Revisiting the Bree Diagram: Derivation with Temperature Dependent Properties
D.W. Spring, Ph.D., C.H. Panzarella, Ph.D., D.A. Osage, ASME Fellow, P.E.
Number of Pages
The Bree diagram dates back to the 1950’s and is used in many modern Codes and Standards for assessing ratcheting in thin-walled cylindrical vessels. This Bulletin revisits the original derivation of the diagram and includes some modifications and re-derivations of the diagram that seem to have been overlooked in the literature. The diagram and its’ modifications are then extended to account for different values of yield stress on startup and shutdown. The derivations are compactly presented as a series of equations defining the regions of elastic and plastic cycling, shakedown, and ratcheting. Appendixes are provided which detail the step-by-step derivations.