For the past two entries on this blog, I looked at Galileo’s valuable insight known to us today as the Square Cube Law. Galileo made the mistake of applying the Square Cube Law to masonry arches. He said (p.33) “The great Master Builders of the past used proportional design rules, which are essentially incorrect. Using these rules they built masterpieces of architecture and engineering of the past.” But it was Galileo who was essentially incorrect.
As we wrap up our discussion of Galileo’s incorrect application of the Square Cube Law, a few things stand out from the insight gained by a correct analysis of arches, stresses, and load-bearing ability.
First, the important concept of a catenary is made even more emphatic, and trumps the role of the Square Cube Law. As discussed earlier, a catenary comes from the Latin word “catena” which means chain. Architects also use the term “funicular” to describe the catenary curve; from the Latin “funis” meaning rope or cable. When speaking of masonry, “catenary” is actually a more accurate term, because a masonry arch is comprised of voussoirs, or individual masonry blocks, which are analogous to the individual links of a chain; not the smooth continuity of a rope or cable.
In every arch which is built and stays standing, there can be traced a catenary curve within the wall thickness, described by the thrust force lines which represent the force of gravity acting on the voussoirs. If this catenary curve goes outside of the wall thickness, then a hinge is created, the arch will buckle at this hinge, and it will collapse.
As long as the catenary curve fits within the wall thickness, walls can be made thinner and thinner. Furthermore, the addition of loads onto a masonry arch tends to keep the thrust force lines within the wall thickness: so that adding weight can actually strengthen a masonry arch or dome.
This is the essential design analysis for masonry arches and domes. It really has nothing to do with Galileo’s Square Cube Law. Whether by conscious design and intuitive insight, or merely by trial and error, the master masons of antiquity always fit the catenary curve within their wall thickness by using their simple rules of geometric proportion; this is why their structures could be made small or large, and this is why their incredible feats of engineering and art still stand today to inspire us and enrich us.