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Strength of Materials

Strain Energy due to Gradually Applied Load and Shear Stress

A mild steel ...

Question

A mild steel bar of uniform cross-section A and length L is subjected to an axial load W. The strain energy stored in the bar would be

A

\frac{W L}{2 A E}

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B

\frac{W^{2} L}{4 A E}

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C

\frac{W L}{4 A E}

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D

\frac{W^{2} L}{2 A E}

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Solution

The correct option is D $\frac{W^{2} L}{2 A E}$
Deformation in the bar, $Δ = \frac{W L}{A E}$

$S t r a i n e n e r g y = \frac{1}{2} W Δ = \frac{W^{2} L}{2 A E}$

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