I am in a high school physics class. For our final grade,
our teacher is having us design, build, and then report facts on a Balsa
Bridge. However, she did not really tell us much of anything, and expects
the report to be detailed on everything. My question is this; what
equations can I use to predict how much weight my bridge will hold?
I am afraid this is a very tough question to answer and would depend on the
type of bridge configuration you are trying to build and how you plan to
load it. If you have the option, I would suggest that you design either a
simple beam or a pin-connected truss because these are somewhat easier to
analyze. If your physics text does not cover this, check your library for
an engineering textbook on statics.
The other thing you need to find are the material properties of the balsa as
far as its strength. Working with wood is somewhat complicated because its
strength is different when measured along the grain or across the grain.
(In scientific terms, this is called an orthotropic material.) To get more
information on this, go to the USDA's Forest Products Laboratory's web site
at www.fpl.fs.fed.us. Look under publications and download "Wood
Handbook -- Wood as an Engineering Material". This is an excellent
publication with information on all types of wood, including balsa. It also
has a chapter on structural analysis equations which you will find very
helpful. You may also want to download the latest West Point bridge design
contest software from the US Military Academy's web site at
bridgecontest.usma.edu. This will give you a feel for how trusses behave.
On a practical note, I built some balsa bridges in college for competition
that never did that well. The problem I had was not with the analysis, but
with the behavior of the connections. I could never get the glued or pinned
connections to behave consistently. The pin connections tend to fail by
crushing around the pin because the stresses tend to concentrate at the pin.
Of course, this is the point of the exercise - to learn that the real world
is much more complex than the mathematical models. So, I am not the best
person to give advice on building a successful balsa bridge. On the other
hand, our concrete canoes were excellent...
You will need two things to be able to complete that project.
First: You will need some raw data. for the size of the balsa wood pieces
you are using, how much weight (tension and compression) can they take before
Second, you will need to apply some geometry. (yes, geometry!) The more
highly angled a support is from the direction of the force applied, the less
able it is to support that force. In other words, 2 pieces acting to
support a load like vertical pillars will support 2 M. (M being the weight
that causes a single piece to fail.) those same 2 pieces, angled at 45
degrees against each other like an arch will only support 1.414 M. lower
those supports down to a 30 degree angle, and you only get 1 M.
It is somewhat difficult to explain this clearly without any diagrams. I
suggest you attempt to look up truss diagrams or stress diagrams for a
better explanation. Once you have figured out what kinds of stress each
component can hold, you can figure out the total load capacity of your bridge
with relative ease.
First you need information on the material.
Here is a brief explanation on materials. Tension and compression are the
critical factors. Picture a beam, with a large load, the beam sags in the
middle. The bottom fibers are stretched, = tension. The top fibers are
squeezed = compression. These "extreme" fiber stresses are what causes
failure, different materials react to the stresses in different ways.
Concrete is very poor in tension, yet very good in compression. Hence, the
reason to add steel bars, the bars take the tension forces.
As far as equation, you have to decide on a shape
for the bridge. Above, I discussed tension and compression. You can see if
the beam was deep it would affect the fiber stresses. Truss designs are
based on that principle. Rather than one piece, the design employees
triangles to transfer the loads to the top and bottom members.
There are bridges using an arch, where the bridge deck is placed across the
top of the arch.
So, you should start with the materials and choose a
shape. Next, a critical factor is the connections, the
loads, or forces have to be transferred from one piece
to another. Failure, more often than not is in the connections. Are you
going to glue ( glue represents welding in a big bridge), or use some pins
(the pins represent bolting in a big bridge).
Bottom line, before you get to the design and equations, there are these
decisions to be made.
There are other bridges, like the cable ones = suspension bridges. Chicago
is famous for the bascule
bridge, which opens in the center. I assume the teacher is leading to a
trial of loading the model you are making. A key question, how will the load
be imposed? Picture the bascule bridge with the opening in the middle, if
the load will be from the middle, that puts a real burden on this type, since
the bridge halves are cantilevers.
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Update: June 2012