Engineering

Question

A copper alloy cylinder that is 1.3 feet long with a diameter of 45.27 inch is subjected to a tensile stress of 1,140 psi along its length. Assuming this applied stress is purely elastic, calculate the diameter, in inches, of the cylinder under this load. For this alloy, the elastic modulus is 904,672 psi and the Poisson's ratio is 0.33.

1 Answer

  • Answer:

    diameter = 45.251 inches

    Explanation:

    initial length = 1.3

    initial diameter = 45.27

    tensile stress = σ = 1140

    modulus E = 904672

    v = 0.33

    we calculate longitudinal strain = σ/E

    = 1140/904672

    = 0.0012601252

    general relation for

    v = -Ed/El

    [tex]0.33=\frac{-Ed}{0.0012601252}[/tex]

    we cross multiply

    -Ed = 0.33 x 0.0012601252

    = -0.00041584132in

    [tex]\frac{df - 45.27}{45.27} =\frac{-0.00041584132}{1}[/tex]

    when we cross multiply,

    df - 45.27 = -0.00041584132*45.27

    df - 45.27 = -0.018825136

    df = -0.018825136 + 45.27

    df = 45.251 inches

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