Stress analysis of pipe bends by ring elements

Pipe bends absorb large thermal deformation in the piping systems for high temperature fluid, because the sectional form of the pipe bends subjected to bending is flattened, and the flexural rigidity is lowered remarkably. High circumferential stress arises at pipe bends due to the flattening together with longitudinal stress, therefore the analysis of this part is important. The approximate solution by von Karman, by which stress and deflection are calculated by superposing the displacement according to the curved beam theory and that due to the flattening of cross section, and applying the virtual work principle, agreed considerably well with measured values, and afterwards, it was corrected and extended by many researchers. In this study, the equation representing the strain-displacement relation for pipe bends was derived on the basis of general shell theory, and the analysis using ring elements was carried out. The ring elements proposed in this study take the term of shearing strain into account, therefore the shearing deformation of pipe bends and the torsional deformation due to twisting moment can be analyzed. Besides, the connection with straight pipes is easy, the boundary conditions at pipe ends can be taken strictly into consideration, the analysis in case of applying internal pressure is possible, and the total degree of freedom is relatively small as the number of elements is small. Because of these advantages, it can be expected that this method is practical for analyzing complex piping systems. (Kako, I.)