Analytical Modeling of Cracked Thin-Walled Beams Under Torsion

Abstract

We present an analytical model, derived using the principle of virtual work, for closed and open thin-walled beams subjected to torsion. Non-classical effects like primary and secondary torsional warping are taken into account. A closed-form expression for Mode II stress intensity factor for thin-walled beams with a longitudinal crack is derived. We start by finding analytical solutions based on the Vlasov’s torsional beam theory for thin-walled beams with any cross-sections. We then use the calc ulated stress of a rectangular thin-walled beam to determine an analytical expression for Mode II stress intensity factor. Finally, we add a correction factor to account for complex beha vior of long cracks. Examples are presented to illustrate the effectiveness of the cu rrent model, and it is validated by comparison with detailed finite element results obt ained using the ABAQUS TM .