Bree图可以追溯到20世纪50年代，许多现代规范和标准都使用它来评估薄壁圆柱形容器中的棘轮作用。本公告重新讨论了图表的原始推导，包括一些在文献中似乎被忽略的对图表的修改和重新推导。然后对该图及其修改进行扩展，以说明启动和关闭时屈服应力的不同值。这些推导简洁地表示为一系列方程，定义了弹性和塑性循环、安定和棘轮作用的区域。附录中详细说明了逐步推导。

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.