Date of Award

Fall 1994

Document Type


Degree Name

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


Mechanical and Industrial Engineering

First Advisor

Benedict C. Sun

Second Advisor

Rong-Yaw Chen

Third Advisor

Bernard Koplik

Fourth Advisor

E. S. Geskin

Fifth Advisor

C.T. Thomas Hsu


This thesis presents a comprehensive study of local stresses around a pipe-nozzle due to internal pressure. The finite element method (FEM) was employed to provide a numerical solution which will furnish a database for stress analysts to compute local stresses of pipe-nozzle due to internal pressure. The local pressure stresses for both the pipe and the nozzle around the pipe-nozzle juncture are first normalized into pressure stress factors which are then plotted as functions of geometrical parameters, beta, β, (nozzle mean radius / pipe mean radius) and gamma γ, (pipe mean radius / pipe thickness). These local pressure stresses at each point on the shell have both the longitudinal and circumferential directional components with respect to the orientation of the nozzle and the pipe, respectively. These stress components are again subdivided into membrane and bending in character. All together, sixteen (16) different stress factor plots are provided in this thesis which allows pressure vessel engineers to compute local stresses on both the outside and inside shell of the pipe, as well as the nozzle, at locations where the longitudinal and circumferential symmetric plane intersect the pipe-nozzle geometry.

The ranges of these stress factors cover the beta, β, varies from 0.1 to 1.0 in an increment of one-tenth, and the gamma, γ, varies from 10 to 300 in nine randomly selected intervals.

To ensure accuracy of the numerical results from the finite element method, the plate / shell elements are used with 96 nodes around the pipe-nozzle juncture. The pipe length is modeled with a parameter alpha p, αp, (pipe length / pipe mean radius) of a value of 8.0. The nozzle length is modeled with a parameter alphan, αn, (nozzle length /nozzle mean radius) of a value of 4.0. As a result, the optimized full pipe-nozzle model has 5268 nodes and 3245 elements, when β=0.5.

The local stress due to pressure may be used in conjunction with the stress computation table of the Welding Research Council Bulletin 107, which computes the local stress around the pipe-nozzle due to other external nozzle loads. Therefore, the stress computation table of WRC 107 is revised in this thesis to accommodate the local pressure stress effects.