I am studying Gaudí and how does he created some of his work. I found that he used inverted weight models (as the shown in the picture below) to recreate the catenary. In many articles it is pointed as a good practice to simplify and find a better/more sophisticated and solid structure, but I can't see why.
A catenary is the shape a cable will hang in under self-weight. Cables only work in tension, not in bending. If you take this shape and flip it upside down, then (due to gravity now operating in the opposite direction relative to the structure) the structure is purely in compression, with no bending.
Clearly this wouldn't work for a cable, as they don't work well under compressive loads. But it does work well for concrete structures, or for steel sections.
Axial force P over an area A causes a stress of P/A. Moment M on a section with an elastic section modulus Z causes a stress +M/Z on one edge, linearly decreasing to 0 at the neutral axis, and further decreasing to -M/Z on the other edge.
So, if you have a section under compression and bending, then stress at one edge is equal to P/A + M/Z, and at the other edge P/A - M/Z. Clearly if you design so that your maximum stress (P/A + M/Z) is equal to your allowable stress, then most of your section is at less than the allowable stress. However, if you only have compression, then your whole section is at P/A, and if you design such that this is equal to your allowable stress then your whole section is fully utilised - much more efficient.