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Structural Mechanisms and Variability

Most engineering concerns things that change over time. The objects of interest to electrical, mechanical, and chemical engineers, for example, are definitely not static. Structural engineering reached maturity in part by simplifying loading to “quasi-static” status: if we assumed that load is applied to our structures so slowly that there are no dynamic effects, the equations for analyzing those structures are a lot simpler than otherwise. That was the nineteenth century; a lot of the twentieth century in structural engineer was spent re-introducing dynamic effects: earthquakes, wind gusts, second-order stresses resulting from the quasi-static deflections, and so on. One time-related change that was taken into consideration in the earlier era was the idea that sometimes the structure itself was dependent on the load. The classic example of this was a double-diagonal Warren truss, where the slender diagonals were ignored in analysis when they were in compression (on the assumption that they would buckle out of plane) but used in tension (see figure 6 here). If the truss was part of a railroad bridge, which diagonals were in tension (and therefore included in the analysis) and which were in compression (and excluded) would change as a train moved across the span.

Let’s take that idea one step further. The picture above is the main hall of the Wagner Free Institute of Science in Philadelphia, a building that I had the opportunity to investigate a few years ago. That vaulted ceiling is showing you the roof form: there are wood joists spanning truss to truss, with only a wood-plank deck and roofing above. The ceiling is plaster hung form the joists’ bottoms. An obvious question: how does the roof function structurally? The trusses are very simple, with single wood sticks for the bottom (exposed) and top (buried in the ceiling) chords, the wood diagonals are loose, held in place by pairs of wrought-iron “verticals” at each panel. The chords are spliced with one scarf joint each, and there are wrought-iron tie rods across the bottom.

If you want my full analysis, got to our Research page and look for “Analysis of an 1864 Long-Span Truss Roof”. I identified six possible mechanisms for the roof, including two versions of a tied arch, an untied arch, two versions of a vault, and one version of a beam. None of them exactly met the observed conditions, which include cracks in the plaster, some (but not too much) outward bowing of the walls, less-than-tight joints in the lower chord, and out-of-plane buckling of the truss lower chords. If you think about it, the lower chord shows signs of both tension and compression, which is odd for a timber arch. Of course, some of the information is based on assumptions: I assumed that there is a washer and a nut of the outboard end of each wood bearing block where a lower chord meets a tie rod, but I never saw it.

The roof structure as a whole is not very stiff, so it readily changes shape with wind and snow loading. The tie rods can stretch enough to explain the wall tilt and to allow the trusses to flatten some. My conclusion is that the roof works differently depending on the load, but unlike the warren-truss bridge, it actually changes mechanism. Under light loads (self weight and a small amount of wind or snow) the well-braced top chord is an arch in compression and the tie rod carries the arch thrust. The lower chord is not engaged except at the end connection seen above, and wood shrinkage would explain the open joints. Under heavy load, the whole truss flattens enough to close the lower-chord joints and that chord begins to carry compression, strengthening the arch. Since the lower chord is not braced against lateral movement, it might buckle sideways on those relatively rare occasions that thjere was heavy snow or high wind.

I doubt the designers and builders of this roof intended to have the structure adapt to different loads in this manner, but the structure is basically okay after almost 160 years. The flexibility and movement, on the other hand, have damaged the plaster.