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Help with a BMD and deflection of beam problem

  1. Oct 19, 2016 #1
    1. The problem statement, all variables and given/known data

    I am given this beam:
    tw6EEJz.jpg
    imgur link: http://i.imgur.com/tw6EEJz.jpg

    and asked to express the slope at A and the max deflection in terms of a, E, I, and Mo.

    I am being told that my answer has the wrong multiplier...so I assume that my overall approach is ok (??) but I've missed dividing something by 2 somewhere or something like that.

    I transform that above diagram into an equivalent:
    uevlWxU.jpg
    imgur link: http://i.imgur.com/uevlWxU.jpg

    (I whited out the bending moments, pretend they aren't there anymore)

    I figure those same bending moments could be produced by a load P like the one I've drawn.

    Doing that leads to the shear force and bending moment diagrams that look something like this:

    mShbv37.png

    The lines on the BMD are [itex]y = \frac{P}{2}x[/itex] and [itex]]y = \frac{-P}{2}x+\frac{3Pa}{2}[/itex]

    Thus I get [itex]P = \frac{2Mo}{a}[/itex]

    and I have the equations [itex]v_{max}=\frac{-PL^3}{48EI}[/itex] and [itex]\theta_{max}=\frac{-PL^2}{16EI}[/itex]

    Now that I have P in terms of Mo and a, and L = 3a, through basic substitution I get [itex]v_{max}=\frac{-9M_0a^2}{8EI}[/itex] and [itex]\theta_{max}=\frac{-9M_0a}{8EI}[/itex]

    It does seem strange to me that the constant is the same out the front of both, and I am being told that my multiplier out the front is wrong. What have I missed?

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Oct 24, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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