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Thread: Strength Of A Beam

  1. #1
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    Strength Of A Beam

    Hi All,

    Not sure if this is in the right section, but would love your help with this.


    Engineers have determined that the strength s of a rectangular beam varies as the product of the width w and the square of the depth d of the beam, that is, s = kwd² for some constant k. Find the dimensions of the strongest rectangular beam that can be cut from a cylindrical log with diameter 48cm.

    Cheers
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Joel View Post
    Hi All,

    Not sure if this is in the right section, but would love your help with this.


    Engineers have determined that the strength s of a rectangular beam varies as the product of the width w and the square of the depth d of the beam, that is, s = kwd² for some constant k. Find the dimensions of the strongest rectangular beam that can be cut from a cylindrical log with diameter 48cm.

    Cheers
    find d with respect to w or find w with respect to d then sub it in the equation after that find the derivative and see the extreme max point I think the relation between them can given by

    24^2=\frac{d^2}{2^2} + \frac{w^2}{2^2}

    24 is the radius of the base of the cylinder

    d^2=4( 24^2 - \frac{w^2}{4} )

    d=2\left(\sqrt{24^2-\frac{w^2}{4}}\right) sub this in the equation of s

    s=kw\left(2\left(\sqrt{24^2-\frac{w^2}{4}}\right)\right)^2

    s=4kw\left( 24^2 - \frac{w^2}{4} \right)

    find the derivative of s to find the extreme value that will be w then sub it in this equation to find d

    24^2=\frac{d^2}{2^2} + \frac{w^2}{2^2}



    Strength Of A Beam-rty.jpg

    I wish that help
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