First approximation to elastic analysis of end-effects in pipe bends

To a first approximation the end effects are considered, which arise due to the elastic junction of a pipe bend with other elements of a piping system. It is emphasized that Karman's assumption about inextensibility of the mid-surface in the circumferential direction can be applied only after exclusion of the circumferential force from the equilibrium equations. For the first time, the general solution for the end effect at a pipe bend is derived analytically, allowing the elastic pipe bend to be considered as only one element in a piping system. Examples are given for calculating the quarter of a torus with different boundary conditions.