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A circular section bar is 2.5 m long and has a diameter of 60 mm. When subjected to a compressive load of 30 kN it shortens by 0.20 mm. Determine Young's modulus of elasticity for the material of the bar. |
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Answer» Force, F = 30 kN = 30000 N and cross-sectional area A \(\pi\)r2 = \(\left(\cfrac{60\times10^{-3}}2\right)^2\) = 2.8274 x 10-3 m2 Stress \(\sigma\) = \(\cfrac FA\) = \(\cfrac{30000}{2.8274\times10^{-3}}\) = 10.61 MPa Bar shortens by 0.20 mm = 0.00020 m Stress \(\sigma\) = \(\cfrac XL\) = \(\cfrac{0.00020}{2.5}\) = 0.00008a Modulus of elasticity, E = \(\cfrac{stress}{strain}\) = \(\cfrac{10.61\times10^6}{0.00008}\) = 132.6 x 109 = 132 .6 Gpa |
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