Limit moments for non circular cross-section (elliptical) pipe bends

It is well known that the curved pipe or pipe bend is a key component in the design of pipework systems. This importance is even greater when the system is subject to combinations of loadings and temperature which cause inelastic effects such as plasticity or creep. Computational methods which include inelastic effects are proving complex and expensive resulting in an increasing interest in simplified approximate methods suitable for design purposes. A number of experiment studies have been reported or are underway which investigate limit moments applied to pipe bends. Some theoretical work is also available. However, most of the work has been confined to nominally circular cross-section bends and little account has been taken of the practical problem of manufacturing tolerances. Many methods of manufacture result in bends which are not circular in cross-section but have an oval or elliptical shape. The present paper extends previous analyses on circular bends to cater for initially elliptical cross-sections. The loading is primarily in plane bending but out of plane is also considered and several independent methods are presented. No previous information is known to the authors. Upper and lower bound limit moments are derived first of all from existing linear elastic analyses and secondly upper bound moments are derived via a plastic analogy from existing stationary creep results. It is also shown that the creep information on design factors for bends can be used to obtain a reasonable estimate of the complete moment/strain behavior of a bend or indeed a system. The results are given in graphical form over the whole range of pipe bend geometries for several levels of ellipticity and should be of direct use to designers in simplified calculations for the integrity of pipework. They should also be of interest to experimenters for comparison with or planning of test work