Effects of local wall thinning on plastic limit loads of elbows using geometrically linear FE limit analyses

This paper provides closed-form plastic limit load solutions for elbows under in-plane bending and internal pressure, via three-dimensional (3D), geometrically linear FE limit analyses using elastic-perfectly plastic materials. Wide ranges of elbow and thinning geometries are considered. To investigate the effect of the axial thinning length on limit loads systematically, two limiting cases are considered; a sufficiently long thinning, and the circumferential part-through surface crack. Closed-form plastic limit load solutions for wall thinning with intermediate longitudinal extents are then obtained from these two limiting cases. The effect of the axial extent of wall thinning on plastic limit loads for elbows is highlighted by comparing that for straight pipes. Although the proposed solutions are developed for the case when wall thinning exists in the center of elbows, it is also shown that they can be applied to the case when thinning exists anywhere within the elbow.