i agree with you
Submitted by napkin rings

You can consider your catenary dome as a set of catenary arches along the "meridians" (vertical cross-sections). The cross-section of your catenary dome would be a catenary arch.

However, I am not sure it would be really catenary because a main difference with an arch is that the load is reduced near the top because the amount of material is reduced proportionately to the reduction of the diameter of the dome, so a catenary dome should be steeper towards the top, maybe even concave instead of convexe! (Obviously, a concave arch would immediately collapse).

But anyway, a dome is much more tolerant to variations of load (wind, etc.) than an arch, and its perfect shape is therefore not structuraly as crucial as with a free-standing arch or vault. The most important thing is to provide a circular tie at the base. Similarly, if you provide an arch or a vault with tympanums (or stiffeners), then the actual shape can be quite far from the ideal catenary.

I am trying to get Jacques Heyman's book "The stone skeleton" which seems to be the most authoritative work on the structural theory of arches and domes. You can also see this web site:

http://www.raeng.org.uk/news/publications/ingenia/issue10/Heyman.pdf

Hope this will give some useful indications!

Laurent