Basket-handle Arches: The Elliptical and the Pseudo-elliptical Arches

Stone Bridge of Granite

Roman arches and segmental arches are the standard arch forms we often see. The Roman arch is simply half a circle, while the segmental arch is a smaller arc of a circle. Though the Roman arch has its weaknesses, one of its huge advantages is the lack of horizontal thrust at the ends of the arch. This means that no massive abutments are required, and it can be quite easily built.

Segmental arches, on the other hand, require large abutments to resist the horizontal thrust, which can become quite serious as the arch becomes flatter. Yet segmental arches can have a huge advantage: They can have a lower rise, which means less of a “hump” on the bridge.

But what about a compromise between the two? This is where the so-called “basket-handle” arch comes in. The elliptical and pseudo-elliptical arches offer a compromise between the Roman and segmental arches.

The Elliptical Arch

The elliptical arch is just that: half of an ellipse. Although the ellipse can be drafted in many ways, the basic elliptical arch has a low rise like a segmental arch, yet still lands flat on the abutments like a Roman arch. This means that the abutments don’t have to be as thick as would be required with a segmental arch. At the same time, the bridge does not have an inconveniently steep road grade.

Elliptical arches are fairly rare. The formwork for the arch can be rather difficult to create.

Historically, where elliptical arches were used, a large number of different stonecutting templates were necessary. The arch stones were cut precisely by first-class stonemasons. Only a given pair of courses of arch stones have the same shape. This makes the job rather difficult.

A common solution was to use a “pseudo-elliptical” arch.

The Pseudo-elliptical Arch

The pseudo-elliptical arch is an arch drawn with an odd number of arcs.

The “three-centered” arch appears to be the most common form of basket-handle arch. It is drawn with three separate arcs. The primary arc consists of a relatively low, flat segment of a circle. Towards the end of the arch it transitions into two identical small, mostly rounded arcs that take it flat to the horizontal plane. The two end arcs often are a large chunk of a small Roman arch, while the middle arc is a low segmental arch. The end result is truly a compromise between a Roman arch and a segmental arch.

The low-rise segmental arch takes most of the span. The two Roman arches tend to put most of the thrust flat onto the abutment. This three-centered arch can resemble a true ellipse more than one might think. Yet it only requires two different templates for a given course of arch stones — one template for the low segmental span and one for the two end spans.

How a Basket Handle Arch is Drawn
A picture showing how a basket-handle arch is drawn. The small radii start as the main radius, then rotate relative to the horizontal plane till they meet with this plane.

It is possible to use more than three arcs and create a “five-centered arch,” “seven-centered arch,” etc. An arch with three separate arcs is the typical solution.

Many bridges in Europe use some form of basket-handle arch, though it does not appear to be as common in the United States.

In theory, there is no rule that says a basket-handle arch has to land on a horizontal plane. It can be started on an angled “skewback” like a segmental arch. However, there is usually no advantage in doing this.

Stone Bridge of Granite
A stone arch bridge employing a basket handle arch. Note how the arch transitions from a relatively shallow arc at the top to a rounded curve at the ends which land flat on a horizontal plane.

Other Variants of the Basket-handle Arch

The Tudor arch is a similar concept, but is more of a cross between a Gothic pointed arch and a Roman arch. The ends of the arch are rounded, but the crown of the arch terminates neatly in a point. Historically, the Tudor arch has seen only occasional use in bridges.

Another alternative to a basket-handle arch consists of two halves of a parabola. Basically, it is as if a parabola is cut in half, the more rounded part of the halves being placed on the abutments of the bridge, with the legs meeting at the crown of the arch. This meeting of the two parabolas creates a slight point at the top of the arch like that of the Tudor arch.