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Birnie's Formula and Calculator for Thick-walled Cylinders of Ductile Material

Fluids Engineering and Design
Pressure Vessels Design and Engineering

Thick-walled Cylinders of Ductile Material, Open Ends Birnie's Formula and Calculator

Birnie's Formula is applicable to cylinders with open ends made of ductile materials. Maximum principal strain theory is taken in this case

A cylinder is considered to be thin-walled when the ratio of wall thickness to inside diameter is 0.1 or less and thick-walled when this ratio is greater than 0.1. Materials such as cast iron, hard steel, and cast aluminum are considered to be brittle materials; low-carbon steel, brass, bronze, etc. are considered to be ductile.

Preview: Birnie's equation thick-walled cylinders of ductile material Calculator

Birnie's Formula


p = internal pressure, psi;
D = inside diameter of cylinder, inches;
t = wall thickness of cylinder, inches;
S = allowable tensile stress, psi.
μ = Poisson’s ratio, = 0.3 for steel, 0.26 for cast iron, 0.34 for aluminum and brass;

If metric SI units are used, then:

p = internal pressure in newtons per square meter
D = internal diameter of shell in meter
S = safe tensile stress in newtons per square meter
t = thickness of metal in the shell, in meter

Reference: Machinerys Handbook 30th Edition