Rules · Arches · Structure · Façades
Cross a deep valley on superimposed tiers of arches, the piers of each tier standing directly over those below, the spans matched from tier to tier, and the smallest arches at the top where they carry only the channel.
Pont du Gard: tiers ≈ 22 m, 20 m and 7 m high; 6, 11 and 35 surviving arches; largest span ≈ 24.5 m
At the Pont du Gard the builders stacked three arcades. The two lower tiers have arches of equal spans one above the other, so that loads pass straight down the piers; the widest arch spans the river. The top tier, only about 3 m thick, has small arches at close intervals, just strong enough to carry the covered channel. The stones of the lower tiers were laid without mortar, and each arch is built of several independent rings of voussoirs side by side.
Projecting blocks left on the faces supported the scaffolding and centring during construction. The bridge was so well built that it continued to serve as a road bridge long after the aqueduct fell out of use.
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.
Classify arches by the geometry of the intrados: the number and position of the centres (one for round and segmental, two for pointed, three or four for basket and Tudor arches), or a single continuous curve (ellipse, parabola, catenary), and distinguish true arches, with voussoirs, from corbelled “arches” of oversailing courses.
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, “Arches over arches”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/aqueduct-tiers. Text, drawings and models licensed under CC BY-NC 4.0.