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 · Plans · Proportion
Three proportions for the atrium
Give the atrium one of three shapes: width to length as 3 : 5, or 2 : 3, or a length equal to the diagonal of the square on the width; and make its height to the girders a quarter less than its width.
L = 5⁄3 W, 3⁄2 W, or √2 W; height to girders = ¾ W
The atrium was the public heart of the Roman house, where the master received his clients each morning. Vitruvius fixes its plan by three ratios, the last of them (the diagonal of a square) irrational and constructed with compasses rather than counted. The rest of the house then takes its dimensions from the atrium: the side wings (alae) from its length, the tablinum and the entrance passage (fauces) from its width.
He also describes five types of atrium by the construction of their roofs: the Tuscan (beams across the room, the roof sloping inward to the central opening), the Corinthian (the same beams carried on columns round the opening), the tetrastyle (four columns at the corners), the displuviate (roof sloping outward) and the fully covered testudinate.
Related rules
Edge the beds before the portico with box, clip box into figures of animals set facing one another, and in the garden beyond cut it into many shapes, even into the letters of the owner’s name.
Make the corner columns thicker than the rest by a fiftieth of their diameter, because, seen against the open sky, they look thinner than they are.
D corner = D × (1 + 1⁄50); Parthenon: 1.95 m against 1.905 m
Divide the height from floor to ceiling into three and a half parts and give two and a half to the opening; make a Doric door five and a half twelfths as wide as it is high (an Ionic one two-fifths), and narrow it slightly at the top.
h = 2½⁄3½ H; Doric w = 5½⁄12 h, Ionic w = h ÷ 2½; top narrowed by ⅓, ¼ or ⅛ of the jamb as h ≤ 16, ≤ 25, ≤ 30 ft
Architecture depends on order (ordinatio), arrangement (dispositio), eurythmy, symmetry, propriety (decor) and economy (distributio).
A column is narrower at the top than at the bottom, but the taller the column the less it should be diminished, because distance already makes its top look smaller.
upper Ø : lower Ø = 5⁄6 (≤15 ft) · 11⁄13 (15–20 ft) · 6⁄7 (20–30 ft) · 13⁄15 (30–40 ft) · 7⁄8 (40–50 ft)
Cite this page Chris Paton, “Three proportions for the atrium”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/atrium-proportions. Text, drawings and models licensed under CC BY-NC 4.0.