THIN WALLED PRESSURE VESSEL STRESS CALCULATIONS
A pressure vessel is a type of container which is used to store liquids or gases
under a pressure different from the ambient pressure. Examples of pressure
vessels can be diving cylinder, autoclave, nitrogen tanks, submarine and storage
vessels for liquefied gases such as LPG. Different shapes of
pressure vessels exist but most generally cylindrical and spherical shapes are
used. Spherical vessels are theoretically 2 times stronger than cylindrical ones
but due to the manufacturing difficulties, cylindrical ones are generally
preferred in the industry.
A pressure vessel is assumed to be a thin walled pressure vessel when the
thickness of the vessel is less than 1/20 of its radius. [Ref2]
The walls of thinwalled pressure vessels have little resistance to bending so
it may be assumed that the internal forces exerted on a given portion of the
wall are tangent to the surface of the vessel. The resulting stress state on
vessel is plane stress situation since all stresses are tangent to surface of
vessel.
The calculation tool was developed to analyze two types of vessels, cylindrical
and spherical type. According to geometric properties and pressure, principal stresses
and maximum shear stress on the surface of the vessel can be calculated. The
formulas used for the calculations are given in the List of Equations section.
Note: Use dot "." as decimal separator.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Hoop stress (Principal stress1) 
σ_{1} 


MPa

Longitudinal stress (Principal stress2) 
σ_{2} 


Maximum shear stress (in plane) 
τ_{max(in plane)} 


Maximum shear stress (out plane) 
τ_{max(out plane)} 


Thickness to inner radius ratio 
t/r 

* 
 
Note: * Red color :t/r > 1/20 , Green color : t/r < 1/20
Definitions:
Gauge(Gage) Pressure: The
pressure relative to atmospheric pressure. Eq: p_{g}=p_{a}p_{atm} : p_{a} is the absolute
pressure of the system and p_{atm} is atmospheric pressure.
Hoop Stress: Stress acts in
tangential direction. It's the 1^{st} principal stress.
Longitudinal stress: Stress acts
in longitudinal direction. It's the 2^{nd} principal stress.
Principal Stress: Maximum and minimum normal stress possible
for a specific point on a structural element. Shear stress is 0 at the orientation where principal stresses occur.
Shear stress: A form of a stress acts parallel to the surface (cross section) which has a cutting nature.
Supplements:
List of Equations:
Parameter 
Symbol 
Formula 
Cylindrical pressure vessel 
Hoop stress

σ_{1} 
p_{g}r/t 
Longitudinal stress 
σ_{2} 
(p_{g}r)/(2t) 
Maximum inplane shear stress 
τ_{max(in plane)} 
(p_{g}r)/(4t) 
Maximum outplane shear stress 
τ_{max(out plane)} 
(p_{g}r)/(2t) 
Spherical pressure vessel 
Hoop stress 
σ_{1} 
(p_{g}r)/(2t) 
Longitudinal stress 
σ_{2} 
(p_{g}r)/(2t) 
Maximum inplane shear stress 
τ_{max(in plane)} 
0 
Maximum outplane shear stress 
τ_{max(out plane)} 
(p_{g}r)/(4t) 
Examples:
Link 
Usage 
Pressure Vessel

An example about the calculation of stresses on a pressure vessel,
evaluation of yield criteria of material and stress transformation to find shear
and perpendicular stresses on welding of the cylindrical body of the pressure
vessel. 
Reference: