Analysis & loading · Sections & mechanics

Thick-walled cylinder (Lamé) calculator

Hoop and radial stresses at the bore and outside surface under internal and external pressure, with von Mises at the bore.

Standard: Lamé equations

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Diagram for the worked example

A = (pi ri² − po ro²)/(ro² − ri²) = (40*50^2-0*80^2)/(80^2-50^2) = 25.641 MPa
B = (pi − po) ri² ro²/(ro² − ri²) = (40-0)*50^2*80^2/(80^2-50^2) = 1.641e+5 N
Hoop at bore A + B/ri² = 25.641+1.641e+5/50^2 = 91.282 MPa
Radial at bore −pi = -40 = -40 MPa
Hoop at outside = 25.641+1.641e+5/80^2 = 51.282 MPa
von Mises at bore (σz = A) = SQRT(((91.282--40)^2+(-40-25.641)^2+(25.641-91.282)^2)/2) = 113.69 MPa

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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.