Over a doorway or window spanned by a lintel, turn an arch in the wall above so that the weight of the masonry is carried round the opening onto the jambs, leaving the lintel to carry only the small triangle of wall beneath the arch.
Rules · Structure · Domes · Walls
Buttress the dome where the semidomes cannot
Where no semidome takes the thrust of the dome, on the north and south, carry it across the aisles to massive buttress piers that rise above the roofs, and fill the great arches with thin walls pierced by windows.
The north and south great arches of Hagia Sophia are closed only by tympanum walls with two rows of windows; the real support is outside, in four towering buttresses joined to the main piers by arches over the galleries. The arrangement anticipates the flying buttress of Gothic architecture: the thrust is taken out through the air to a mass standing clear of the interior.
Even so the piers leaned outward during construction, and the first dome, shallower than the present one, fell after earthquakes in 558. Later centuries added further massive buttresses round the building, and the Ottoman architect Sinan strengthened it again in the sixteenth century.
Related rules
To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.
sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2
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
If the sphere that forms the pendentives is simply continued above the ring, the bay is covered by a single shallow dome, the sail vault or pendentive dome, which springs directly from the four corners.
crown = h₀ + S⁄√2 (lower than a hemisphere on the ring, h₀ + S)
Lift the dome on a cylindrical or polygonal drum pierced with windows between the ring of the pendentives and the springing of the dome, to light the centre of the church and to make the dome visible from afar.
drum height ≈ ⅓–1 × its radius (Byzantine); much taller in Russian churches
Pierce the base of the dome with a close ring of windows between buttressing ribs, so that the shell seems to float on light rather than to rest on the arches.
Hagia Sophia: 40 windows and 40 ribs; dome ≈ 31 m across, crown 55.6 m above the floor
Cite this page Chris Paton, “Buttress the dome where the semidomes cannot”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/buttress-piers. Text, drawings and models licensed under CC BY-NC 4.0.