A study of the behaviour of pressurized piping elbows
The behaviour of piping elbows under bending and internal pressure is more complicated than expected. The main problem is that the coupling of bending and internal pressure is non-linear; stress and displacement cannot be added according to the principle of superposition. In addition, internal pressure tends to act against the effect caused by the bending moment. If bending moment ovalises the elbow crosssection, with internal pressure acting against this deformation, then the deformed cross-section tries to deform back to the original circular shape. It is then introduced the term ''pressure reduction effect". Current design piping code treats the pressure reduction effect equally for in-plane (closing and opening) moment and out-of-plane moment. In this thesis, the pressure reduction effect is reassessed for in-plane closing moment through parametric study by performing detailed large deformation finite element analysis. The study is then extended to assess the pressure reduction effect for inplane opening moment and out-of-plane moment. Approximate formulae for ovalisation, flexibility, and stress-intensification factor are developed through a systematic analysis of the finite element generated data. Comparison of results presented in this thesis and the current ASME piping code for the pressure reduction effect under in-plane closing bending confirms that the ASME code formulae underestimates the pressure reduction for flexibility and stress-intensification. If the ASME formulae are applied for in-plane opening bending and out-of-plane bending, it overestimates the pressure reduction for the flexibility factor. If the ASME formulae for the pressure effect on stress-intensification factor is applied, it underestimates the pressure reduction for closing bending and out-of-plane bending, but overestimates for opening bending. It is therefore proposed that different formula for different direction of bending load should be used and the results presented in this thesis should be useful for this purpose.