Thickness Calculation
The shell and head thickness calculations are the fundamental design calculation. This thickness can be calculated either through internal diameter based or outer diameter based. Minimum thickness values can be calculated by using the formulae shown below. Calculated thickness of shell cylinder and head are required thickness, so we need to add corrosion allowance to get actual thickness of shell cylinder and head.
                                                ta = t +CA
THICKNESS CALCULATION (BASED ON INNER DIAMETER)
THICKNESS OF SHELL
According to specifications in UG-27 (c) which deals with the thickness of shells under internal pressure and clause “c” with the cylindrical shells and spherical SHELLS
1) FOR CYLINDRICAL SHELLS
It gives formulae for the thickness based on either longitudinal joint or circumferential joint. The required thickness value for shell is maximum value which may be either circumferential stress or longitudinal stress
a) CIRCUMFERNTIAL STRESS (LONGITUDINAL JOINTS)
The stress which acts tangent to the circumference and perpendicular to the axis of the cylinder is called circumferential or hoop stress. It means that the governing stress will be the circumferential stress (hoop stress) in the long seam. For this it has to satisfy that P does not exceed 0.385SE .In which case we shall use the following formulae for thickness of shell is
                        t = PR/ (SE -0.6P)
b) LONGITUDINAL STRESS (CIRUMFERENTIAL JOINTS)
The stress which acts normal to circumference and parallel to the axis of the cylinder is called longitudinal stress. It means that the governing stress will be the longitudinal stress in the circumferential joint. For this it has to satisfy that P does not exceed 1.25SE. OR if the circumferential joint efficiency is less than than ½ the longitudinal joint efficiency. In which case we use the formula for thickness is
                          t = PR/ (2SE +.4P)
2) FOR SPHERICAL SHELLS:
            When the thickness of the shell of a wholly spherical vessel does not exceed 0.356 R or P does not exceed 0.665SE, shall be determined by
                                      t = PR/ (2SE - 0.2P)
THICKNESS OF HEAD
            According to specifications in UG-32 which deals with the thickness of heads under internal pressure
a) 2:1 SEMI ELLIPTICAL HEAD
            The required thickness of a dished head of semi ellipsoidal form shall be determined by
                                                 t = PD / (2SE – 0.2P)
b) TORISPHERICAL HEADS
            The required thickness of a dished head of Torispherical form shall be determined by
                                                 t = 0.885PL / (SE – 0.1P)
c) HEMISPHERICAL HEADS
            The required thickness of a dished head of hemispherical form shall be determined by
                                                 t = PL / (2SE – 0.2P)
d) CONICAL HEADS
            The required thickness of a dished head of hemispherical form shall be determined by
                                                t = PD / (2 cos α (SE - 0.6P))
THICKNESS CALCULATION (BASED ON OUTER DIAMETER)
                        Outer diameter based thickness calculation procedure for shell and heads are same as that inner diameter based thickness calculation, but the formulae slightly varied. They are,
Thickness for shell
For cylindrical shell based on circumferential stress
                                      t = PR/ (SE + 0.4P)
            Where,
                        R = outer radius of shell in inches
For spherical shell based on circumferential stress
                                      t = PR/ (2SE + 0.8P)
Thickness for head:
2:1 semi elliptical heads
  t = PD/ (2SE + 1.8P)
Torispherical heads
t = (PLM) / (2SE+P(M-0.2))
Where,
            M = 0.25 (3+ (L/r) ^0.5)
 Hemispherical heads
  t = PR/ (2SE + 0.8P)
Conical heads
  t = PD / (2 cos α (SE + 0.4P))
NOTATIONS USED:
            ta = Actual thickness in inches
t = Required thickness in inches
CA = Corrosion allowance in inches
P = internal design pressure in psi
D = inner/ outer diameter of shell/head in inches
R = inner/ outer radius of shell/head in inches
S = allowable stress (for shell/head material) in psi
E = weld joint efficiency
L = inside/outside crown radius in inches
R = inside/outside knucle radius in inches
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