The picture above shows the inside of the 1869 White’s Bridge, a wooden covered bridge over the Flat River, south of Smyrna, Michigan. Most wood covered bridges in the US have very dense lattice trusses of small-dimension timbers or the slightly weird Burr truss, which is a truss/arch hybrid. White’s uses a patented heavy-timber design, the Brown truss.
The Burr truss is difficult to analyze without using a modern finite-element program, since apportioning the load between the truss and the arch depends on being able to figure their relative stiffnesses. A Brown truss is technically statically indeterminate, which should make it difficult to analyze by hand, except that there’s a simplifying assumption that can be made which allows this to be readily solved using either of the straightforward methods in common use in the mid-1800s: the method of joints and the method of sections. The Brown Truss consists of two single-diagonal trusses overlaid on one another. As long as the members in both are the same size or are of a known ration of sizes to each other, the analysis can look at only one of those “half trusses.” As seen in the picture above, one of the trusses at Whites bridge has doubled timbers for its diagonals and the other has single timbers. All of the diagonals are fastened to the same ganged four-timber chords, so you can treat one half truss as twice as stiff as the other and solve a single half.
Arguably, Brown should never have been granted his 1857 patent, since his truss design is, for all intents, simply a double-intersection Warren truss. The Warren truss was patented in 1848, and that probably was also wrong, since triangulated trusses had been around for a long time before that. Brown’s patent was for the entire assembly of a through-truss bridge but it was not widely used. I suspect the problem was that bridge design in the US was bifurcating right around that time. Heavily-loaded bridges (i.e., railroad bridges) were being designed by engineers and built in iron; while lightly loaded bridges like White’s Bridge were being designed empirically by carpenters and built in wood, as they had been for some time. The carpenters weren’t necessarily interested in a new and possibly improved design; the engineers weren’t interested in wood trusses.
A view of the wind bracing and the bottom ends of the truss diagonals:
And an overall view: