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Strength of Materials

Elastic Constants

A bar of 40 m...

Question

A bar of 40 mm diameter and 400 mm length is subjected to an axial load of 100 kN. It elongates by 0.150 mm and the diameter decreases by 0.005 mm. What is the Poisson's ratio of the material of the bar?

A

0.25

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B

0.28

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C

0.33

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D

0.37

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Solution

The correct option is C 0.33
Longitudinal strain $= \frac{Δ L}{L} = \frac{0.150}{400} = 3.75 \times 10^{- 4}$
Lateral strain $= \frac{Δ d}{d} = - \frac{0.005}{40} = - 1.25 \times 10^{- 4}$
Poisson's ratio $= - \frac{Lateral strain}{Longitudinal strain} = 0.33$

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