Pure bending of a beam having crack perpendicular to its axis

The infinite isotropic cracked beam under pure bending conditions is considered in this paper. Crack is perpendicular and nonsymmetrical with respect to longitudinal axis of a beam. Using theory of functions of complex variable and complex potentials the given problem is reduced to linear conjunction problem. Obvious expressions for complex potentials, contact forces between crack edges and stress intensity factors are written. There are three kinds of a crack at issue: perfect contact of a crack edges, particular contact and no one. In particular case presented results coincide with known in literature results for symmetric crack. There, solution of this problem was reduced to singular integral equation about contact stresses.The infinite isotropic cracked beam under pure bending conditions is considered in this paper. Crack is perpendicular and nonsymmetrical with respect to longitudinal axis of a beam. Using theory of functions of complex variable and complex potentials the given problem is reduced to linear conjunction problem. Obvious expressions for complex potentials, contact forces between crack edges and stress intensity factors are written. There are three kinds of a crack at issue: perfect contact of a crack edges, particular contact and no one. In particular case presented results coincide with known in literature results for symmetric crack. There, solution of this problem was reduced to singular integral equation about contact stresses.