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Slope and deflection of beam sample problem question

  1. Sep 19, 2013 #1
    1. The problem statement, all variables and given/known data
    The sample question explains how I can use superposition to determine the slope and deflection of the beam. I have made a picture of the page. I know how to use the method as I've used it on other, much difficult problems. However, this sample problem has been stuck in my head for a quite long time. The problem starts by determining the deflection at the end of the beam. I've underlined the equation where I'm confused.

    This is the sample problem.

    https://www.dropbox.com/s/x025uvs253hne0f/Sample problem.jpg

    I understand that by superposing the beam into two seperate loadings, you can add the maximum deflection of those two in order to attain the maximum deflection of the original beam. In loading II, the beam goes straight half through so the angle is the same at the end of the beam. But in the book, they multiplied the angle with length of the part that goes straight. I have absolutely no idea why they did that. The angle is in radians and within my knowledge it made no sense to me.

    2. Relevant equations

    Case 1

    http://4.bp.blogspot.com/-wVZ-cJsAc...QgKKf2Q/s1600/beam+deflections+and+slopes.png

    3. The attempt at a solution

    I converted the angle into degrees and then used sinus on that. Then I multiplied with the length of the straight beam but that didn't really gave me the answer I hoped for. I tried to look on the internet up if there was a relation between them but I couldn't find the answer.


    A huge thanks to anyone who can explain to me what they did!
     
    Last edited: Sep 19, 2013
  2. jcsd
  3. Sep 19, 2013 #2

    SteamKing

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    For small angles (in radian measure), sin(theta) is approximately equal to theta.
     
  4. Sep 20, 2013 #3
    Thanks alot!
     
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