Cover two bays of the nave with a single square vault divided into six cells by its diagonals and an extra transverse rib through the centre. The main piers carry three ribs each, the intermediate piers only one, so the supports may alternate strong and weak.
Sexpartite vaults belong to Early Gothic: Sens Cathedral (begun about 1140), Laon and Notre-Dame de Paris (begun 1163), and in Normandy the abbey churches of Caen. They keep the square bay of Romanesque design while introducing the rib. After about 1200 they gave way to quadripartite vaults over single oblong bays, which gave the nave a uniform rhythm and uniform supports.
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, “The sexpartite vault spans a double bay”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/sexpartite-vault. Text, drawings and models licensed under CC BY-NC 4.0.