How Do Stone Ceilings Stay Up? Ribs, Arches and the Forces They Send Sideways

An arch carries load by compression, with each stone pressing against its neighbours, and the consequence is that the weight above is converted partly into a sideways push at the base. A vault is an arch extended in three dimensions and does the same thing along its whole springing line, so a stone ceiling over a wide space is continuously trying to push the supporting walls outward. That single fact dictates almost everything about the buildings. The wall must be thick enough to contain the thrust, or it must be buttressed from outside, or the thrust must be reduced. Raising the vault higher and making the arch more pointed reduces the sideways component, which is one reason the pointed arch replaced the round one and why the buildings got taller as the technique improved.

The forms developed in a rough sequence and each solved a problem the last one had:

• •Barrel, a continuous half-cylinder, simple and requiring continuous heavy walls along its length
• •Groin, two barrels crossing, which concentrates load at four corners and frees the walls between
• •Ribbed, with stone ribs along the intersections and lighter infill between them
• •Quadripartite and sexpartite, dividing each bay into four or six panels
• •Fan, with ribs radiating in identical curves, which is largely decorative over a different structure
• •Net and star patterns, where ribs multiply well beyond any structural requirement

The traditional explanation holds that the ribs form a skeleton carrying the load while the panels between merely fill the gaps, and the picture is at best partly true. Ribs certainly served during construction, since they could be built first on timber centring and then support the infill, which saved an enormous amount of expensive timber and allowed the panels to be built without full formwork. Whether the completed vault depends on them is another matter, and there is evidence on both sides, including vaults that survived the loss of their ribs in wartime damage and stood perfectly well, and analyses showing the ribs carrying a modest share of the load. The consensus now treats them as important during construction, structurally helpful but not essential afterwards, and increasingly chosen for appearance as the style developed.

Medieval builders had no structural calculations and the question of what they did instead is genuinely interesting. The evidence points to proportional rules of thumb, passed within the trade and expressed geometrically rather than numerically, specifying buttress thickness as a fraction of the span and similar relationships that encode accumulated experience. Those rules produce structures that work, and they were derived by building, observing and adjusting over generations, including from failures, several of which are documented, with towers and vaults collapsing and being rebuilt more heavily. Drawings scratched into tracing floors survive at a few sites and show how the geometry was set out full size. Modern analysis of the standing buildings generally finds them conservative rather than marginal, and the safety margin came from proportions that were empirically tested rather than from any theory of forces.

Following the force to the ground explains the exterior of these buildings completely. The vault delivers its thrust to the tops of the piers, from where it must reach the foundations without pushing anything over. A flying buttress catches that thrust partway up and carries it across the aisle roof to a heavy pier standing clear of the building, which is why the structure looks as it does and why the aisles could be roofed at all. The pinnacle on top of that outer pier adds weight, which steepens the line of force inside the masonry and keeps it within the stone, which is why these apparently decorative spikes are structural. Inside, the flow of force is why piers are massive at the base, and why the great windows are possible at all, since the wall between the piers carries almost nothing.

A vault converts weight into an outward push along its springing line, and every feature of the building exists to get that push to the ground. A pointed arch reduces the sideways component, which is why the form replaced the round arch and the buildings grew taller. The ribs mattered most during construction, and vaults have survived losing them.