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A bar of 16mm diameter is subjected to a pull of 30kN.The measured extension on gauge length of 80mm is 0.06mm and change in diameter is 0.0036mm. Calculate Poisson's ratio , Yo modulus and bulk modul
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Data: d=30 mm, L=200 mm, P =60 kN, δL=0.09 mm, δd = 0.0039 mm Calculate: μ and E

$\mathrm{A}=\frac{\pi \mathrm{d}^{2}}{4}=\frac{\pi \times 30^{2}}{4}=706.858 \mathrm{mm}^{2}$

$\mathrm{E}=\frac{\mathrm{PL}}{\mathrm{A} \delta_{\mathrm{L}}}=\frac{60 \times 10^{3} \times 200}{706.858 \times 0.09}=188628.08 \mathrm{N} / \mathrm{mm}^{2}$

$\mathrm{E}=1.89 \mathrm{N} / \mathrm{mm}^{2}$

$\begin{aligned} \mu &=\frac{\text { Lateral Strain }}{\text { Linear Strain }} \\ \mu &=\frac{\left(\frac{\delta_{\mathrm{d}}}{\mathrm{d}}\right)}{\left(\frac{\delta_{\mathrm{L}}}{\mathrm{L}}\right)}=\frac{\left(\frac{0.0039}{30}\right)}{\left(\frac{0.09}{200}\right)}=0.29 \\ \mu &=0.29 \end{aligned}$

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