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Mechanical - Deflection and Slope, cantilever beam

  1. Mar 27, 2014 #1
    Hi guys, I have been a question to solve this week to do with deflections and slopes at the free end of a cantilever beam. I have calculated the deflection and slope for the point load and UDL, but I'm not sure whether to add them together or not?.. as they're both acting on the beam?

    A cantilever beam with a length of 7meters, has a 2KN point load at the free end and a UDL of 3KN/m along its length. Calculate the deflection and slope at the free end. *Assume the flexural stiffness [EI]is 800MPa.


    This is what I've calculated so far, some steps have been omitted:

    For the point load
    dy/dx = (FL^2) / 2EI

    dy/dx = 61.25x10^-6


    y = (FL^3) / 3EI
    y = 285.83μm

    For the udl:
    dy/dx = (wL^3) / 6EI

    dy/dx =214.4x10^-6


    y = (wL^4) / 8EI
    y = 1.12mm

    Now what? Do i add them?
    Thanks,
     
  2. jcsd
  3. Mar 27, 2014 #2

    SteamKing

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    Yes. Beams are subject to superposition for small deflections.
     
  4. Mar 27, 2014 #3
    Okay, what does that mean?

    I add the deflections together? What about the slopes?
     
    Last edited: Mar 27, 2014
  5. Mar 27, 2014 #4

    SteamKing

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  6. Mar 27, 2014 #5
    If the deflections add, then the slopes, which are their derivatives, must add also.

    Chet
     
  7. Mar 27, 2014 #6
    Nice source, thanks guys
     
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