Longitudinal Stress (Circumferential Joint). When the thickness does not exceed one-half of the inside
radius, or P does not exceed 1.25SE, the following formulas
shall apply:

This calculator and associated formulas will govern only when the circumferential joint
efficiency is less than one-half the longitudinal joint efficiency, or when
the effect of supplementary loadings (UG-22) causing longitudinal bending
or tension in conjunction with internal pressure is being investigated.
An example illustrating this investigation is given in L-2.1 and L-2.2.

E = joint efficiency for, or the efficiency of, appropriate joint in cylindrical or spherical shells, or the efficiency of ligaments between openings, whichever is less.
For welded vessels, use the efficiency specified in UW-12. For ligaments between openings, use the efficiency calculated by the rules given in UG-53.

P = internal design pressure (see UG-21)

R = inside radius of the shell course under consideration. (For pipe, the inside radius R is determined by the nominal outside radius minus the nominal wall thickness.)

S = maximum allowable stress value (see UG-23 and the stress limitations specified in UG-24)

t = minimum required thickness of shell

U1 = Undertolerance allowance (%) typically 12.5%

U2 = Adjusted thickness by Undertolerance (U1 x t)

nt = Nominal thickness adjusted for corrosion and undertolerance, (= t - Ca - U2)