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Strength of Materials by V. Ramasamy, P. Purushothama Raj

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10.6 THICK SPHERICAL SHELLS

Let a spherical shell of external radius, Re, and internal radius, Ri, be subjected to an internal fluid pressure p be considered.

Also, an elemental disc of the spherical shell of thickness dr at a radial distance r subtending an angle of dθ at centre is considered (Figure 10.3).

 

Spherical shell subjected to internal pressure

 

Fig. 10.3 Spherical shell subjected to internal pressure.

 

Let the radius be increased to (r + u) and the thickness to (dr + du) due to the internal fluid pressure.

Let ec and er be circumferential strain and radial strain, respectively.

 

 

i.e.,

 

Similarly

i.e.,

 

From Equation (10.30)

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