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Building
Model Bridges
January
2002 Back to Bridges
back to Home page Links
See
links at end of this page.
Building small
bridges ought to be easier than building large ones, and of course it
is. But it is not trivial. There are a few problems that
would not occur on a large scale. Did you know that a 100 gram
balsa wood bridge has held 209.4 kilograms – that’s a load to weight ratio of
2094. It was built in 2000 by Matt Sullivan. Do you think that a
1000 foot span could be built to hold two thousand times its own weight.
What is the ratio of a spider’s weight to the weight of its web?
Scale is the clue. As Galileo said, doubling the the length,
width, and height of an object increases its area by a factor of four,
and its volume and weight by a factor of eight. Whereas in very
large suspension bridges the designer might be fighting for rigidity, in
a model suspension bridge a big problem is making it flexible enough.
Here
are two principles that you can bear in mind.
A
If you need to counteract a load using other forces, and these
are at an angle to the load, these new forces will be bigger than if they
were parallel to the load.
B
If you apply a force at a distance from the force you need to
counteract, you will need a bigger force than you would if you applied the force
in the right place.
Both
principles apply to bridges. By definition, you cannot support the load by
a force underneath it, or you wouldn’t need a bridge. The supports of the
bridge will be some way from the load, and in the case of an arch or a
suspension bridge, the supporting forces will not even be parallel with the
load.
Parts that should be flexible should be genuinely flexible, to
prevent the structure becoming indeterminate. You won’t learn
anything from a model that is too rigid. But if you are building
a bridge across a stream in your garden you are probably more concerned
with rigidity than with learning.
Remember
that materials such as popsicle sticks and more especially balsa wood
are anisotropic, that is, their properties differ with direction.
If you push a pin through a piece of balsa wood, and then pull along the
grain, the pin may cut through the wood. To pin two strips of
balsa wood together, it is a good idea to glue a small piece of balsa at
each end of each strip, with the grain at right angles to the
strip. Lighter still than a pin is a piece of thread.
Why
not just glue the wooden strips together? Don’t forget that some
glues are stiffer than the wood, and may set up unpredictable stresses in
the wood. If the glue is very strong, and you spread it outside
the joints, you may strengthen the structure in a way which is
unacceptable in a competition. The design of a simple truss is based on the assumption
that all the joints are pinned.
What
about the structure of individual members? In theory, making a box girder
or a tube from balsa wood should be more efficient than using a solid rod.
But what happens if a joint fails? Will the strut fail more, or less,
gracefully than the rod?
To
find out exactly how your model bridge fails when its maximum load is exceeded,
you could use a video camera or a still camera in a multi-frame mode. A
still camera could be triggered by the load pressing on a cable release.
Watching carefully as the the load is increased may also provide valuable
information. A detailed follow up of all failure mechanisms is more
instructive than merely awarding points.
After
a test, you could ask – "Did it fail at a joint?" – "Did a single
member fail?" – "Were there members that were never highly
stressed?" – and so on.
Model
Suspension Bridges
The deck of a suspension bridge must be sufficiently flexible that
every hanger does its job. Depending on the span of the bridge,
the deck could be made of hardboard, thin modellers’ ply wood, thick
card, or similar materials. If the span is to be long, joining
sections must be done in an unobtrusive way, preserving the line, but
not introducing too much local rigidity.
It is
essential that the lengths of all hangers be accurate: if they are not,
some may hang loose, which looks absurd. A good
plan is to calculate the lengths using a simple computer program or a
calculator. If the main cables are made of string or twine, the
deck is likely to be much heavier than the cables, and the cables can
hang in a parabolic shape. By accurately marking lengths of strong
thread using a pen, it is possible to tie these lengths to the main cables well
enough to give a good appearance. The essential thing is to keep
hanger length errors small enough to avoid any part of the main cable being
straight, which would render at least one hanger limp and unrealistic.
The bridge will look better with a small rise towards the centre.
This should be taken into account when calculating the hangers. If
the main cables form parabolas, the deck profile can be parabolic as
well, to simplify the calculations.
If the model is to be built indoors, anchoring the main cables can be
difficult, since you can hardly drill holes in the floor or the
carpet. Weights inside the anchorages will help. You could
try Velcro on the bottom, but this will probably lift the carpet.
If you need to transport your model, you need to plan very carefully,
so that it can be disassembled simply and stored conveniently without
risk of damage. It is quite possible to build a suspension bridge
up to twelve feet long, and still transport it quite easily. The
deck can be made in sections, as it does not have to be rigid.
Design
and build a model suspension bridge
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