The I-beam has a destructive history due to a little-known fatal flaw.
The images you see here show ruins resulting from I-beam failures.
How exactly do such failures happen?
How can such failures be prevented?
In a previous video we reviewed the secret of the I-beam's strength. Click here for a
refresher on that.
To summarize, the I-beam's strength comes from having more area further from the centre.
This makes the shape very strong in bending which means it can take lots of downward loads.
So why then, do we not take this strength of the I-beam to the extreme?
When we add more and more area, further and further from the centre, at a certain point
the beam will buckle.
Buckling can occur like this, globally
or like this, locally
One example of I-beams being taken to the extreme like is something called plate
girders which are typical
for highway bridges.
Notice how deep the I-beams are, and how they need stiffeners at regular intervals.
These stiffeners are to prevent local buckling of the web, and these braces are to prevent
global buckling of the member.
In these ways, buckling can be easily dealt with.
However, the I-beam still has one other flawed property which causes even more problems than buckling.
Until now, we ve been applying downwards loads to the I-beam straight on top in the middle
of the web.
However, in practice beams can have load applied slightly off to the side engineers call this
eccentric loading.
This eccentric load causes twisting or torsion on the I-beam.
The I-beam happens to be quite weak against torsional forces, but why is that?
To demonstrate, let's repeat the comparison of square, I, and circle shapes from our previous video.
Again in this example, all of these shapes have the same area, and thus the same amount of material.
The beams are loaded at midspan, but this time the load is eccentric.
As this eccentric load increases, let's plot the stress in each of our three beams.
As the load increases in each beam, the internal stress due to torsion also increases.
Even though the area in each of these beams is the same, the amount of torsional stress
they can take is different.
As we can see in this plot, the square tube is able to withstand the highest eccentric
load (AKA torsion or twisting) before failure.
But, why is that?
A beam's ability to resist torsion depends on how much continuous area exists, and how
far that area is from the center.
These little arrows are following paths of what engineers call shear flow. The more
distance that the shear flows from the centre, the better a beam can resist torsion.
Notice how in the solid circle, the shear flow is distributed from the centre outwards,
and is greater further from the centre.
This is because the material further from the centre contributes more to resisting torsion
than the material near the centre.
And in the hollow square, all of the shear flow is far from the centre in a continuous
path, since all of the material is continuously far from the centre.
In the I-beam however, there is no continuous path for the shear flow other than through
the centre, so the shear flow arrows are forced to move through the centre.
Having the area run through the center (i.e. not having a tube or hoop) restricts the I
beams ability to resist torsion.
So the beam with the most continuous area furthest from the center will have the best
ability to resist torsion.
An avid watcher might ask doesn't the corner of the square tube technically cause a discontinuity
because of its sharp edge?
The answer is yes sharp corners do cause some discontinuity in stresses.
One way to make a beam with equivalent area even stronger than we've shown is to make
a hollow circular tube.
Now this beam has the most possible continuous, smooth area as far from the center as possible.
Now, this shape is optimized for resisting torsion.
In summary, the I-beam is strong in bending (from downwards loads) due to more area in
the flanges being further from the centre.
However, if the area is spread too far the center, the I-beam can be weak in buckling
plus the I-beam is weak against torsion in general because it does not have continuous
area far from the centre.
We hope this video gave you some insight into the engineering considerations that go into
designing I-beams.
Engineers spend unthinkable amounts of time choosing shapes and cross sections for their
beams so that failure events can be as rare as possible.
Next time you are inside a building, look up and see what shapes you observe!
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