It is assumed that the axial bending stresses which arise from this type of weld have a linear distribution. From these stresses, axisymmetric solutions in the literature enable the stress intensity factor to be calculated for an internal circumferential crack. In this paper it is shown that the same solution may be obtained from the plane strain solution for bending of a cracked beam. This approach applies to any radius to thickness ratio for thin-walled pipe while the axisymmetric solutions apply only for the specific ratios taken in the numerical solutions. Also, the present procedure allows the radial deflection and moment on the crack plane to be determined as a function of crack depth with simple calculations.

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