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Question 3.209: A 0.5-m-long steel rod with a 1-cm diameter is stretched in ...

A 0.5-m-long steel rod with a 1-cm diameter is stretched in a tensile test. What is the required work to obtain a relative strain of 0.1%? The modulus of elasticity of steel is 2 × 10^{8} kPa.

 

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-_{1} W _{2}=\frac{ AEL _{0}}{2}( e )^{2}, \quad A =\frac{\pi}{4}(0.01)^{2}=78.54 \times 10^{-6} m ^{2}

 

-{ }_{1} W _{2}=\frac{1}{2} \times 78.54 \times 10^{-6} m ^{2} \times 2 \times 10^{8} kPa \times 0.5 m \left(10^{-3}\right)^{2}

 

= 3.93 J

 

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