Weighted catenary
A weighted catenary is a catenary curve, but of a special form. A "regular" catenary has the equation
for a given value of a. A weighted catenary has the equation
and now two constants enter: a and b.
Significance[]
A catenary arch has a uniform thickness. However, if
- the arch is not of uniform thickness,[1]
- the arch supports more than its own weight,[2]
- or if gravity varies,[3]
it becomes more complex. A weighted catenary is needed.
The aspect ratio of a weighted catenary (or other curve) describes a rectangular frame containing the selected fragment of the curve theoretically continuing to the infinity. [4][5]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/00/St_Louis_night_expblend_cropped.jpg/350px-St_Louis_night_expblend_cropped.jpg)
The St. Louis arch: thick at the bottom, thin at the top.
Examples[]
The Gateway Arch in the American city of St. Louis (Missouri) is the most famous example of a weighted catenary.
Simple suspension bridges use weighted catenaries.[5]
References[]
- ^ Robert Osserman (February 2010). "Mathematics of the Gateway Arch". Notices of the AMS.
{{cite web}}
: Missing or empty|url=
(help) - ^ Re-review: Catenary and Parabola: Re-review: Catenary and Parabola, accessdate: April 13, 2017
- ^ MathOverflow: classical mechanics - Catenary curve under non-uniform gravitational field - MathOverflow, accessdate: April 13, 2017
- ^ Definition from WhatIs.com: What is aspect ratio? - Definition from WhatIs.com, accessdate: April 13, 2017
- ^ a b Robert Osserman (2010). "How the Gateway Arch Got its Shape" (PDF). Nexus Network Journal. Retrieved 13 April 2017.
External links and references[]
General links[]
On the Gateway arch[]
Commons[]
Categories:
- Plane curves
- Arches and vaults
- Architectural history