Calculate elastic stresses in a closed-end cylinder or sphere under internal and external pressure. The main calculation includes all three principal stresses in von Mises stress. It does not certify code compliance or external-pressure stability.
S = σY/3 (assumed); thin-wall reference: t = pi ri/S (cylinder), pi ri/(2S) (sphere), po = 0
Model and input definitions
The model assumes homogeneous, isotropic linear elasticity. The cylinder has closed ends and is evaluated away from end effects. The main calculation always uses a Lamé solution, regardless of the thin-wall badge.
Reproduce a result
Enter inner radius ri and wall thickness t in mm, pressures pi and po in MPa, then choose material and cylinder or sphere.
Read the main hoop stress, inner-wall radial stress and maximum three-dimensional von Mises stress.
The upper animation is a separate thin-wall demonstration with its own pressure slider. It excludes external pressure and is not the main calculation.
Worked example
Closed cylinder: ri=250 mm, t=25 mm, pi=10 MPa, po=0, SS400. With ro=275 mm, A=47.619 MPa and B/ri²=57.619 MPa at the bore, σθ=105.2 MPa, σr=−10.0 MPa and σz=47.6 MPa. The three-component von Mises stress is 99.8 MPa, giving 245/σvM=2.45. Changing only the geometry to a sphere gives σvM=60.3 MPa.
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What should I check in this example?
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Change one input at a time and compare the formula with the displayed result. The upper animation is a separate thin-wall demonstration with its own pressure slider. It excludes external pressure and is not the main calculation.
Limits and interpretation
The reference thickness inverts the thin-wall hoop-stress equation using an assumed S=σY/3. It is not an ASME calculation using code allowable stresses, joint efficiency, corrosion allowance or temperature corrections. It is unavailable when external pressure is nonzero. Buckling, fatigue, creep, nozzles and residual stresses require separate evaluation.
Frequently asked questions
No. The main solver always uses the cylinder or sphere Lamé solution. t/ri<0.1 is only an indication for considering a thin-wall approximation.
Radial stress is not negligible in thick walls. A closed cylinder also has axial stress, and a sphere has two equal tangential stresses.
No. It is an educational estimate with an assumed allowable stress, not a code-compliance or manufacturing approval check.
No. Elastic stresses can be calculated, but buckling may govern even when the displayed stresses are small.
Checks cover displayed units, reference calculations, input sensitivity, boundary conditions and cross-language results. They do not certify code compliance or real-world accuracy.