Strength of Materials

10.6 THICK SPHERICAL SHELLS

Let a spherical shell of external radius, R_e, and internal radius, R_i, 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).

 

 

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 e_c and e_r be circumferential strain and radial strain, respectively.

 

∴

 

i.e.,

 

Similarly

i.e.,

 

From Equation (10.30)