws ( quasi-tangential and semi-tangential) and consistent variational arguments.