Building Model Bridges
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/305 m span could be built to hold two thousand times its own weight? In fact, when a certain size is reached, a bridge can only just hold itself up, and cannot take a useful load. What is the ratio of a spider's weight to the weight of its web? If you look at this page you will find that there is a span for which suspension cables will only just hold their own weight, without even a deck. The load to weight ratio is then zero. So the larger the structure, the lower the load to weight ratio. The bicycle is better than the car. Why, then, is a Pitts Special not better than an Airbus A380? What do we mean by "better"? And why don't we make many little airliners and buses and trucks instead of a few big ones?
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 exactly 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. Perhaps it is a good idea to think about the load path by which the forces are distributed from the load to the ground.
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 about structures.
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.
This is perhaps not an easy project to undertake, and any results should be interpreted very carefully, taking note of all circumstances. Simply making several bridges using the same quantities of the same materials will not suffice, for the following reasons.
Failure modes differ so much.
It is very difficult to use exactly the same materials.
It is very difficult to make joints of equal strength.
Let us look at these statements in turn.
Failure can be caused by any of the following, which can in most cases happen to structural members or to joining materials.
Pulling apart under tension
Buckling under compression
Crushing under compression
Buckling under shear
Pulling apart under shear
Effects of bending
Effects of torsion
Using the same materials is seen to be difficult when you consider cable-stayed bridges and suspension bridges. If you have use popsicle sticks for a beam or a truss, what will you use for cables? In principle, you could make very thin strips from a popsicle stick, and join many of those together. A solution to this problem might be to say that if you are going to use the same weight of materials for all your models, the weight of cables is a small fraction of the total. As a result, you can simply make them big enough that they will never be the cause of failure. But then you have to ask - "What then could be the cause of failure."
Joints can be a problem in this type of work, because they may behave quite differently from those in a large structure. A blob of glue may be stronger and more rigid than the material that you are using for the bridge. That sounds good, but in fact, the joints may impose stresses that would not be present in a real example. In a real truss, for example, the joints might behave as if they were pinned, but strong glue imposes a rigidity that can place parts under unwanted shear stress and bending stress.
Using actual pins would solve this problem, but under heavy load, they may tear through a thin piece of wood, especially balsa. One solution is to glue a thin piece of wood on each side of the main piece, with the grain at right angles to that of the main piece. The pin can be placed behind these. You can use thicker pins, for example, round nails, but you also have to consider the problem of making holes in wood. If they are not very accurately round and smooth, irregularities may concentrate stress to the point of early failure.
An extreme example is the use of strong wood and weak glue. Tests would probably show an arch as the strongest design, because the parts are all in compression, leaving the glue little or nothing to do.
So for these and other reasons that you can probably work out yourself, comparing different structures is far from easy. It might be easier to work with one structure only, and to try different ways of making it. With a truss, for example, you could compare a truss with many narrow members with a truss comprising a few thick ones. With a beam you could try different cross-sections. You can also draw designs on paper and then try to work out the possible modes of failure before beginning to build.
In any case, although it may be disappointing if your model "fails", or doesn't win a prize, you can learn something by examining the parts afterwards, to see how they failed. From this you may be able to work out a better design. You can also think of it, not as failing, but as being tested to destruction, which is a genuine engineering practice.
It is not difficult to prove that the question "What is the strongest type of bridge?" has little real meaning. If we ask about the strongest bridge with a span of more than 3000 feet/914 m, only a suspension bridge has been able to do this, to date, so the strongest type of bridge for the longest spans is a suspension bridge. At over 1800 feet/539 m, only the cable-stayed bridges and suspension bridges have succeeded. So the answer depends on the span. Furthermore, for a span of say 30 feet/9 m, to carry a railway train, a suspension bridge would need a very strong beam as its deck, to prevent undue deflection, so strong, in fact, that that the suspension cables would not be needed. So we might as well simply build the beam.
Model Suspension Bridges
The deck of a suspension bridge must be sufficiently flexible that every hanger does its job - a few slack hangers will ruin the appearance of the model. 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.
This picture has been compressed vertically by a factor of five, to show what can happen. The hangers are very stiff, and the appearance is somewhat untidy. The picture actually shows a real suspension footbridge, though the fault is rare in full sized bridges. Perhaps the hangers of this footbridge were bent by people walking along and pulling them inwards.
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. It is better to have a small number of well spaced hangers than a large number, because the effect of errors will be less.
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.
You might be interested in this web-page, which is about the design of full-size suspension bridges.
Model Arch Bridges
Here you need to provide for resistance against the thrust of the arch. If you are not allowed to drill into the floor, weights can be used to provided resistance to thrust. You must not make an arch stiff to stop it spreading - if you do that, it is a beam and not an arch. If it is to simulate a masonry or concrete arch it can be made of well fitting blocks, and it can be easily assembled and disassembled. A labelling scheme will help to get all the blocks in the right place.
diagram shows an arch based on a catenary, the red curve.
To generate catenary arches with different ratios of height to span, click here to download program Brancat. By pressing the PrintScreen key, you can copy the picture into the clipboard to use it as the basis of a model.
Model Truss Bridges
As in any other model, a truss bridge should do what it is supposed to do, meaning that all the parts must actually so something. Joints should be pinned or hinged, and only tightened up when the whole thing has been assembled. Lateral as well as vertical stability has to be provided. See also Trusses three for a discussion on the relative merits of different trusses.
Let us look at some possible model trusses. If you are making a model for a competition, the rules may affect your choices very greatly. For example, the rules may stipulate that the load may hang from any point at the centre of the bridge, eg top, middle, bottom, or the may stipulate that it must rest on a platform. Sometimes the load has to pass through the bridge on a trolley.
This page includes two computer programs which calculate the forces in very light trusses carrying very heavy loads. The examples assume a load of one unit: the forces can be scaled up or down for other loads.
Click here to download a program simulating a kingpost truss.
Click here to download a program simulating a kingpost truss, a Warren truss, and a third type of truss.
Here we will look only at the case of a central load.
A Simple A - Frame
Here is a simple calculation about a simple structure - two struts and a tension member, with a load on top. It isn't offered as a potential bridge model, it's only an example of the type of thinking that might (or might not) be useful.
If we use light materials like balsa wood we can neglect the weight of the structure. The chart below shows the variation of two ratios, as angle A goes from 0° to 180°. One is H / S, giving the height of the frame: the other is W / F, where F is the maximum force that the strut can take. This neglects the possibility of buckling, which would have to be prevented by subsidiary members. If the weight of the structure cannot be neglected, the calculation is a little more complicated.
From the chart we see that once A has been reduced to about 30°, there is little gain in load bearing, but a great increase in height, using more material, and making the system less rigid.
If you got this far, try a superb game about bridge building - http://firingsquad.gamers.com/games/pontifex/default.asp .