Understanding bridges, Part 2

In the previous post, I discussed the most fundamental principle of bridge design, the importance of beam or bridge depth, relative to length. The key point is that the stiffness of a beam (or bridge) depends on the width to the first power, but the depth to the third power. You can read that post at this link: https://modelingthesp.blogspot.com/2024/03/understanding-bridges.html .

Probably the most familiar type of large railroad bridge is the truss bridge. This is really just a beam bridge, but with unnecessary material removed, leaving just the material that ensures the depth of the “beam” (or bridge) is maintained, i.e. keeps the top and bottom apart. The familiar framework of a truss bridge can be understood in that way. I will show a typical railroad bridge, then delve into explanation.

Below you see Southern Pacific’s bridge across the Salinas River at Nacimiento, on the Coast Route, being crossed by a freight behind a pair of rebuilt GP9Es, in 1974 (Ed Workman photo). This is a Pratt truss, as I discuss below.

In the sketches below, imagine that the components shown are a stiff rubber. I think you can readily see in (a) that the bottom has to get longer (tension) and the top will get shorter in response to a load on the top. 

In (b) I show the simplest possible truss, known as a king truss, simply a triangle, and imagine that you have a handle underneath that you can pull down on. Again, I think it’s clear that the two upper members will be squeezed together as the lowest member lengthens. The problem with such a design is that the span is fairly long. Adding a rod between top and bottom (c) would minimize flex of the bottom member and in effect, hangs a floor beam from the top of the truss.

These are the fundamental ideas of how truss members behave. If we now draw a truss that can span a larger gap (it happens to be a Pratt truss; more on that in a moment), I can indicate the names of the truss members (posts, ties, chords, etc.) and you can see the stresses for uniform loading, in effect, equal loads on each floor beam.

Note that I have drawn some members (the top chord and end posts) heavier than the remaining members. This is because they are in compression, while all the other members are in tension and can be lighter. This is one of the attractions of the Pratt truss.

Over the decades, especially in the 19th century, there were a great many truss designs invented, many of them with numerous redundant members (as we now recognize). But quite a few are reasonably efficient designs and have been used for railroad bridges. I show a dozen of them below (a figure from Mallery’s book, citation in the first post of the series). Some, like the Pratt and Warren, are used today. The Howe truss, a carry-over from wooden bridge design, is less efficient as it has numerous members in compression, which have to be heavier.

Finally, one more important bridge type is the arch bridge. This bridge design directly reflects the fact that forces in the bridge are carried in the curvature of the arch, and thus are exerted entirely through the ends of the arch. The best arch bridge, then, is a a full half-circle, and the forces are directed exactly downward. But partially circular arches are also feasible, if sufficiently strong areas at the side of the bridge exist, so that the arch can bear into those sides.

This is not a new idea. Arches were used in ancient times, perhaps most impressively by the Romans. The famous aqueduct near Avignon, France, the Pont du Gard, still stands (photo from USGS website). This was part of a 31-mile aqueduct, and the engineering skill involved is evident because there was only a 56-foot drop over the whole 31 miles of the system.

Modern arch bridges for railroad use, thought not the most common type, certainly do exist. Among the most famous is the Great Northern’s bridge across the Mississippi River at Minneapolis, built in 1883 and carrying rail traffic into the 1980s, but now a hiking trail. In this view (Burlington Northern photo) GN No. 12, the Red River, is leaving Minneapolis for St. Paul behind an E7 diesel.

However, the drawback to the arch bridge is that it is normally erected over falsework which temporarily has to fill the space beneath it, at least if it is a masonry arch. The carton below shows an unlikely alternative (originally published int the Saturday Evening Post, now found throughout the internet):

My purpose in collecting this information and illustrations is to help modelers understand what they are doing when they choose a type of bridge for a layout situation. Mallery’s book contain a great deal more detail on this topic than is practical to show here, but this should suffice as an introduction. And the article by Larry Kline and me, also cited in the first post, contains more information on the history of railroad bridges.

Tony Thompson