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.
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