Parabolic arch

A parabolic arch is an arch, shaped like a parabola. While a parabolic arch may look "close" to a catenary arch, the parabola and the catenary are different curves:

1. A parabola is a quadratic function,
2. but a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. While they look "close," the two curves aren't even related; see graphs, below.

Why they are used

• A catenary, in blue, graphed against a parabola, in red
• 
  Parabola (red) graphed against a catenary (blue), view to simulate an arch.
• 
  Parabola (red) graphed against a catenary (blue), view to simulate an arch. Zoomed out.

Parabolic arches in Celler de Sant Cugat

Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve. Of all arch types, the parabolic arch produces the most thrust at the base. Also, it can span the widest area. It is commonly used in bridge design, where long spans are needed.

When an arch carries a uniformly distributed vertical load, the correct shape is a parabola. When an arch carries only its own weight, the best shape is a catenary.

Uses

Parabolic arches are commonly used in bridges; see parabolic bridge. They are also used in cathedrals.

Cathedrals and churches

A few examples:

• Casa Milà is a famous example, and
• Llandaff Cathedral,
• St Leonard's Church,
• St Paul's Anglican Church,
• St Leonard's Church.

all used parabolic arches.

Architects

Oscar Niemeyer used parabolic arches, and Antoni Gaudí was another well known architect who used both parabolic and catenary arches.

Bridges and their technology

The Golden Gate Bridge's parabolic arches

• 16th Street Bridge (Washington, D.C.)
• Balclutha Road Bridge
• Bardwell's Ferry Bridge
• Bayonne Bridge
• Berlin Iron Bridge Co.
• Cape Creek Bridge
• Dell Bridge
• Golden Gate Bridge
• Hadley Parabolic Bridge
• Hulme Arch Bridge
• Galata Bridge

The Hulme Arch Bridge's parabolic arch, singular

• Krasnoyarsk Bridge
• L'Umbracle
• Memorial Bridge (Massachusetts)
• Maurzyce Bridge
• Ordish–Lefeuvre system
• Puente Nuevo (Murcia)
• Raymondville Parabolic Bridge
• Shahrestan Bridge
• Simple suspension bridge
• South Washington Street Parabolic Bridge
• Suspension bridge
• Tyne Bridge

See also

• Arch bridge
• catenary arch
• Catenary
• Catenary bridge
• Catenary lighting
• Catenoid
• Cathedral
• Dome
• Gothic arch
• Gothic architecture
• Lancet arch
• Lancet window
• Mathematics and architecture
• Musgum mud huts
• Natural arch, some of whom are catenary arches
• Nubian vault
• Overhead line
• Simple suspension bridge
• Steel catenary riser
• Suspension bridge
• Toothpick bridge
• Truss arch bridge
• Vault (architecture)
• Voussoir

External links

• On why suspension bridges are parabolic
• Many parabolic arches
• One the difference between a parabola and a catenary
• On parabolic versus catenary arches
• On a variety of curves, parabolas, catenaries, hyperbolas, and ellipses
• YouTube video