Conical sections knuckle section

A formed section would normally be used for the transition between a cylindrical section and conical section except for vessels operating at low pressures, or under hydrostatic pressure only. The transition section would be made thicker than the conical or cylindrical section and formed with a knuckle radius to reduce the stress concentration at the transition, Figure 13.11. The thickness at the knuckle can be calculated using equation 13.46, and that for the conical section away from the transition from equation 13.45. 

The following equations were developed with the assumption that the conical transition contains a cone section, knuckle, and flare. If the transition does not contain a knuckle or flare, you should set the radii of these components to 0 when computing the half-apex angle. 

---