Cylinder &Sphere Design Calculation due to Internal Pressure
Cylinders and spheres under internal pressure
Cylindrical and spherical shells under internal overpressure are loaded by tensile stress. In order to avoid failure of the component, the wall must be sufficiently dimensioned.
The UG27 module determines the required wall thickness of cylindrical or spherical shells under internal pressure as well as the allowable overpressure for a given wall thickness.
For the calculation of openings, the required wall thickness for a usage factor of 100% is presented.
Notation:
P = Design pressure or Maximum Allowable Working Pressure (MAWP), psi
S = Stress value of material, psi
E = Joint efficiency
Ro = Outside radius, inches
Ri = Inside radius, inches
Do = Outside diameter, inches
Di = Inside diameter, inches
t = Wall thickness, inches
C.A. = Corrosion allowance, inches
Rd = Inside radius of dish, inches
r = Inside knuckle radius, inches
1.) Shell
a) Cylindrical shell
The compressive stress due to external pressure and tensile stress due to internal pressure shall be determined as follow formula:
S1 = P.Dm / 4t (Longitudinal stress (Axial Stress), circumferential joint, psi)
S2 = P.Dm / 2t (Circumferential stress (Hoop stress), longitudinal joint, psi )
Where:
S1 = Longitudinal stress, circumferential joint, psi =e.g. 100/4 = 25 PSI
S2 = Circumferential stress, longitudinal joint, psi =e.g. 100/2 = 50 PSI
Dm = Mean diameter of vessel, inches
Pressure vessels have two stresses to check - hoop stress and axial stress. Hoop stress is always twice the axial stress.
Circumferential stress/Hoop stress,(S2) is greater than (>) Longitudinal stress, (S1) S2 > S1
¨ Stress due to internal pressure based on inside diameter "
According to UG-27, the minimum thickness or MAWP as follow:
a. S2 = Circumferential Stress (Longitudinal Joints)
If t ≤ 1.5Ri or P ≤ 0.385 SE
t = P.Ri / (SE – 0.6P) and P = SEt / (Ri + 0.6t)
Circumferential stress/ Hoop stress, (S2) is greater than (>) Longitudinal stress, (S1)
Always = S2 > S1
b. S1= Longitudinal Stress (Circumferential Joints)
If t ≤ 1.5Ri or P ≤ 0.665 SE t = PRi / (2SE + 0.4P) and P = 2SEt / (Ri – 0.4t) and P = 2SEt / (Ri – 0.4t)
Longitudinal stress in Pressure vessel: (Greek symbol sigma) = axial stress
(S1 ) Longitudinal or Axial stress is usually less than the Circumferential (S2) or Hoop stress
always S1< S2
¨Stress due to internal pressure based on outside diameter "
a. S2= Circumferential Stress (Longitudinal Joints)
t = PRo / (SE + 0.4P) and P = SEt / (Ro – 0.4t)
b. S1 =Longitudinal Stress (Circumferential Joints)
t = PRo / (2SE + 1.4P) and P = 2SEt / (Ro – 1.4t)
Spherical shell
b) Spherical Shell
When t ≤ 0.356R or P ≤ 0.665SE,
the following formula shall apply:
t = PR / (2SE – 0.2P) and P = 2SEt / (R + 0.2t)
Source :
additional information:
http://www.scribd.com/ 6386787-Pressure-Vessels-the-ASME-Code-Simplified
Rao, K. (2012) Companion Guide to the ASME Boiler and Pressure Vessel Code, Volume 1, Fourth Edition, ASME.
Annaratone, D. (2007) Pressure Vessel Design. Springer, Berlin, 47-125.
Moss, D. (2013) Pressure Vessel Design Manual. Elsevier.
