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 strength 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!

A catenary is indeed a nice form, but there is nothing that says all arches must be catenaries. In fact, few are. Any arch you design must be analyzd for the specific loads you need it to support - in yr case the roof loads. Keep in mind that the St. Louis Arch is only supporting itself - it has no other load to carry, and so the caternary is a natural form for it to take. You may already know this, but a catenary is actually the shape taken by a string or rope suspended between two points, carrying no other loads. Compare that with the shape taken by the cables between the two towers of a suspension bridge (like the Golden Gate Bridge) - the form of the cables is much closer to a parabola than a catenary, because the suspension cables are carrying the weight of the roadway and hence are deformed from their original catenary.