Maximum Stresses and Flexibility Factors of Smooth Pipe Bends With Tangent Pipe Terminations Under In-Plane Bending

A theoretical solution is presented for the in-plane bending, linear elastic behavior of smooth, circular cross-sectional constant thickness pipe bends with connected tangent pipes of similar section. The analytical method employs the theorem of minimum total potential energy with suitable kinematically admissible displacements. Integration and minimization is performed numerically. Results are given for bend flexibilities and peak stresses covering a wide range of practical geometries. These are compared with other theoretical predictions and finite element results as well as with some recent experimental data.