Catenary Structures & Ruled Surface (Research)

What is Catenary? In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. 

In this concept or way of architecture many famous contractors made colossal structures that are know and still present today like the following:

But how can we create such said art? By Ruled surface is the answer. In geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar examples are the plane and the curved surface of a cylinder or cone.