Build the arches of the vault first (transverse, wall and diagonal ribs) on light centring, then fill the triangular cells between them with thin webs of stone laid course by course from rib to rib.
The earliest rib vaults in the West are those of Durham Cathedral, begun in 1093; by the 1140s the choir of Saint-Denis showed how ribs could vault even the irregular trapezoids of an ambulatory. Viollet-le-Duc read the ribs as a skeleton that carried the webs and concentrated their thrust on the springers. Later critics showed that a finished vault works as a shell and can stand with its ribs damaged, but the ribs remained the key to construction: they needed little centring, fixed the geometry of every groin, and let the webs be made only twenty or thirty centimetres thick.
The ribs also made the structure legible. Carried down the wall as shafts to the floor, they tie vault, wall and pier into a single articulated system, the most characteristic visual trait of Gothic.
Build an arch of wedge-shaped stones (voussoirs) whose joints all point towards the centre of the curve: each stone can then fall only by forcing its neighbours apart, and so the ring holds itself up once the last stone, the keystone, is in place.
joints ⟂ intrados (radial to the centre)
An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
A chain hanging freely takes the one shape in which it is in pure tension; turn that shape upside down and it is the shape of an arch in pure compression for the same loads.
free-hanging chain (catenary) ↔ ideal arch under its own weight
Trace the path of the resultant force through the stones from crown to foundations. If a line can be found that stays everywhere within the masonry, the arch will stand; where it touches an edge, a hinge will open, and four hinges make it collapse.
A round arch must rise half its span, so arches of different spans on one springing line have crowns at different heights. A pointed arch can be given any rise at least half its span, so arches of different widths can all be made to reach the same height.
round: f = s⁄2 (fixed) · pointed: r = (s²⁄4 + f²) ⁄ s for any f ≥ s⁄2
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
Cite this page Chris Paton, “Ribs first, webs after”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/rib-vault-skeleton. Text, drawings and models licensed under CC BY-NC 4.0.