I used the same amount of material to build a truss and a beam bridge and loaded them to
failure. But before we get to the destructive testing let us see how these bridges work in
theory. If you are not interested in hearing about these engineering concepts, skip directly
to the tests near the end of the video. But I do encourage you to stay, by the end of the video you
will have a better theoretical understanding of trusses than the bridge builders from the 1700s
that were great at constructing these structures but didn’t really know how they stood up.
We have already talked on this channel how beams carry loads. They bend such that the top of the
beam is getting compressed and the bottom of the beam is being stretched. The combined action
of these forces plus the shear resistance is what transfers the load to the end supports.
The further apart these forces are the higher the bending capacity of the beam is,
hence why the wide-flange beams have most of their cross-sectional
area offset to the top and bottom of the beam. The truss takes this concept to the next level.
If you think about it, the truss is basically a beam where the top and the bottom flange are
structural members of their own. The beauty of the truss is that all of its members are only
subjected to axial loads which makes the whole structure efficient and also incredible stiff.
This may not be obvious so let’s have a deeper look. But just to be clear,
stiffness in engineering terms means the amount of load a structure can take per
unit of deformation. Or another way to think about it is what load causes the
structure to deform by 1 mm or 1 inch or whatever unit you prefer. Intuitively you
know that it is much easier to deform a member by bending it, rather than compressing it.
So it follows that bending members such as beams exhibit low stiffness for longer spans.
This is because the stiffness of a simple beam is scaled with the cube of the length of the span.
This means that doubling the length makes the beam 8 times more flexible. If you have worked
with long beams, you have probably noticed how wobbly they are compared to shorter beams
of the same cross-section. Now trusses do not have bending members so this formula does not
directly apply. Trusses are arranged in such a way that all of its members are loaded axially.
The stiffness of axially loaded members scales linearly with the length.
So axially loaded assemblies are naturally more suitable for longer spanning structures
such as bridges. However it takes a little bit of thinking to arrange such assembly of
elements in a way that all members are axially loaded yet they span a longer distance. One way
to achieve this is to construct an arch or a trestle bridge as our ancestors did. Still
these bridges require frequent piers that are not always possible, especially not in deep waters.
The truss is an alternative structure that doesn’t require regular supports and yet
uses the axial stiffness of its members. In fact, the high stiffness of the truss is
why it is often used for railway bridges. Railways have very strict deflection requirements because
an excessive deformation of the bridge and rail would lead to a derailment of the train.
For that reason, even today, bridges that service a rail connection utilize some sort of a truss
structure within them, usually to stiffen the deck. Suspension bridges, due to their high
flexibility, very rarely have railway traffic unless the deck is stiffened with a truss-like
structure. Let me know in the comments if you know of any suspension bridges open to railway traffic
or any cool bridges in general. Trusses do also have disadvantages,
for example buckling of the compression elements, increased construction complexity
and so on. Depending on the length, the effects of these parameters determine the feasibility of
a particular bridge type. Beam bridges due to their low material utilization but ease
of construction are the preferred choice for spans up to 100m. Beyond 100m and up to 300m,
the truss becomes the optimal bridge choice. For longer spans, the cable stayed and suspension
bridges become optimal. In many cases, a combination of these techniques are used.
The truss is efficient because its members don’t bend, but It feels like we still haven’t explained
why this is the case. Why do truss elements not bend? Our intuition suggest otherwise!
When elements are loaded perpendicularly they should be bending. In the case of the truss,
the overall structure is bending but its individual elements are not!. They are
only being compressed and stretched. There are two main reasons why this is the case:
The first reason is because trusses are usually only loaded at the joints. This is not always
obvious but if you have a closer look at a truss assembly, you can see that the
deck is usually not directly attached to the truss itself but it’s resting on floor beams
that run in a perpendicular direction. The floor beams are then connected to the joints
where the load is distributed into the truss and then transferred to the end supports.
The second reason is less obvious and requires a slight understanding of statics. In engineering,
the joints of a truss are modelled as pin connections which means the members can
freely rotate around the pin. But in reality, we never see these pins. In fact, we see heavy gusset
plates scattered with dozens of bolts. Surely this cannot be a pin. Well it is not an actual
pin but the connection does behave like a pin as long as a very important condition is satisfied.
The requirement for the gusset connection to behave as a pin is that all of the connected
members intersect at the same point. If they do, then there are no couple moments generated
at the joint. In contrast, if one of the members was installed incorrectly and did not intersect
at the same point, then for the joint to be in equilibrium, there has to be a bending moment
present. This becomes obvious if we sum moments about the intersection point which clearly leads
to a non-equilibrium condition which can only be balanced bybending of the offset member.
Of course in reality the connected members are not perfectly intersecting but as long as they satisfy
a particular tolerance then the pin assumption holds and the structure is incredibly efficient.
Now lets see a practical example of a Warren truss compared to a
beam of the same cross-sectional area. I decided to go with a Warren truss mostly
because all members are of the same length so it is a bit easier to cut and build.
My craftsmen skills are limited so as you can notice the truss is far from perfect. The beam
was significantly easier to build since it was only about gluing the sticks together.
Even though these are far from real bridges, they do, to some extend,
reflect on the difference of manhours required for each structure. For that reason,
the beam bridge is sometimes preferred. From a material point of view the beam is less efficient
but the extra material expenses are quickly recovered due to the simpler construction.
The loading was performed with a bucket of wet sand hanging under the table. For brevity,
only the final stage is shown here. The truss managed to carry 45 kg or 99 lb before failing.
In reality, a better constructed truss would have performed much better. Also,
the failure was not pure tension failure but had a significant amount of bending
and sideways twisting which would not appear in a real structure as we discussed earlier.
I know this experiment is far from perfect, I will try to get better in the future so try not
to be too harsh in the comments. The beam on the other hand,
performed fairly decent and reached 38 kg or 84 lb which is probably close to
its real capacity since it did not suffer from significant construction deficiencies.
In summary, besides the poor construction, the truss still managed to outperform the beam by
more than 15%. Depending on the application, this 15% difference (or possibly more) might
be the deciding parameter for going with a truss rather than a beam bridge.
But truss structures do not appear only in bridges. You can find them in roofs,
large venues, antennas and many other places. This video is a good introduction but if you want to
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can find the link down in the description! Thanks for watching, if you liked the video,
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