Analytical Solutions of Openings Formed by Intersection of a Cylindrical Shell and an Oblique Nozzle Under Internal Pressure

Abstract

This paper presents the analytical solutions of local circumferential and longitudinal stresses due to internal pressure on a cylindrical pressure vessel at the juncture of an opening formed by a nozzle with various intersecting angles in the case of thin wall vessels. First, we present the exact mathematical expression for the shell-nozzle intersection curve in mid-surface, and then solve the equations for the desired stresses using Fourier series methods. The resulting stresses are then normalized into stress concentration factors by means of the circumferential pressure stress. The influence of thickness is considered for stresses that have linear distribution along the thickness from inside to outside because of the thin wall vessel. For the ratio of nozzle radius/shell radius β = 0.4 and the ratio of shell radius/shell thickness γ = 40, the numerical calculations were performed for the stress concentration factors in both circumferential and longitudinal directions along the symmetric axes, and then plotted and tabulated for the intersection angles of 90, 75, 60, 45, and 30 deg, respectively. Numerical stress results indicate that the stresses for 30 deg intersection have the largest value. When the intersection angle is 90 deg, the results are in good agreement with the existing literature.