Use of a Catenary Curve for a roof structure.?

Supposedly, an inverted catery curve would create one of the most stables and self-supporting curves for a structure (See St. Louis Arch).



I am an architecture student and I am currently working on a structure with a curved roof over a very large span, therefore, I would like to try to take advantage of the properties of the catenary curve.

My problem is that the structure is very long in plan, but not very tall. Also, I would like it to NOT be symmetrical in elevation, therefore my question is if "slice" a section of the catenary curve to derive the shape of my roof, would I completely lose the strenght that is gained by using the catenary curve?



The lack of symmetry might completely destroy the properties of the catenary, but maybe it could be compensated in some other way? Or maybe it would lose some, but not all of its self-supporting qualities...?



See this sketch:

The blue line on the sketch on the right would represent the shape of my roof.

http://www.gtalarico.com/catenary.jpg



Thank you so much!Use of a Catenary Curve for a roof structure.?
An arch corresponding to the inverted shape of a uniformly loaded cable is called a funicular arch. See the link below for more information on establishing the funicular shape of an arch, from the book Fundamentals of Structural Analysis by Leet and Uang. To make the shape non-symmetric, raise one end of the cable model or insert intermediate supports as required and then invert the plot of the draped cable(s).