» Pressure Vessels
PRESSURE VESSELS are used to contain gasses or liquids under (high) pressure. There are two common shapes: cylindrical and spherical. Due to internal pressure, the walls of pressure vessels are generally in tension. Pressure vessels can often be considered to be thin-walled (the wall thickness is much less than the vessel's radius). A vessel is generally considered to be thin-walled if t < 0.1R (or R > 10t).

» Cylindrical Pressure Vessels
Some examples of CYLINDRICAL PRESSURE VESSELS include propane tanks, fire extinguishers, shaken soda cans, and boilers. Cylindrical Pressure Vessels are subjected to two types of stresses: Hoop (Circumferential) Stress, s_H and Axial (Longitudinal) Stress, SL These stresses are derived by taking a cuts through the cylinder and noting that the forces that act across that cut must sum to zero:

» Spherical Pressure Vessels
Due to the 3-dimensional symmetry of SPHERICAL PRESSURE VESSELS, stress is generally uniform throughout. The stresses in Spherical Pressure Vessels (called Spherical Stress, s_S ) is calculated in the same fashion as with Cylindrical Pressure Vessels:

F = 0     ppR² = s_S(2pRt)

sS = pR 2t

» Deformation of Pressure Vessels
DEFORMATION of Cylindrical and Spherical Pressure Vessels can be derived from the stresses using Hooke's Law. Because of the biaxial stress state, the Poisson Effect must be considered.

Pressure Vessel	Stress/Strain Elements	Strains (the reader should be able to derive these)	DR, DL
Cylinder
Sphere