Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Neutral Axis - Does it move?

  1. Sep 17, 2007 #1
    Hi

    Consider a symmetrical beam, where as we know the Neutral Axis (NA) would be at the Geometric Center. If that beam was simply supported at both ends, there would be equal tension and compression to ensure that beam was in equilibrium.

    Now if we applied a vertical load, downwards, in the center, the beam would sag and be in compression at the top and tension on the bottom. My question is: Would the NA move to accommodate the increase in tension on the bottom surface? If it doesn't, how can this be, as tension has increased?

    Thanks in advance...
     
  2. jcsd
  3. Sep 17, 2007 #2
    Hi

    Consider a symmetrical beam, where as we know the Neutral Axis (NA) would be at the Geometric Center. If that beam was simply supported at both ends, there would be equal tension and compression to ensure that beam was in equilibrium.

    Now if we applied a vertical load, downwards, in the center, the beam would sag and be in compression at the top and tension on the bottom. My question is: Would the NA move to accommodate the increase in tension on the bottom surface? If it doesn't, how can this be, as tension has increased?

    Thanks in advance...
     
  4. Sep 17, 2007 #3

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    Yes it does, but not enough to bother about if you are doing a conventional beam bending analysis.

    The cross section also deforms because of Poisson's ratio. The tension side gets narrower, the compression side gets wider, and the top and bottom surfaces curve (anti-clastic curvature).

    You can see this easily if you bend short, thick, flexible beam - e.g. a rectangular-block-shaped pencil eraser.
     
  5. Sep 17, 2007 #4

    radou

    User Avatar
    Homework Helper

    Well, the term "neutral axis" refers to a situation where the beam *is* loaded. What exactly is your question?
     
  6. Sep 17, 2007 #5
    Thanks AlephZero.

    Good point about Possion's Ratio, I never really appreciated that in beam bending. Thanks for the eraser analogy too, I like to keep things simple.

    So just to confirm, when the beam is relaxed, in equilibrium, there will be no stress at the top or the bottom. But when it hogs, we get compression on the top and tension on the bottom. My friend was saying that there is always some stress on the top and bottom, but I can't see this.

    Thanks again...
     
  7. Sep 17, 2007 #6

    FredGarvin

    User Avatar
    Science Advisor

    It depends on just how technical you want to get in regards to what your friend is saying. Technically, every beam will deflect slightly under its own weight. So in that context, yes. There is always a slight tensile and compressive stress in a beam.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?