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For a given material, Young's modulus is 110 $GN/m^{2}$ and shear modulus is 42 42 $GN/m^{2}$. Find the bulk modulus and lateral contraction of a round bar of 37.5mm diameter and 2.4m length

when stretched by 2.5mm. When subjected to an axial load.

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$$ \begin{array}{l}{\text { Data- } \mathrm{E}=110 \mathrm{GN} / \mathrm{m}^{2}=110 \times 10^{3} \mathrm{N} / \mathrm{mm}^{2} \mathrm{G}=42 \mathrm{GN} / \mathrm{m}^{2}=42 \times 10^{3} \mathrm{N} / \mathrm{mm}^{2}} \ {\mathrm{d}=37.5 \mathrm{mm}, \mathrm{L}=2.4 \mathrm{m}=2400 \mathrm{mm}, \delta \mathrm{l}=2.5 \mathrm{mm}} \ {\text { Find- } \mathrm{K}=?, \delta \mathrm{b}=?}\end{array} $$ $$ \begin{array}{l}{\text { To Calculate Possion's ratio }(\mu) :} \ {E=2 G(1+\mu)} \ {110 \times 10^{3}=2 \times 42 \times 10^{3}(1+\mu)} \ {\mu=0.309}\end{array} $$ $$ \begin{array}{l}{\text { To Calculate change in diameter( } \delta \mathrm{d}) :} \ {\mu=\frac{\text {Lateral Strain}}{\text {Linear Strain}}=\left(\frac{e_{L}}{e}\right)=\frac{(\delta d / d)}{\left(\delta_{L} / L\right)}} \ {0.309=\frac{(\delta d / 37.5)}{(2.4 / 2400)}} \ {\delta d=0.012 m m}\end{array} $$

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