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On Roman Arches

On Roman Arches
The Roman arch, consisting of one half of a circle, is the typical rounded arch often seen with stone bridges. The Roman arch need not have a thick abutment to resist a horizontal thrust; rather, they start (“spring”) on a flat, horizontal plane. This makes them very easy to build, which is always an advantage in construction.

However, whereas a flat arch can be made with almost any rise-over-run ratio, a Roman arch will always have a rise equal to one half of the span. This can rapidly lead to grade complications. For instance, an arch with a span of 50 feet will have a rise of 25 feet. Add to this number the arch ring thickness and the height of the fill, and you often will have an impractical situation. Yet the simplicity of the Roman arch and the ease with which they are constructed is not to be ignored, which is why many of them were built — even though some of the bridges using the Roman arch have difficult grades.

The Roman arch features one important design challenge that is often overlooked. Whereas the thrust of a given arch follows a somewhat parabolic curve, the Roman arch is not at all a parabolic shape. For an arch to be stable, the thrust is best kept within the middle third of the arch ring, which leads to the necessity of making the ring of a Roman arch relatively thick to accommodate.

Another way to look at this is to consider the fact that the bottom 45 degrees or so of a Roman arch can free-stand without the help of the top of the arch. The top 90 degrees, however, needs to be pushing against something solid to keep from buckling. What we have in effect is a 90-degree segmental arch resting on curving “abutments.” While the curvature of the abutments helps direct the force down somewhat, the fact remains that unless these abutments are thick enough, the 90-degree segment of the arch will slide horizontally, the top will buckle, and the arch will collapse.

A Roman arch has the distinct tendency to buckle at the top and push out at the 45-degree points, just like one might expect given the alternative way of looking at things as explained above. To compensate, the arch ring needs to be made accordingly thicker. There is no hard-and-fast rule for how thick the arch needs to be, but it would often need to be absurdly thick — a 50-foot span in the example given above would require at least a four-foot thick arch ring. This extra thickness is often impractical, as it adds to the expense and rise of the bridge, so the fill of the bridge is often relied on to provide the necessary weight to counteract the sliding tendency of the top part of the Roman arch.

Unless the fill is of stone or cement, the fill has a certain “softness” to it that makes one question the stability of the arch, as there is room for the fill to move. And, even if we use stone or cement fill, the whole tendency of the arch is to fall, which is not ideal from an engineering standpoint.

For small culverts, the Roman arch is perfect. After all, the arch ring is going to be relatively thick compared to the size of the arch anyway, and the Roman arch, with its simplicity, lends itself readily to about anything with a span less than 10 feet. If you were to build a 50-foot-span Roman arch bridge with an arch ring somewhere around 8  to 9 feet thick, you would have a fantastically strong and durable structure that would certainly be a monument to the ages — even if you needed to add stairs to aid in climbing to the top of the bridge.

The primary advantage of a Roman arch is its ease of construction. After all, no angled stones (skewbacks) are required to build it, no heavy abutments are required, and the arch itself tends to be more forgiving than a segmental arch, allowing one to not be as concerned about precision fit stones.

The main disadvantages of the Roman arch is its notable rise-over-run ratio, and the fact that the thrust line of the arch can be difficult to contain within the arch proper. These two factors are of the utmost importance to keep in mind when designing a Roman arch.