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Math Help - Qudratic equation for bending point

  1. #1
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    Derry
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    Qudratic equation for bending point

    I have completed an assignment but for this 1 question, any help would be appreciated

    In construction it is important to be aware of weak points in a beam to ensure they can hold the maximum possible weight
    The bending moment M at a point in a beam is given by the formula below

    3x(20-x)
    M = _______

    2

    Where x metres is the distance from the point of support. Calculate the value of x when the bending moment is Nm. A trial and error method will not be accepted.
    Attached Thumbnails Attached Thumbnails Qudratic equation for bending point-qudratic-equation.jpg   Qudratic equation for bending point-qudratic-equation.png  
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Qudratic equation for bending point

    If the bending moment is Nm then we have:

    Nm=\frac{3x(20-x)}{2}

    Multiply through by 2, then distribute on the right:

    2Nm=60x-3x^2

    Arrange quadratic in standard form:

    3x^2-60x+2Nm=0

    Now, apply the quadratic formula to find x.
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