The continuous pipe bend behavior is well elaborated in literature. It is characterized by local ovalization of each cross section during bending which results in enhanced flexibility of it as compared to straight pipe. When pipe bend approaches some other structural elements of a piping system the end effect take place which can be described by so called long shell solution. This long solution is, in fact, a semi-membrane Vlasov’s solution when the derivative of any geometrical or force function in axial direction is much smaller than in the circumferential one .
Mitred bend is formed by conjunction by welding of two oblique sections of initially straight pipes. Its behavior during loading by pressure or bending moment is not evident and poorly described in standards. The goal of this paper is to give a set of general functions within a thin cylindrical shell theory which will give the opportunity to consider the mitred bend as an element of a piping system. Here we additionally introduce the so called short solution when the derivative of any parameter in axial direction is much bigger than that in circumferential one. Its main goal is to give the local behavior of stress in the vicinity of the oblique weld. Each of these two solutions satisfy by differential equations of forth order.
The complete theoretical solution for a particular mitred bend is compared with
a) existing analytical solutions and formulas;
b) numerical results obtained by FEM with distinction of the zones of influence of a long as well as short shell solution;
c) experimental data on real mitred bends given in the literature.