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 · Doors & windows · Arches · Façades
Keep the arch, vary the sides
Where an old structure fixes bays of unequal width, keep the central arch of every Serliana the same and let the flat-headed side openings take up the differences.
Palladio’s loggias round the medieval Palazzo della Ragione in Vicenza (designed 1546, built from 1549) had to follow piers whose spacing was irregular. Each bay is a Serliana (The Serliana) framed by a larger order of half-columns: because the eye reads the round arch as the motif, it can stay constant while the narrow side openings stretch or shrink by a few centimetres unnoticed. Small oculi pierce the spandrels between the arch and the big columns. The building made Palladio’s reputation, and he called it a basilica after the ancient law courts.
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 unify a façade of two or more storeys, run a single order of pilasters or columns through all of them, from the base to the main cornice.
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
Take the plan, the orders and the details from the builders’ pattern books, simplified for timber and for the carpenter: a symmetrical front, a central hall and stair with rooms either side, a doorway under a pediment or fanlight, and mouldings drawn to be made with the plane.
Cite this page Chris Paton, “Keep the arch, vary the sides”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/basilica-constant-arch. Text, drawings and models licensed under CC BY-NC 4.0.