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.

A catenary 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].

...
Wikipedia