It is also important to know the working/design temperature of the tank in order to calculate and provide the proper equipment and adequate thickness of insulation.
A pressure vessel is a container designed to hold gases or liquids at a different pressure from the one outside. Usually the fluid inside the container is at a higher pressure than the one outside.
Some examples of pressure vessels are: pulsation dampeners for reciprocating compressors, distillation towers in refineries and petrochemical plants, nuclear reactor vessels, gas and liquids tanks.
In the structural design of a component under pressure, the designer receives as input a mechanical "data sheet" including all project data and specifications and his task is to size the pressure membering. The calculation complies with codes that vary depending on the destination country.
Among the most important we mention ISPESL VSR (Italy), ASME VIII Div 1 and Div 2 [1, 2] (USA), Stoomwezen (Netherlands), PD 5500 (United Kingdom), AD 2000 (Germany), Codap (France), Swedish Pressure Vessel Code (Sweden), Tbk (Norway), GOST (Russia), JIS (Japan), AS 1210 (Australia) and, within PED standards, the European code EN-13445.
Pressure vessels should be designed to operate safely at a given pressure. The pressure difference between inside and outside, in fact, creates a tension in the material of which the container is made. The designer must create a container that can withstand stress without any strain that may cause loss, damage or danger to persons or property. The pressure is the most important operational parameter, but also others cannot be neglected. The working temperature influences the material mechanical properties and can cause permanent deformation (creep phenomena). The fluids in contact with the container are also sizing parameter, as they can determine chemical attacks on materials, such as corrosion or embrittlement. Finally it is important to assess the vessel working condition, as cyclical pressure and temperature variations (fatigue stress) tend to reduce the residual life.
The parameters on which the designer can act, subject to the constraints of cost and project (maximum overall dimensions, the need for nozzles, etc. ...), are:

• shape of the container
• wall thickness
• material selection
• NDT under construction
• check in service

The most convenient form to minimize the tension in the container is spherical. In this case the voltage is:
In the formula, sigma is the voltage, p the pressure, D the diameter, s the thickness of the vessel;
if diameter and thickness are expressed in the same unit, the stress on the vessel is in the same units of pressure.
Given the practical difficulties in manufacturing a spherical vessel, the most commonly adopted form is cylindrical. In that case:
Another important detail concerning the form is the need to reduce the geometrical discontinuities such as edges, abrupt changes in thickness, notches, etc. ... These formulas are calculated using a simplified theory (membrane theory), and are used if the thickness is negligible compared to the diameter. They are applicable if the thickness is less than about 7-10% of the diameter.
After selecting the construction material, the allowable stress is set (it is closely related to the material mechanical properties). From the formulas we note the container thickness increase with increasing pressure and diameter, so that the actual stress does not exceed the allowable stress. When the thickness is no longer negligible compared to the diameter, the formulas above are no longer accurate enough, so it is necessary to assess the state of tension in each part of the container. It can be shown that in a thick vessel, with internal pressure greater than the outside one, the stress changes in the container thickness and the most stressed area is the inner one, in contact with the fluid. Once set the inner radius of the container, it is not convenient from an economical point of view, to increasing the thickness beyond a certain limit, because of the difficulties and costs that arise in the manufacturing of very thick containers. For this reason we adopt special construction solutions in order to manufacture containers under very high pressures.
All the regulations for pressure vessels, although different for the details, agree on some requirements related to their construction:

• use of materials with controlled and certified origin
• use of qualified and verified construction processes
• making of destructive and non destructive tests before the commissioning of the vessel

The first requirement comes from the importance of the allowable stress, and the constancy of this parameter in the design safety of the container.
The second requirement comes from the fact that, unless limited exceptions, pressure vessels are designed for welding of sheets, so you must ensure that the presence of welded joints does not depress the mechanical characteristics of the basic material, and in the case of containers subject to aggressive environment, that does not represent a weakness against corrosion.
Finally, the checks and controls shall ensure that the container quality complies with the standard regulations.
The stress analysis is a critical step in assessing the safety design of pressure vessels. The first adopted legislation requiring the testing of components by stress analysis was ASME Boiler and Pressure Vessel Code Sec. III (Nuclear Vessels) in 1969.
The stresses in a body subject to external loads and constraints may be due to two reasons:

• Equilibrium Stress due to the need to satisfy the equilibrium conditions for the external loads system
• Congruence Stress due to the need to comply with structure external and internal constraints

The equilibrium stresses are directly related to mechanical loads (ex. the normal stress due to the force of external traction on a prismatic bar). These stresses are independent from the frame material, so there are no internal limitation mechanisms.
The congruence stresses are related to the geometry of the body and to the external constraints system (ex. the stresses generated at the attack of a hemispherical bottom and a cylindrical shell in a pressure vessel) and are different depending on the stiffness of structures (or, slightly less accurate, depending on the elasticity of material of the structure). This implies that increasing the structure deformation, particularly if part of the structure exceeds the yield strength, these stresses are kept to the plastic limit of the material.
In some cases, both the equilibrium stresses and the congruence stresses may have a distribution that causes a significant increase of stress in a very small proportion of the material (ex. the stresses near a geometric cut-out). These stresses have the peculiarity of not being related to widespread deformation in the structure.
The ASME Boiler and Pressure Vessels provides a classification of stress by imposing different limits for different categories. In this categorization, given the particular application for which it was studied, there are some assumptions that may not always be extrapolated to other structure types.

• Primary Membrane Stress (P_m) are due to external loads in the average thickness of the container, far from discontinuities. In other words, assuming that the thickness of the vessel is infinitesimal compared to the curvature radius (here the name "membrane"), these stresses are required for the equilibrium of the acting external forces. Obviously, in case of pressure vessels, these stresses must be limited to values far enough from the limit imposed to the material, which can be both the yield strength and the breaking point. For each material and each temperature at which it can operate, the ASME Code provides the value to which these stresses are limited (S_m).
• Primary Bending Stress (P_b) are the variable stresses in the thickness of the vessel (or, in mechanical terms, the stress portion which takes into account that the load acts on one side of the container, while the stresses act on the whole thickness ). By limiting these stresses we want to reduce the risk of a complete plasticization of the section, whereas the ratio of the load causing the first section yield and the load that leads to the complete plasticization of the same section (plastic hinge) is a constant dependent only on geometry of the section (k) itself, the limit for the membrane and bending stress (P_m+P_b) is given by k*S_m, for pressure vessels k of a rectangular section is assumed, i.e. 1.5.
• Local Primary Stress (P_l) are due to mechanical loads that are generated with abrupt geometrical changes in the pressure vessel (usually at the attack between the cylindrical shell and curved bottom and at the attack of the nozzles). These stresses, due to the need of continuity in the deformed structure, have stress consistency features and cannot exceed the material yield strength. However, given their typically mechanical origin, they are subject to more restrictive limits than secondary stress.
  In practice they are always (membrane) thickness mediated stresses, and are limited to a 1.5*S_m. In this way the plasticization only at the extreme section edges is guaranteed.
• Secondary Stress (Q) are the real consistency stresses, mainly due to temperature differences between the various container sections and, especially, to the temperature differences between the inner and outer vessel sides. These stresses cannot cause the component collapse, in the case of components made of elastic-plastic materials an behaviour, since they are limited by the yield stress. In addition, if the stresses are made on an ideal perfectly plastic material (i.e. once it reaches the limit of elasticity, it does not absorb more energy to increase stress, but only for deformation increase) and if the given distortion is less than twice the stress that occurs at the elastic limit, we can prove the phenomenon called shake down, i.e., after a few cycles, the deformation stabilizes with no increase in the component lifetime. This limit is imposed by limiting the maximum stress variation (if calculated assuming a perfectly elastic material) 3*S_m.
• Peak Stress (F) occur only in material limited volumes, such as near cuts or at the interface between the container resistant material and a (cladding). These stresses can reach very high ratings, but they do not cause, under normal working conditions, an immediate structure collapse. So the peak stress are checked through fatigue analysis. The ASME regulation provides a series of curves for the materials classes used for containers, these curves representing the boundary curves envelope of the various fatiguing cycles types. In these curves we have already incorporated safety factors for both cycles and stresses, so they can be directly compared with the stresses obtained from the calculation.