Date of Award

Fall 1996

Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)


Mechanical Engineering

First Advisor

Benedict C. Sun

Second Advisor

Bernard Koplik

Third Advisor

Rong-Yaw Chen

Fourth Advisor

A. C. Ugural

Fifth Advisor

C.T. Thomas Hsu


This dissertation presents a comprehensive study of local stresses, due to internal pressure around a pipe-nozzle with 45 degree angle intersection_ The resulting circumferential and longitudinal stresses on the pipe around the pipe-nozzle region are normalized as local stress factors and plotted as function of beta, β, (the radius of the nozzle/the radius of the pipe) and gamma, y, (the radius of the pipe/the thickness of the pipe) through the finite element method. The range of beta, [3, is from 0.1, to 1.0, and gamma, y, from 10 to 300. Comprehensive studies were made for the boundary parameters, such as αp ( pipe length / pipe mean radius ) and αn ( nozzle length / nozzle mean radius ), the optimized numbers of nodes around the pipe-nozzle juncture and total elements of the model. To justify a wide range of application of the 45° degree pipe-nozzle angles, extensive studies and a set of plots are provided to show that local stress factors vary with the pipe-nozzle intersection angle, from 90° to 30°.

An approximate theoretical analysis, which is based on thin-shell theory together with stress multipliers for the peak stresses at the both inside and outside crotch points, has derived to compare the data from 3D finite element models.

This study concludes that the maximum local stress is in the circumferential direction and occurs at the inside crotch point. The 45° intersecting angle yields relatively less local stresses when the pipe-nozzle intersecting angle other than 90° must be used for operational purposes. The local pressure stresses in the pipe-nozzle juncture are mostly in tension except on the inside surface of pipe in longitudinal direction. For certain combinations of13 and y, however, the longitudinal stress at point C (see Figure 2) on the outside surface of pipe may be compressive also.

Twelve (12) plots of local pressure stress factors are provided in this thesis allows design engineers of pressure vessel to compute local stress on both the outside and the inside shell of pipe when the pipe-nozzle intersecting angle is 45°. A numerical example is given.