More on Arch Thickness

How thick should an arch be? That is one of the major questions when designing a stone arch bridge, and one we have discussed many times. After all, correctly setting the thickness of the arch is crucial to building a structure that stands and functions properly.

Determining the Thickness

While in theory, at least, the thicker the better, extra-thick arches are rarely advantageous. For one thing, the form required to hold the weight of the stone will become enormous. Also, thicker arches will have more rise. Furthermore, fitting extra-thick arches becomes laborious and time-consuming, and the amount of stone used quickly will become excessive.

So how do we determine how thick is needful for an arch? Part of the question will depend on what the bridge is used for. For the average small sidewalk bridge (something about a few feet in span), the arch will almost certainly end up being 1′ thick. Even thinner arches are possible for small spans if the arch stones are very carefully fitted. Based on experience, a 9″-thick arch is completely practical to build even in rubble masonry if the span is in the 2′ range.

Bridges carrying heavy loads, such as vehicles, are an entirely different story from sidewalk bridges. Very thin arches are not advantageous here. Unfortunately, it is very difficult to create a hard-and-fast rule, since arch behavior is still only barely understood. However, if you were designing a new bridge to carry a specific load, you could look up a current load-rating method for arch bridges, such as the MEXE method, and create a bridge with an arch that is thick enough that way.

While we previously proposed an arch thickness formula taking the square root of the span in feet and dividing it by 2.5, we have since found a different empirical formula that gives outstanding results:

Natural log(span/2 + 1)

The span is to be measured in feet.

This formula gives results that, based on observation, makes very durable arches for heavy loads. As a plus, the results end up being thick enough for well-made arches of even very small spans, whereas the previous formula could give answers that were obviously too small if the spans were small. Our tests show it is possible to end up with an answer less than one foot for particularly small arches, but in these cases, if care in laying the stones is used, this thickness should be adequate. That said, if the builder has doubts about precisely fitting such small stones it may be easier just to make the arch one foot thick. This formula has so far proved very practical for bridges carrying heavy loads.

A stone arch bridge under construction. This arch was designed using the natural log empirical formula proposed above.

Strengthening the Arch

One important factor to keep in mind is that an arch can be substantially strengthened by increasing the depth of the fill over the arch. For purely aesthetic considerations, a stone bridge will look rather well if the depth of the fill is made about three fifths as deep as the arch is thick. But if necessary, much greater depths can be used to achieve greater strength. Some authorities recommend using at least two feet of fill, though for small spans this will likely be excessive and the results will not necessarily be visually appealing.

With so much fill over this arch the structure itself is quite strong, as long as scour is under control. Unfortunately, such a tall wall over the arch tends to look strange to say the least. In this particular case, the walls being made of concrete actually help the aesthetics by obviously differentiating the old arch bridge from the new walls on top. If the bridge had been originally built with towering stone walls over it, it would have looked highly unusual.