Strengthen a barrel-vaulted nave with transverse arches at every bay, springing from shafts on the piers; they stiffen the vault, mark the bays and serve as ribs on which the vault can be built bay by bay.
The transverse arch (doubleau) is the ancestor of the Gothic rib: an arch built first, on which the lighter vault is then laid. In Burgundy the barrel itself became pointed, at Cluny and at Autun, which reduced its thrust and allowed higher naves.
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.
In a row of arches the thrusts of neighbouring arches cancel over each intermediate pier, which may therefore be slender; at the ends of the row nothing balances them, so the outermost piers must be made wider or buttressed.
Cite this page Chris Paton, “Transverse arches beneath a barrel”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/rom-barrel-transverse. Text, drawings and models licensed under CC BY-NC 4.0.