For plain round pipe, where tranverse shear and torsion are negligible, the 3 principal stress components of primary membrane stress are radial stress R, hoop stress H, and axial stress A (actually a contribution of axial & bending stress). The design stress must equal or be greater than:
SQRT[((R-H)^2 + (H-A)^2 + (A-R)^2)/2]
For thin walled pipe, where thickness/Diameter (t/D) < 20
R = Internal Pressure + External Pressure = Pi + Po
H = (Pi-Po)*D/(2*t)
A = [True_Wall_Tension/Area] +(-) [Moment*D/(2*Moment_of_Inertia)]
For thick walled pipe
R = (Po*Do + Pi*Di)/(Do+Di)
H = (Pi-Po)*Do/(2*t) - Pi
A = same as above
where, Do is outer diameter, Di is internal diameter
Design stress = Design_Factor * 2/3 * Yield Stress
Design_Factor depends on load category. Use 1.0 for normal operation load case, 1.2 for extreme load case, and 1.5 for survival load case.
True_Wall_Tension is the sum of applied tension (or effective tension) and end-cap pressure induced tension (or separation force). The end-cap pressure induce tension equals (Pi*Ai+Po*Ao), where Ai=(pi*Di^2)/4 and Ao =(pi*Do^2)/4.
For more information, please refer to API-Recommended Practice 2RD Standards
Hope this help,
Regards