Closed-form formulation for torsional analysis of beams with open or closed cross sections having a crack

In this article, a semi-analytical approach is used to formulate the torsional analysis of beams having a crack. The formulation is based on analytical and accurate numerical analyses. The cross section is decomposed into several segments, including straight and curved segments with or without a crack. A dimensionless formulation is introduced and used to analyze the problem. The cracked segments are analyzed using the finite element method. The other segments are analytically formulated. The crack is supposed to be perpendicular to the boundary and located in the inner or outer surface of the beam. The thickness of the cross section is assumed to be uniform. Some numerical results are provided to show the accuracy of the presented method.