KEVOS® MAKEOS · Strength
Spherical Shell under Internal Pressure
What stress does internal pressure cause in this spherical vessel or dished end?
Membrane stress of a thin sphere and the maximum (inner surface) stress of a thick sphere by Lamé’s equations, with the safety factor and the thickness needed for an allowable stress.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Inside diameter | mm | Inside diameter of the sphere or hemispherical head. |
| Wall thickness | mm | Minimum wall thickness. |
| Internal pressure (gauge) | MPa | Internal gauge pressure. |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
Method and formulas
- Thin sphere: σ = p d ÷ 4t (half the hoop stress of a cylinder of the same diameter).
- Thick sphere (Lamé), inner surface: σt = p (ro³ + 2ri³) ÷ 2(ro³ − ri³).
- Thickness for the required factor (thin wall): t = p d × factor ÷ 4 Sy.
- Example: a 600 mm sphere 6 mm thick at 2 MPa has 50 MPa membrane stress.
Limitations
- Elastic stress away from nozzles, supports and welds.
- Pressure equipment must be designed to its code (AS 1210, ASME VIII).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check spherical tanks, floats and hemispherical heads
- Find the thickness for a spherical pressure part
- Compare spheres with cylinders
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Thin-wall membrane stress
- Thick-wall maximum stress (Lamé)
- Safety factor and thickness for the required factor
Interpreting the result
- A sphere needs about half the wall thickness of a cylinder of the same diameter and pressure.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 290–294. Topic reference; no source tables or recommended settings are reproduced.
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