Rules · Vaults · Structure · Walls
A barrel (tunnel) vault is an arch extruded along its axis. It thrusts outward all along both sides, so it must rest on continuous thick walls, which can be pierced only sparingly, and only below its springing.
thrust per metre of wall ≈ constant along the whole length
Romanesque builders who wanted a fireproof stone ceiling over a nave reached first for the barrel. At Saint-Savin-sur-Gartempe (c. 1100) the painted barrel rests directly on the arcade, with no clerestory at all; at Cluny III (begun 1088) the pointed barrel rose some thirty metres, with windows squeezed in below its springing, and part of it fell in 1125.
Transverse arches (doubleaux) under the vault, springing from shafts on the piers, stiffen it and divide it into bays, but do not change the fact that its thrust is spread along the whole wall.
In a bonded masonry wall the courses above an opening corbel over it of their own accord, so the lintel carries roughly the triangle of wall with sides rising at 60° from its ends; everything above that triangle arches onto the jambs.
load ≈ equilateral triangle on the span: W ≈ 0.43 · L² · t · ρ g
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)
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
An arch cannot support itself until it is complete. Build it on a timber centring shaped to the intrados, strike the centring only when the keystone is set and the mortar has taken, and reuse it from bay to bay, which is one reason to keep the spans of an arcade equal.
Cite this page Chris Paton, “A barrel vault needs a continuous wall”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/barrel-vault. Text, drawings and models licensed under CC BY-NC 4.0.