Thick-Wall Cylinder Calculator (Lamé)
Bore stress of hydraulic cylinders and HP tubing where thin-wall lies.
Stress crowds the bore — adding wall helps less and less (k→∞ still leaves σ = P). Past ~σ_allow/2 working pressure, autofrettage or compound shrink-fit cylinders take over.
Formula
Thick-Wall Cylinder Calculator (Lamé) is a free lame equations for mechanical and machine-design engineers — instant, accurate and 100% client-side, with the governing formula and reference shown next to the result so the number can be defended, not just quoted.
About Thick-Wall Cylinder Calculator (Lamé)
Bore stress of hydraulic cylinders and HP tubing where thin-wall lies. The calculation implements σ_θ(r_i) = P(k²+1)/(k²−1), k = r_o/r_i (Lamé (1833); high-pressure design). Stress crowds the bore — adding wall helps less and less (k→∞ still leaves σ = P). Past ~σ_allow/2 working pressure, autofrettage or compound shrink-fit cylinders take over.
How to use Thick-Wall Cylinder Calculator (Lamé)
- 1Enter Internal pressure in MPa.
- 2Enter Inner radius in mm.
- 3Enter Outer radius in mm.
- 4Read Hoop stress at bore (max), Hoop at outside instantly — no submit button needed.
- 5Need US units? Flip the SI/Imperial toggle and every field converts.
Why use Thick-Wall Cylinder Calculator (Lamé)?
- ✓Implements the standard formula — σ_θ(r_i) = P(k²+1)/(k²−1), k = r_o/r_i
- ✓Reference cited on-page: Lamé (1833); high-pressure design
- ✓One-click SI ⇄ Imperial toggle — values convert in place, physics stays in SI
- ✓Live worked example: the substitution recomputes from your numbers
- ✓Runs entirely in your browser — nothing uploaded, free forever
Frequently asked questions
What formula does the Thick-Wall Cylinder Calculator (Lamé) use?+
It computes σ_θ(r_i) = P(k²+1)/(k²−1), k = r_o/r_i, per Lamé (1833); high-pressure design. The formula is displayed under the result along with a worked example substituted with your own inputs.
What should I keep in mind when using this calculator?+
Stress crowds the bore — adding wall helps less and less (k→∞ still leaves σ = P). Past ~σ_allow/2 working pressure, autofrettage or compound shrink-fit cylinders take over.
Is this suitable for machine design coursework?+
Yes — these are the exact Shigley/Machinery's-Handbook formulas, with the substitution shown step by step, so you can follow the worked example into your own calculation sheet.
Is the Thick-Wall Cylinder Calculator (Lamé) free to use?+
Yes — completely free, no sign-up, no limits. It runs client-side in your browser, so inputs stay private and results are instant even on slow connections.
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