Rules · Arches · Façades · Proportion
Pierce a massive rectangular pier with one arch, or with a tall central arch between two lower ones; frame the openings with columns on pedestals carrying an entablature, and crown the whole with a high attic for the dedicatory inscription.
Arch of Titus: 13.5 × 15.4 m, one opening 5.4 × 8.3 m; Arch of Constantine: 25.9 × 21 m, openings 6.5 × 11.5 m and 3.4 × 7.4 m
Triumphal arches commemorated victories and emperors; they stood astride the processional routes of Rome and of provincial cities. The single-bay type, like the Arch of Titus with its early Composite capitals, is a compact block about as high as it is wide; the three-bay type, like the arches of Septimius Severus and Constantine, adds lower side passages and free-standing columns whose entablature breaks forward over each column (a ressaut), carrying statues in front of the attic.
The motif of an order framing an arch, with an attic above, became one of the most fertile in Western architecture. Alberti turned it into a church façade at Sant’Andrea in Mantua; it reappears in city gates, palace portals and the Arc de Triomphe in Paris.
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.
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
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, “The triumphal arch”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/triumphal-arch-scheme. Text, drawings and models licensed under CC BY-NC 4.0.