Analytical solutions of openings formed by intersection of a cylindrical shell and an oblique nozzle under internal pressure

This paper presents the analytical solutions of local circumferential and l ongitudinal stresses due to internal pressure on a cylindrical pressure ves sel at the juncture of an opening formed by a nozzle with various intersect ing angles in the case of thin wall vessels. First, we present the exact ma thematical expression for the shell-nozzle intersection curve in mid-surfac e, and then solve the equations for the desired stresses using Fourier seri es methods. The resulting stresses are then normalized into stress concentr ation factors by means of the circumferential pressure stress. The influenc e of thickness is considered for stresses that have linear distribution alo ng the thickness from inside to outside because of the thin wall vessel. Fo r the ratio of nozzle radius/shell radius beta = 0.4 and the ratio of shell radius/shell thickness gamma = 40, the numerical calculations were perform ed for the stress concentration factors in both circumferential and longitu dinal directions along the symmetric axes, and then plotted and tabulated f or the intersection angles of 90, 75, 60, 45, and 90 deg, respectively.. Nu merical stress results indicate that the stresses for 30 deg intersection h ave the largest value. When the intersection angle is 90 deg, the results a re in good agreement with the existing literature.