Why are I beams shaped like an I? Have you ever actually taken a moment to think
about this? This simple technology forms the basis of
all our largest structures and even features in one of the world’s most famous photos,
but after asking some of my friends few actually knew the answer to this simple question. The I beam is designed in that way to handle
a maximum bending load while using the least amount of material. Let’s look at an I beam supported on either
end to understand more. When we apply a uniform load across this beam
the max deflection will occur here in the middle. We can calculate the deflection with this
equation. This may look complicated, but it really isn’t. W represents the uniformly distributed load
in terms of Newtons per metre, l is the span between supports, E is the youngs modulus
which as explained in my Material Properties 101 video describes the stiffness of the material. But the variable we want to focus on is this. I represents the second moment of area sometimes
called the moment area of inertia. This describes the shape of the beam, more
specifically it describes how the material is distributed throughout the shape. These two shapes have the same area, but that
area is distributed very differently and that is important. A see-saw is a good analogy for this idea. When we place weight in the middle, it is
very easy to lift, in fact if it is placed exactly over the middle, we aren’t lifting
it at all. but the further we move that weight to the
end, the more difficult it is to lift, due to the increasing leverage. A very similar thing happens with beams in
bending. Material at the centre of the beam, which
is called the neutral axis, does not resist bending and the material furthest away from
the centre,resists the bending the most. It is called the neutral axis because if we
place a bending load downward the same way we did before, the beam will bend in a way
that will cause the lower edge to be in max tension and the upper edge to be in max compression
and the values of stress gradually decrease to 0 at the neutral axis where there is neither
tension or compression. Because the tension and compression is maximum
the furthest from neutral axis we want to maximise the amount of material on the outside
of the profile where it is needed most The more material further from the neutral
axis the larger the second moment of area will be. Applying that to the equation we can see that
a larger second moment of area will result in a smaller deflection. So if we to place this section under the same
bending load, it would actually be stronger if we flipped it over 90 degrees, because
more material now located future from the neutral axis. We could make it even stronger again, by reducing
this thickness to a minimum just enough to resist the shear stress and placing that material
at the the top and suddenly we are back to the I beam shape. You can see this idea put into action all
around you. In my last video I mentioned just one of them
when I spoke about the Willis Tower using a bundled tube structure. This structure maximises the amount of steel
on the outside of the building to maximise it’s resistance to lateral bending from
wind and other loads. I will be talking about another application
of this technology in my next video and if you can think of any other examples of the
second moment of area being applied in the world around you be sure to share it in the
comments. Thanks for watching. Like my last video I wanted to experiment
with a shorter format and it’s thanks to sponsors like the TheGreatCoursesPlus that
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Hey OP, thank you for posting my vid!
Just trying to calm down now. Published the video in the middle of a pitch to a shark tank type panel for the best young Irish entrepreneur awards. The notification people did me proud!
As always feel free to ask me any questions here or on my twitter www.twitter.com/fiosracht
If it wasn't it wouldn't be called an I beam, duh.
Oh, I learned this in mechanics of materials last semester but I didn't understand at all. This explained it way better than my teacher did.
This is the same reason why our long bones are hollow.
This guy posts really good topics regularly, and actually quite useful for people doing engineering in college. Check his channel out
....
I don't get it. One doesn't need math to see why bonded opposing axes will create stiffness in a structure.
The answer I want to know is why they are actually called W-beams? In the American steel handbook referred to by engineers thats what they are called.