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Aweighted 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.
Acatenary arch has a uniform thickness. However, if
it becomes more complex. A weighted catenary is needed.
Note that "aspect ratio" is important, which see, [4], [5].
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].