Cover a wide nave with triangulated timber trusses rather than a vault: their tie-beams take the outward thrust, so the walls need only carry weight and may stand on slender columns.
nave span ≈ 13–24 m on trusses (Santa Sabina ≈ 13.5 m; Old St Peter’s ≈ 24 m)
A vault pushes outward and needs thick walls or buttresses; a truss is a closed triangle whose tie-beam holds the feet of the rafters together, so it presses straight down. That is what allowed the Christian basilica to rise quickly, cheaply and very large on colonnades of reused columns, and also why many of them burned.
The trusses were often left open to view, or hidden above flat coffered ceilings of gilded timber. The open truss roofs of later medieval halls and of Victorian churches descend from them.
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.
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.
Throw an arch diagonally across each upper corner of the square, backed by a small conch or cone; the four squinches and the four walls between them make an octagon, on which a round dome can sit.
octagon side = S (√2 − 1) ≈ 0.414 S; squinch span = octagon side
Cite this page Chris Paton, “Span the nave in timber”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/basilica-timber-roof. Text, drawings and models licensed under CC BY-NC 4.0.