Lame’s equations are applicable for

This question was previously asked in

UPPSC AE Civil 2019 Official Paper I (Held on 13 Dec 2020)

Option 1 : Thick cylinder

**Explanation**

**Lame's equation is used to find the thickness of the thick cylinde**r 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