The Catenary, Segmental Arches, and Roman Arches

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Construction

Segmental arches have a certain strength that is due to the fact that they closely approximate a catenary. Thus, low-rise arches can be very thin and able to free-stand.

In our post on The Secret of the Arch: The Principles, we showed how the line of thrust in an arch is a catenary, and how, if an arch is capable of free-standing, it is because a catenary can be contained within the arch’s thickness. One significant feature of this trait of arches is that low-rise arches can be made to free-stand with but little thickness.

The Catenary Vs. The Circle

A half-circle does not approach closely to a catenary in shape. However, as the arch becomes flatter and flatter (thus a smaller and smaller arc of a circle), the curve more and more closely follows a catenary shape. Thus, it will follow that a segmental arch, assuming fixed abutments, of course, will be more and more capable of free-standing the lower-rise it is.

A low-rise arch built of wooden blocks with thick paper used for shims to make the angles. The span is 26.5 inches, while the rise is a mere 2 inches. The blocks are .5 inches thick. As can be seen, the arch thickness is much thinner than the span of the arch. However, the very low rise allows this thin structure to be stable.

This is borne out by the fact that the flatter the arch, the thinner it can be made and still free-stand. This is because less and less material is required for there to be a catenary contained within the thickness of the arch.

The Strength of the Low-Rise Arch

Unless very flat, a low-rise arch is quite a strong structure, provided the abutments are firmly fixed in place. With the stones tightly wedged in place, because the line of thrust is contained in the center of the arch, the structure is extremely stable. In fact, low-rise arches can be more stable than higher-rise arches like the Roman arch. Of course, a very flat arch becomes rather vulnerable to “snapping” under loads; the relative stresses are fairly high and there is much less room for error due to crushing or shifting.

Thompson Bridge — A low-rise segmental arch. The graceful curve of the arch rather closely approximates a catenary.

Based on observation, a 130-degree segment of a circle is about as high as you can go and the arch still approximate a catenary reasonably closely, while a 90-degree segment of a circle is so close an approximation to the catenary that going flatter is probably unnecessary, and, at any rate, below this angle horizontal thrust will become a major consideration.

The Roman Arch: Partly Arch, Partly Abutment

The Romans found a solution to making thin Roman arches stable without resorting to low-rise shapes. The solution was the use of solid backing. Since the Roman arch tends to “blow out” where the catenary shape ceases to track closely with the overall shape of the arch, the Romans found they could still build a thin Roman arch if they used solid backing built up to this point on the arch. Thus, though the thrust escapes the Roman arch, it travels through the solid backing, and stability is reached. It will be noted from this that the lower parts of the arch are not really doing much, but are more of a face for the abutment. This can be visualized by observing a Roman arch where the arch has collapsed. It will be seen that the bottom portions of the arch remain intact even after the top is gone.

Remains of a Chase County, KS. Stone Bridge — The remains of a demolished multi-span stone arch bridge. Note how the lower part of the Roman arch is still intact though the rest of the bridge is gone. Clearly, this lower portion of the Roman arch is not dependent on the thrust from the upper portions of the arch for stability.

Furthermore, from this it can be observed that in all Roman arches, the bottom of the arch acts merely as the “abutment,” if you will, of the “segmental arch” on top.