Make the roof visible, and bring its eaves down low enough, and far enough out, that the building reads as a shelter from the street and the garden.
Rules · Structure · Vaults · Roofs · Materials
Strength from form
A thin curved shell carries load by the membrane forces in its surface, not by bending; so shape it to its loads and supports, and it can span great distances with a thickness of a few centimetres.
span ÷ thickness of a good shell ≈ 400–1000 (an egg: ≈ 100)
Flat slabs and beams resist load by bending, which wastes most of their material near the neutral axis. A curved shell turns the load into compressions and tensions within its own surface, which every part of its thickness shares. The engineers of the twentieth century (Eduardo Torroja, Pier Luigi Nervi, Félix Candela, Heinz Isler) built shells that a traditional mason would have thought impossibly thin. Los Manantiales at Xochimilco (1958) spans about 42 m with a concrete surface about 4 cm thick, stiffened only by the thickening of its groins.
Related rules
A saddle surface in which two opposite corners are raised and two lowered is a hyperbolic paraboloid; it contains two families of straight lines, so it can be formed with straight boards and yet has double curvature.
y = k·x·z (or any bilinear patch through four points not in one plane)
A fabric or cable-net roof is stable only if it is prestressed into an anticlastic (saddle) shape, curved upward in one direction and downward in the other, so that wind from either side meets a surface already in tension.
Hang a chain (or a model of strings loaded like the building) from two points; the curve it takes, turned upside down, is the ideal shape of an arch carrying the same loads, in pure compression.
A masonry arch stands if a line of thrust (the path of the compressive force through it) can be drawn entirely within its thickness; the catenary arch contains its own line of thrust exactly, the semicircle only if it is thick enough.
catenary: thrust line = centre line · semicircle: needs t ⁄ R ≳ 0.11
Span the whole depth of the building with the structure so that each floor is a single open plate, adaptable to uses that cannot be foreseen.
Pompidou: 48 m clear span between column lines, 13 bays of 12.8 m
Cite this page Chris Paton, “Strength from form”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/shell-form-active. Text, drawings and models licensed under CC BY-NC 4.0.