Roark's Equations for Discontinuity Stresses Syntax

[josep233]

I am looking for clarification of some terms found in Roark's Formulas for Stress and Strain 9E. Table 13.4 pg 543 as well as preceding tables frequently reference R_A as the radius of common circumference. I take this to mean that this value could include any radius that both cylinders share through their thicknesses, but do not know for sure. To further confuse this, some tables say R_A = R_1. Does anyone with more exposure to this understand what R_A means?

 

[onatirec]

R_A =radius of common circumference, i.e. it is defined as the intersection of the midsurfaces of the two different shells (not just any shared radius). It is generally defined as a vertical distance from an axis bisecting the shell horizontally. So if the left-most section isn't curved, then R_a should equal R_1.

If the left section is e.g. more circular, then the R_a is a function of R_1*sin() -> since R_a is measured vertically in the fashion the diagrams are usually portrayed, not radially.

It's maybe worth saying that R_A is not delta R_A, which is all I see in the table you shared.