When designing a pressure vessel do longitudinal stress and hoop stress need to be individually calculated? Say hoop stress would need a thickness of .063 and long. being .032. Would the larger figure be used or the sum of each thickness? 
If you use an example try to use these numbers:
P=1000 psi            (Pressure)
R=2.875 inches      (I.R.)
T=.125 inches       (Thickness)
S=40,000 psi         (Allowable Stress)
E=90%                 (Weld Eff.)
When considering a tensile strength of 40,00 is the sum of the total stress in all directions? (X+Y+Z=40,00psi) Or 40,000 psi in each direction?
Thanks,
Race
Edit:Changed I.D. to I.R.