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)
Rules · Ornament · Structure · Materials
Timber ceilings of beams and coffers
Ceil the rooms of a palace in timber: in the lesser rooms with beams across the shorter span and boards between them; in the great rooms with coffers framed by beams both ways, painted and gilded, each with a rosette.
Serlio closes his book on the five orders with designs for wooden ceilings divided into compartments, squares, octagons and crosses, for the architect to adapt; they were copied across Europe, in England as much as in Italy. The plainer ceiling of exposed beams and boards was the ordinary one of the Italian house.
Related rules
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
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.
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
Make the architrave round a door or window as wide as a sixth part of the opening’s breadth, and dress the openings of the principal floor more richly than those of the storeys above and below, with a frieze and cornice, and on the grandest a pediment.
architrave = ⅙ × width of the light
Break the architrave of a door or window with blocks of plain stone laid across it, alternately larger and smaller, and set a keystone in the middle of the head.
Cite this page Chris Paton, “Timber ceilings of beams and coffers”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/serlio-ceilings. Text, drawings and models licensed under CC BY-NC 4.0.