Hope you mean "maximum working pressure", it depends on your reference standard (ASME B31.1, B31.3,...). The allowable stress in each standard is not the same.
Pipe thickness = Pressure x Mean Pipe Diameter/ ( 2 x Design Stress)
Design stress depends on the material you use and the design code you are working to. The maximum advisable design stress at ambient temperature for common pipe materials is 2/3 x the materials yield stress.
The pipe thickness should take into account thinning, usually 12.5%. and any corrosion/erosion allowance.
However pipework is seldom designed to its maximum capability because there are too many other unknown forces, such as pipe flexibility, cold pull caused by residual stress from welding. Pipework can also be subject to overpressure so it is not a good idea to design it close to its limit unless all these other factors are considered carefully.
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
