Date of Award

Spring 1990

Document Type


Degree Name

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


Mechanical and Industrial Engineering

First Advisor

Benedict C. Sun

Second Advisor

Bernard Koplik

Third Advisor

Harry Herman

Fourth Advisor

Rong-Yaw Chen

Fifth Advisor

C.T. Thomas Hsu

Sixth Advisor

Harry V. Kountouras


This thesis presents a comprehensive study of local stresses and spring coefficients of pipe with a nozzle connection, analyzed by the finite element method (FEM). Six types of loading are discussed: radial force, circumferential moment, longitudinal moment, circumferential shear force, longitudinal shear force, and torsional moment.

For the local stresses, the bending and membrane stress factors due to each of these loadings are presented in a series of plots with various gamma (piping radius/thick-ness) and beta (nozzle radius/pipe radius) values. These stress factors will readily replace those previously published in WRC No. 107. This work not only gives more accurate results, but also provides an extended range of beta for large combinations of previously unavailable nozzle-pipe geometries. Comparisons with data from available literature sources show that the finite element results from the thin shell model are very reasonable.

In the study of spring coefficients, three types of spring constant coefficients are presented: the coefficients in the radial direction and rotational coefficients in the circumferential and longitudinal directions. This study was previously conducted by Murad & Sun, and Sun & Sun. They used Bijlaard's double Fourier series solutions of displacement due to a distributed square load on the surface of a closed cylinder to derive the spring coefficients at the nozzle-pipe connection.

Due to the convergence problem in the double Fourier solution, the beta value in all the previous work on local stresses and spring coefficients is limited to a maximum of 0.55. Using the ANSYS FEM code, the maximum beta has been extended from 0.55 to 0.9, the gamma's (pipe radius/pipe thickness) range is 5 to 200, while the alpha (pip length/pipe radius) has been taken as 8.0 to isolate the effect of the pipe end conditions. The use of the double Fourier series solution for radial direction deflection used in previous studies represents neither the real geometry nor the real loading conditions. The finite element method used in this thesis does describe the real piping-nozzle geometry and actual loading conditions and hence produces results that provide a significant improvement over previous studies. Discussion and comparison of data with various literature are included in this thesis.