Comparison of analytical and the FEM method for deriving the Mode I stress intensity factor of thin-walled beams containing a crack

The problem considered in this paper is of the cracked thin-walled beams. They are subjected to combined loading by the bending moment and the axial force. The profiles with the I (H), T and U cross-sections were analyzed. The analytical method is based on application of classical expressions for Mode I SIF of such beams with taking into account the cross sections' warping. The classical expressions for SIF for the thin plate are adapted by including the reduced forces and moments characteristic for the thin-walled beams. The numerical simulation for calculating the stress intensity factor of the cracked thin-walled beams consisted of application of the Finite Element Method (FEM) by use of the J-EDI method. It is found that the Mode I SIF of cracked thin-walled beams increases with crack length increase. The conducted comparison of results obtained by application of the two methods confirms the validity of the proposed analytical expressions only for the small crack lengths.