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Math Help - Bending moment

  1. #1
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    Bending moment

    Hello .the question is ,The bending moment,M.at a position x m from the end of a simply supported beam of lenght l m carrying a uniformly distrbuted load
    of wkNm-1 is given by
    M= w/2 l (l -x)-w/2 (l-x)^2
    Show using the above expression, that the maximum bending moment occurs atthe mid point of beam and determines its value interms of w and l
    I have not got a clue !
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  2. #2
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    Quote Originally Posted by Jaffa View Post
    Hello .the question is ,The bending moment,M.at a position x m from the end of a simply supported beam of lenght l m carrying a uniformly distrbuted load
    of wkNm-1 is given by
    M= w/2 l (l -x)-w/2 (l-x)^2
    Show using the above expression, that the maximum bending moment occurs atthe mid point of beam and determines its value interms of w and l
    I have not got a clue !
    your notation leaves much to be desired. Is the equation ...

    M = \frac{w}{2} L(L-x) - \frac{w}{2} (L-x)^2

    or

    M = \frac{w}{2L(L-x)} - \frac{w}{(L-x)^2}

    or something else?
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  3. #3
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    Sorry , the first one is how it is meant to be, hope you can help
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  4. #4
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    M = \frac{w}{2} L(L-x) - \frac{w}{2} (L-x)^2

    \frac{dM}{dx} = -\frac{w}{2}L + w(L-x)

    set \frac{dM}{dx} = 0

    w(L-x) = \frac{w}{2}L

    L-x = \frac{L}{2}

    x = \frac{L}{2}

    \frac{d^2M}{dx^2} = -w < 0 ... x = \frac{L}{2} is where M will be a maximum

    substitute \frac{L}{2} for x in the original equation and determine the maximum value of M.
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  5. #5
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    Thanks for your help,makes things clearer.
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