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In the design of piping systems the importance of the pipe bend is well established. Recent publications have been increasingly concerned with the effect of end constraints on the behaviour of smooth pipe bends. This has been aimed almost exclusively at in-plane bending, there being no serious attempts at the solution to out-of-plane bending. In PART (1) of this thesis a theoretical solution is presented for the out-of-plane bending of linear elastic curved pipes with rigid flanges. The analysis employs the theorem of minimum total potential energy with suitable kinematically admissable displacements in the form of fourier series. Integration and minimisation is performed numerically. Results are given for a wide range of practical bend geometries. A comparison with previous theoretical predictions highlights the inadequacy of these earlier solutions. The present results are shown to be in favourable agreement with results from tests conducted by the author and more recent results using a different solution procedure. Work in the creep of pipe bends necessitates a substantial amount of experimental work and expertise. Most publications dealing with the creep of pipe bends under bending loads fail to present much information on this aspect. In PART (2) of this thesis a general description is given of an experimental creep programme on pipe bends. The measurement of strain at elevated temperature was accomplished using the CERL-PLANER capacitance strain gauge. It is shown that the application of this gauge to pipe bends requires particular techniques if meaningful results are to be obtained. The results of development work arising from other problems encountered during the test programme are also presented. These include the measurement of displacement and distortion at elevated temperature and the provision of an efficient and novel heating system.

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The use of single mitre oipe bends, in pipework and ducting, is evident in many areas of industry. However, it has been recognized that a theory which embraced all aspects of the elastic behaviour o£ single mitre bends does not exist. The present investigation demonstrates ~~e feasibility of using finite element methods for such a task. After an extensive series of 'verification comparisons' with experimental results obtained by the aUL~or and also with D~eoretical and experimental results available in the literature, a study of a wide range of ~~reinforced and fully fixed mitres was carried out. As a result of this study, useful design curves illustrating ~~e variation of stress concentration factor and flexibility factor, WiL~ radius to ~~ickness ratio and mitre angle, were produced for an inplane bending load. The above verification comparisons included in-plane bending, out-ofplane nending, torsion, internal pressure and transverse force loadings. An investigation into the effect of leg length and material properties on ~~e behaviour of mitre bends was also conducted. As a result of these studies, the limitations of currently used design Code formulae became evident. Possible difficulties in the numerical solution of thin shell problems are highlighted. In addition, a study of various methods of modelling shell intersections is reported. The most comprehensive review of literature to date, on all aspects of mitre bend behaviour, is presented in the Supplement to this thesis.

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.