Derive expression for strain energy
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The expression for strain energy is 1/2 × stress × strain.
The energy stored in a body is the strain energy, and the per unit volume is strain energy density, when a work is done on it by an external force to stretch or deform the body.
Strain energy = U = 0.5 Fl, where f is external force applied to produce an extension 'i.
The strain energy density, u = U/V = (0.5 F l)/V
or u = 1/2 F/A l/L where A is the area and L is the length of the body before the external force is applied V = AL)
or u = 1/2 × stress × strain
Thus the energy density of a strained wire or the potential energy per unit volume of a stretched wire is derived.
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