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Weighted catenary

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Weighted catenary

A weighted catenary is a catenary curve, but of a special form. A "regular" catenary has the equation

Contents

y = a cosh ⁡ ( x a ) = a ( e x a + e − x a ) 2

for a given value of a. A weighted catenary has the equation

y = b cosh ⁡ ( x a ) = b ( e x a + e − x a ) 2

and now two constants enter: a and b.

Why they are important

A catenary arch has a uniform thickness. However, if

  1. the arch is not of uniform thickness, [1],
  2. the arch supports more than its own weight, [2],
  3. or if gravity varies, [3],

it becomes more complex. A weighted catenary is needed.

Note that "aspect ratio" is important, which see, [4], [5].

Examples

The Gateway Arch in the American city of Saint Louis is the most famous example of a weighted catenary.

Simple suspension bridges use weighted catenaries, [6], or parabolas, [7], [8].

References

Weighted catenary Wikipedia
(Text) CC BY-SA