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The National Park Service – in the form of the Historic American Engineering Record – was kind enough to create this illustrated guide to trusses. It’s incredibly handy to have around when you want to categorize an old bridge, but it occurs to me that it inadvertently says something about the way engineers design.

First, while there’s a group of diagrams labelled as roof trusses, the authors’ hearts are pretty clearly with bridges. It’s also worth noting that most of the “bridge trusses” can be and have been used in roofs. The axonometric diagram at the upper left is as good a way to identify the pieces of a truss bridge as I’ve seen; same for the contrast between pinned and riveted connections at the lower left.

A piece of insight into design is in the side-elevation and cross-section comparison of through, pony, and deck trusses. The side elevations make it clear that deck trusses have less clearance below (if the decks are at the same height) or require more elevation in their approaches (if the clearance is held constant). The cross-sections make it clear that pony trusses are less well-braced than the other types. The third leg of this three-way trade off is difficult to illustrate: through trusses are more vulnerable to vehicular impact than deck trusses, which is not so important with road bridges but a serious concern with railroad bridges. Each of the three types has its disadvantages.

The thing that really struck me looking at the right half of the page is that almost all of those types are essentially simple beams. Except for the bedstead and Wichert forms, all of the trusses have a single span with only vertical reactions at each end support when loaded by gravity, which is as good a simple definition of a simple beam as you’ll get. So if you simplify each of the trusses (from here on, assume I’m excluding the two outliers) by (a) squinting (if you’re not an engineer) or (b) drawing a free-body diagram of the truss as a whole (if you are an engineer) then they all look like beams.

The actual state of stress inside a simple beam is quite complex, and in ordinary practice we just look for the maximum stresses and design for those. If the “beam” is a truss rather than an actual beam, then we have artificially limited the stress patterns to being constrained within the pieces of the truss. For example, web shear has to be carried as tension and compression within the verticals and diagonals of the truss sides, rather than more complicated patterns that exist within a solid web. This greatly simplifies the analysis – the forces can only exist within the members that we have semi-arbitrarily put there – at the cost of being somewhat less efficient. “Somewhat” is often “slightly”: if the overall “beam” is dominated by bending rather than shear, the loss of efficiency is low. That’s true when the truss is reasonably long compared to its depth, maybe in the range of 5 or 6 to 1, or longer.

If you think about it, it’s a neat trick. We force the forces to go where we say they should be, and we pick a pattern that we know we can analyze easily. The multiplication of truss forms is the flip side of that coin: the ideal would be a truss pattern that could closely replicate the complicated pattern of stress in a solid beam, but that’s not possible. So people invented one type of truss after another trying to get close to that pattern, trying to be more efficient. None is exact and all have their plusses and minuses.

Analytic design is the core of engineering, and it can be a lot of fun. The guide to trusses shows why.