Pipe Stress Engineering
Pressure vessels usually contain regions where abrupt changes in geometry, material, or loading occur. These regions are known as discontinuity areas, and the stresses associated with them are called discontinuity stresses by the code [1, 2]. These codes have outlined a general procedure for analyzing the discontinuity stresses and discussed examples of some common occurrences. This chapter will discuss some of the applications relevant to the design of piping systems.
Because of dissimilar characteristics, each of the adjacent parts joining at a discontinuity area behaves differently to an applied load, such as internal pressure or temperature. The deformations of the disconnected free bodies are different from each other. Because these parts are joined together, they share a common displacement that is different from their free displacements. The difference between the free displacement and the actual joint displacement is a forced displacement, which produces forces and stresses. These additional stresses are referred to as discontinuity stresses.
Calculation of discontinuity stresses is generally based on the behavior of the longitudinal strip of the cylindrical shell. Because a longitudinal stripe of a vessel behaves like a railroad sitting on an elastic foundation, the discontinuity stresses at the vessel are generally calculated based on the theory of “Beams on Elastic Foundation” [3, 4]. A beam on an elastic foundation receives a lateral reaction force that is proportional to the displacement. The rail track is a typical example of a beam on elastic foundation.