Lame’s equations are applicable for

Explanation

Lame's equation is used to find the thickness of the thick cylinder subjected to internal pressure, it is given by,

\(t = \frac{{{D_i}}}{2}\left[ {\sqrt {\frac{{{\sigma _t} + {P_i}}}{{{\sigma _t} - {P_i}}}} - 1} \right]\)

Where,

t = thickness of thick cylinder,

Di = Internal diameter of the thick cylinder, σt = Allowable tensile stress in the material of thick cylinder, Pi = Internal pressure in the thick cylinder

Important Points

• Lame's equation is based on the maximum principal stress theory of failure, as this theory is more suitable for brittle materials, Lame's equation is also applicable to brittle materials like Cast iron or Cast Steel.

Additional Information

Clavarino's equation is used to find the thickness of the cylinder when the material is ductile and the cylinder has closed ends, it is given by

\(t = \frac{{{D_i}}}{2}\left[ {\sqrt {\frac{{{\sigma _t} + \left( {1 - 2μ } \right){P_i}}}{{{\sigma _t} - \left( {1 + μ } \right){P_i}}}} - 1} \right]\)

Birnie's equation is used to find the thickness of thick cylinders, which are made up of ductile material and has open ends, it is given by

\(t = \frac{{{D_i}}}{2}\left[ {\sqrt {\frac{{{\sigma _t} + \left( {1 - μ } \right){P_i}}}{{{\sigma _t} - \left( {1 + μ } \right){P_i}}}} - 1} \right]\)

μ is the Poisson's ratio