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.
Why they are important
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.
Note that "aspect ratio" is important, which see,[4][5]
![](../I/m/St_Louis_night_expblend_cropped.jpg)
The St. Louis arch: fat at the bottom, skinny 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". Mathematics of the Gateway Arch. Notices of the AMS. Missing or empty
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(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
- 1 2 Robert Osserman (2010). "How the Gateway Arch Got its Shape" (PDF). How the Gateway Arch Got its Shape. Nexus Network Journal. Retrieved 13 April 2017.
External links and references
General links
On the Gateway arch
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