The influence of end constraints on pipe bends, a study of smooth pipe bends with flange and tangent pipe end constraints under in-plane bending

The importance of smooth pipe bends in design of piping systems is well established. Recent publications have been increasingly concerned with the effect of end constraints on the behaviour of smooth bends but there have been relatively few attempts at a solution to the problem. The divergence between the results of those which do exist tend to confuse the picture for pipework designers. The present thesis is aimed at clarifying the situation. After an historical review of the literature on smooth bends, a theoretical analysis is formulated for the in-plane bending of linear elastic curved pipes with rigid flange terminations. The method employs the theorem of minimum total potential energy with suitable kinematically admissible displacements in the form of fourier series. Integration and minimisation is performed numerically, thereby permitting the removal of several of the assumptions made by previous authors. Results are given for a wide range of practical bend geometries. These are compared with the previous theoretical predictions, highlighting the problems in same earlier works and substantiating more recent results using different solution procedures. During the development of the theory several possible simplifications to the method are examined. The theoretical predictions are shown to be in favourable agreement with published experimental data and with results from tests performed by the author. The approach is extended to examine the behaviour of smooth bends with connected tangent pipes under in-pane bending. The tangent pipes can be of any length and are assumed to be terminated by rigid flanges. Comprehensive results are given for bends with tangent pipes ot length greater than one pipe circumference. Finally, possible extensions ot the solution procedure to other configurations and loadings are discussed.The importance of smooth pipe bends in design of piping systems is well established. Recent publications have been increasingly concerned with the effect of end constraints on the behaviour of smooth bends but there have been relatively few attempts at a solution to the problem. The divergence between the results of those which do exist tend to confuse the picture for pipework designers. The present thesis is aimed at clarifying the situation. After an historical review of the literature on smooth bends, a theoretical analysis is formulated for the in-plane bending of linear elastic curved pipes with rigid flange terminations. The method employs the theorem of minimum total potential energy with suitable kinematically admissible displacements in the form of fourier series. Integration and minimisation is performed numerically, thereby permitting the removal of several of the assumptions made by previous authors. Results are given for a wide range of practical bend geometries. These are compared with the previous theoretical predictions, highlighting the problems in same earlier works and substantiating more recent results using different solution procedures. During the development of the theory several possible simplifications to the method are examined. The theoretical predictions are shown to be in favourable agreement with published experimental data and with results from tests performed by the author. The approach is extended to examine the behaviour of smooth bends with connected tangent pipes under in-pane bending. The tangent pipes can be of any length and are assumed to be terminated by rigid flanges. Comprehensive results are given for bends with tangent pipes ot length greater than one pipe circumference. Finally, possible extensions ot the solution procedure to other configurations and loadings are discussed