The picture below shows a footbridge over the M5 motorway at Michael Wood service station.

All the parts are made from hollow rectangular section steel tubes. We will examine the consequences of changing the design. The diagram below shows a cross section of the four main members, relatively wide and thick, compared with the real bridge, to make the diagram clearer.

In the next diagram, all the members, both horizontal and sloping, are made from solid steel. The mass of the bridge is increased by a factor of about 1.7 as a result of this change.

In the next diagram, the sides, top and bottom of the bridge are filled in to make a large rectangular tube. The mass of the bridge is increased by a factor of about 2.9, making a total factor of about 5 over the original.

Finally, we fill in the hollow interior, creating a solid beam, and multiplying the mass by a factor of about 2.9, making a total factor of about 14 over the original.

You can see from the photograph that the dimensions used in this calculation (for clarity) have resulted in a rather conservative result for the mass increase, but the benefit of truss design has been illustrated. Each mass increase does make the bridge (unnecessarily) stronger, but not in proportion to the extra mass. Estimating from the photograph, the mass factors might be about 2 x 6 x 6 = about 70 times.

If you look at any truss bridge, especially a large one, you will see how much of the total volume is occupied only by air. And that is not the limit – large suspension bridges and cable-stayed bridges are held up by relatively thin cables.