Does the Neutral Axis Move in a Symmetrical Beam?

[ripson]

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...

 

[ripson]

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...

 

[AlephZero]

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.

 

[radou]

Well, the term "neutral axis" refers to a situation where the beam *is* loaded. What exactly is your question?

 

[ripson]

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...

 

[FredGarvin]

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.