All the time I am asked “How tall should I make my bridge?” This article will attempt to answer this question by illustrating a principle in model bridge building. There is no cut and dry answer, as you should evaluate your bridge specifications and guidelines and conduct experiments to reach the best answer for you.
How Changing Height Affects a Bridge
This is our control bridge. The bridge is 8 inches long and 3 inches tall. I have added two load points with a total load of 100. This means the numbers you see act as percentages. For instance, the very middle of the top chord of the bridge is supporting 50% of the total load.
Now I will show you another bridge, with the same design. The only difference is that this bridge is 4 inches tall, one inch taller than before.
You can see in this second bridge that the middle section of the top chord is only holding 38% of the total load. All I did is increase the height of the bridge by one inch.
What does this mean to you?
As you saw in the example bridges, by increasing the height of the bridge you decrease the load on the top (and bottom) chord. A decrease in load means you can make it smaller. Smaller means lighter in this case. However, there is a catch.
Look back at the two examples. By increasing the height, the load decreased on the top and bottom chords but remained the same on the middle “truss members”. Why is this a drawback? By increasing the height, the middle members have to become longer. That inherently adds weight. However, bridge builders have another problem when pieces become longer. The amount a piece of wood can support in compression before buckling decreases with length. So that means the middle members will have to be made stronger the taller the bridge is. Adding strength usually means adding weight.
So we have a draw
By increasing the height of a bridge, you can make the top and bottom chords lighter. But at the same time, the middle truss members have to be made heavier. The goal is to find a balance. I believe that there is an optimal height for a model bridge in every situation. The trick is to find that height, by balancing out these two factors. I was once told that the optimal height for an arch bridge is 1/6th the length of the span. That means if your bridge is 6 inches long, it should be 1 inch tall. My experience has confirmed that this is a very good starting place for an arch bridge. And I believe the same ratio of height to length can be applied to regular truss bridges.
The Optimal Height
Interestingly, the Golden Gate Bridge uses the 1/6th ratio almost exactly. Perhaps you can do some studying on other real bridges and see if they follow this idea also.
Data taken from the Bridge Designer.