Rules · Pediments · Roofs · Proportion
Divide the whole front of the cornice into nine parts; give one of them to the height of the tympanum, measured at its centre.
tympanum height = cornice width ⁄ 9 (≈ 12½°)
The rule gives a slope of about twelve and a half degrees, close to the low pitch of Greek temple roofs covered with large marble or terracotta tiles. Renaissance authors, building for northern rains and seen from closer, often steepened it: Serlio and Palladio give constructions that produce roughly 2⁄9 of the width.
Weight for weight, timber is many times stronger in bending than stone; long spans in trabeated buildings are therefore roofed with timber beams resting on stone walls and columns.
bending strength ÷ density: oak ≈ 70 · limestone ≈ 3 (kPa per kg ⁄ m³)
Cut a shaft with sixteen shallow flutes or facets, give it a square abacus and a low round base: the “proto-Doric” column of the Middle Kingdom rock tombs at Beni Hasan.
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)
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
Proportion every step so that twice its height plus its depth equals the length of a natural pace on the level: two feet, or 24 pouces.
2 r + g = 24 pouces ≈ 65 cm (modern practice: 60–66 cm)
Hold that the beauty of the orders comes from fixed proportions that please by nature, as consonances do in music; where the ancients differ, the differences answer to circumstances such as distance and height.
Cite this page Chris Paton, “The height of the pediment”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/vitruvius-pediment. Text, drawings and models licensed under CC BY-NC 4.0.