The influence of end constraints on smooth pipe bends

With present trends in the power industries towards higher operating temperatures and pressures, problems associated with the design and safety assessment of pipework systems have become increasingly complex. Within such systems, the importance of smooth pipe bends is well established. The work which will be presented will attempt to clarify the situation and unify the results. An analytical solution of the problem of a linear elastic smooth pipe bend with end constraints under in-plane bending will be presented. The analysis will deal with constraints in the form of flanged tangents of any length. The analysis employs the theorem of minimum total potential energy with suitable kinematically admissible displacements in the form of Fourier series. The integrations and minimisation were performed numerically, thereby permitting the removal of several of the assumptions made by previous authors. Typical results for flexibilities will be given along with comparisons with other works. The differences in some earlier theory are clarified and other more recent work using different solution techniques is substantiated. The bend behaviour is shown to be strongly influenced by the pipe bend parameter, the bend angle, the tangent pipe length and the bend/cross-sectional radius ratio. (orig./GL)