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14 May, 17:58

A square steel bar has a length of 8.4 ft and a 2.1 in by 2.1 in cross section and is subjected to axial tension. The final length is 8.40392 ft. The final side length is 2.09967 in. What is Poisson's ratio for the material

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  1. 14 May, 18:24
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    Poissons ratio = - 0.3367

    Explanation:

    Poissons ratio = Lateral Strain / Longitudinal Strain

    In this case, the longitudinal strain will be:

    Strain (longitudinal) = Change in length / total length

    Strain (longitudinal) = (8.40392 - 8.4) / 8.4

    Strain (longitudinal) = 4.666 * 10^ (-4)

    While the lateral strain will be:

    Strain (Lateral) = Change in length / total length

    Strain (Lateral) = (2.09967 - 2.1) / 2.1

    Strain (Lateral) = - 1.571 * 10^ (-4)

    Solving the poisson equation at the top we get:

    Poissons ratio = - 1.571 / 4.666 (10^ (-4) cancels out)

    Poissons ratio = - 0.3367
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