How to use the Thin Cylinder Stress Calculator
- 1. Pick the vesselThin cylinder or thin sphere, and whether you need stresses or thickness.
- 2. Enter the dataPressure, diameter, thickness, joint efficiencies, E and ν.
- 3. Read the resultsHoop and longitudinal stress, strains, and the change in volume.
Thin shell formulas
- Hoop stress σh = pd / (2t), divided by the longitudinal joint efficiency.
- Longitudinal stress σl = pd / (4t), divided by the circumferential joint efficiency.
- Sphere: σ = pd / (4t) in every direction.
- Change in diameter δd = (pd² / 2tE)(1 − ν/2).
- Change in length δL = (pdL / 2tE)(1/2 − ν).
- Volumetric strain = (pd / 2tE)(5/2 − 2ν) for a cylinder and 3(pd / 4tE)(1 − ν) for a sphere.
Thin-shell theory needs a thickness below about d/20. For thicker walls, use Lamé's thick cylinder equations.
Worked example and exam tips
A cylinder 3 m long and 1 m in diameter has a 15 mm wall and an internal pressure of 1.5 N/mm². E = 200 GPa and ν = 0.3. σh = 1.5 × 1000 / 30 = 50 MPa and σl = 25 MPa. δd = 0.2125 mm, δL = 0.15 mm and δV = 1.119 × 10⁶ mm³ (about 1.12 litres).
- The hoop stress is twice the longitudinal stress, so a cylinder splits along its length.
- Joint efficiency reduces the strength, not the strain. Use the plain-plate stresses to find δd and δV.
- 1 MPa = 1 N/mm² = 10 bar. Keep pressure in N/mm² and lengths in mm.
Frequently asked questions
Why is hoop stress twice the longitudinal stress?
The force bursting the cylinder along its length acts over a strip of length L, while the end force acts over the smaller ring area πdt. Working this out gives pd/2t against pd/4t.
Which joint efficiency goes where?
The longitudinal seam carries the hoop stress, so its efficiency divides σh. The circumferential seam carries the longitudinal stress.
When can I use thin-cylinder theory?
When the wall thickness is less than about one-twentieth of the diameter, so the stress is nearly uniform through the wall.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.