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### Thin Walled Sphere Stress Equations and Calculator

Pressure Vessel Design Formula and Calculators Resources

**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

Preview: Thin Walled Sphere Stress Pressure Vessel Calculator

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:

σ_{sph} = ( p_{i} r_{m} ) / ( 2 t )

Where:

p_{i} = internal gage - pressure meaning above atmospheric pressure ( psi, MPa ),

r_{m} = 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:

- Pressure Vessel External Pressure Calculations
- Pressure Vessel, Thin Wall Hoop and Longitudinal Stresses Equation and Calculator
- Pressure Vessel Design Calculations Handbook
- Identifying and Reducing Stresses in Pressure Vessels

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