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### Thin Walled Sphere Stress Equations and Calculator

Thin Walled Sphere Stress Pressure Vessel Equations and Calculator

Thin-walled vessels are typically either spherical or cylindrical. Other geometries are possible, but their complexity precludes their inclusion in this webpage. Pressure vessels can be considered thin if the diameter is greater than ten times the thickness of the wall.

Spherical Pressure Vessel Geometry

Spherical Pressure Vessel Geometry

Spheres. For the thin-walled spherical pressure vessel shown in Fig. 1, the normal stress (σsph) in the wall of the sphere is given by:

σsph = ( pi rm ) / ( 2 t )

Where:

pi = internal gage - pressure meaning above atmospheric pressure ( psi, MPa ),
rm = mean radius -can be assumed to be the inside radius of the sphere ( in, m ),
t = wall thickness ( in, m ).

External pressure on any thin-walled vessel causes buckling of the vessel wall long before excessive stress is reached. The study of the buckling of thin-walled vessels is very complex, and is beyond the scope of this document.

Related:

Source:

Marks' Calculations for Machine Design,
Thomas H. Brown, Jr. Ph.D., PE
Faculty Associate
Institute for Transportation Research and Education
NC State University
Raleigh, North Carolina