Final answer:
The shape of the arch beneath a bridge can be circular, semi-elliptical, parabolic, or rectangular, with parabolic arches often chosen for their structural efficiency in distributing forces. Arches are pure compression forms and their shapes like circles, ellipses, and parabolas are mathematically considered as conic sections.
Step-by-step explanation:
The shape of the arch beneath a bridge can vary, but common types include circular, semi-elliptical, parabolic, and rectangular. The shape is typically chosen based on structural and aesthetic considerations. Parabolic arches, for instance, are often used in bridge design because they provide a strong and efficient way to distribute forces.
Architectural history tells us that an arch is a pure compression form, allowing it to span large areas and carry weight. The physical properties of an arch dictate that as long as it is supported on the sides, it is very stable.
Moreover, from the perspective of mathematics, shapes like circles, ellipses, and parabolas can be described as conic sections, which are the intersections of a plane with a cone. This geometrical property is closely related to the structural efficiency and aesthetics of different arch shapes.