A parabola-shaped arch is referred to as a parabolic arch. Their curve is an effective manner of load in buildings, and may thus be found in bridges and architecture in a variety of shapes. The simplest example is the arc of a circle, which is also called a cycloid. A less familiar but more practical example is given by the shape of the Wilson window frame. These windows were once popular in American homes, but are now rarely seen because they did not meet code requirements for structural strength.
The parabola-shaped arch is the simplest form of hyperbolic arch. It has two diverging lines on its surface, like two parabolas that overlap and touch at their bases. This is in contrast to the elliptical arch, whose surface has only one line running through it (like two ellipses that do not touch).
The term "parabolic" comes from the fact that the upper part of the arch resembles the surface of the Earth's atmosphere near its horizon, where objects appear to be magnified due to the curvature of space and time.
Parabolic arches have many advantages over other arch types. They require little or no bracing, which makes them suitable for large spans.
A curving structure that spans an open space is known as an arch. Arched bridges were among the first large-scale engineering and building endeavors. Arched bridges may span large areas because the forces acting on them are converted into compressive stresses, which avoids tensile stresses. This allows arches to support very heavy loads while keeping their dimensions reasonable.
The word "arch" comes from a Greek word meaning "keystone". In architecture, an arch consists of two curved sides called arches meeting at a central point called the keystone. The keystone is the heaviest part of the arch, so it needs to be strong enough to carry the entire weight of the roof. As you can see, this is a very important role in an arch bridge.
Other parts of the arch include the base, where the ground or floor beneath the bridge meets it; the crown, which is the top of the arch; and the web, which is the area between the two arches. The arch itself is not visible from the road or rail line, but rather its existence is inferred from the fact that a vertical wall has been allowed for the construction of the bridge. This is because once the foundations have been laid for the bridge, the depth of the hole required depends on how much material will be used for the arch. The deeper the hole, the stronger the arch must be to resist the load applied to the bridge.
Parabolas are frequently used in architecture, particularly in suspension bridge cables. This is due to the fact that the strains on the cables when the bridge is suspended from the tops of the towers are best dispersed along a parabola. The bridge can withstand the pressures that act against it. A straight line would cause higher stresses on the cable at any one point.
The shape of a bridge is determined by its functional requirements. A parabolic arch supports an overhead structure and so requires less material than a similarly strong straight-sided arch. This means that a parabolic bridge needs to be lower than a straight-sided bridge of equal strength. A parabolic arch also causes the cable to work harder because more of it is under tension than if the arch was flat.
A parabolic arch results in a curved surface spanning between two points. For structural integrity, a bridge needs to be thick enough at the base to support its weight and load. The thickness increases as you move upward away from the ground toward the center of the arch where the maximum stress occurs.
The curvature of the bridge changes the effective cross sectional area across which the load is distributed. Because a smaller cross section requires a stronger component, this keeps down the amount of material needed for the bridge's construction. It also reduces the weight of the bridge compared with a similar-sized straight-sided structure.