A cylindrical specimen of some metal alloy having an elastic modulus of 108 GPa and an original cross-sectional diameter of 3.7 mm will expe

Question

A cylindrical specimen of some metal alloy having an elastic modulus of 108 GPa and an original cross-sectional diameter of 3.7 mm will experience only elastic deformation when a tensile load of 1890 N is applied. Calculate the maximum length of the specimen before deformation if the maximum allowable elongation is 0.45 mm.

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Khánh Gia 5 years 2021-09-05T07:53:15+00:00 1 Answers 55 views 0

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  1. Sigrid
    0
    2021-09-05T07:55:06+00:00
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    Answer:

    L= 276.4 mm

    Explanation:

    Given that

    E= 180 GPa

    d= 3.7 mm

    F= 1890 N

    ΔL= 0.45 mm

    We know that ,elongation due to load F in a cylindrical bar is given as follows

    \Delta L =\dfrac{FL}{AE}

    L=\dfrac{\Delta L\times AE}{F}

    Now by putting the values in the above equation we get

    L=\dfrac{0.45\times 10^{-3}\times \dfrac{\pi}{4}\times (3.7\times 10^{-3})^2\times 108\times 10^9}{1890}\ m

    L=0.2764 m

    L= 276.4 mm

    Therefore the length of the specimen will be 276.4 mm

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