Question 26.3.42: The strain energy stored in a body of volume V subjected to ...

The strain energy stored in a body of volume V subjected to uniform stress σ is

(a) \frac{σ × E}{V}              (b) \frac{σE^2}{V}              (c) \frac{σ × V^2}{E}              (d) \frac{σ^2}{2E} × V.

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(d)

EXPLANATION

The maximum stress induced in a thin cylinder is hoop stress (σ_c). It is given by

\sigma_c=\frac{p \times d}{2 t}

The maximum hoop stress produced in spherical vessel = \frac{p \times d}{4 t}

∴            \frac{\text { Max. stress in cylindrical vessel }}{\text { Max. stress in spherical vessel }}=\frac{\frac{p d}{2 t}}{\frac{p \times d}{4 t}}=2.0 .

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