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 · Roofs · Geometry · Materials
A membrane must be a saddle
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.
A flat or single-curved membrane flutters and folds under wind, because it can only resist load by changing shape. Pulled between high and low points (masts and anchors, or arches and ground), the membrane takes on double curvature, and each fibre is held by the fibres crossing it. The simplest such surface is the four-point saddle; the Munich Olympic roofs (1972) join many saddles into a cable-net landscape.
Frei Otto found these forms by experiment, with soap films, stretched stockings and hanging nets, and only then calculated them: the form is not designed but found.
Related rules
Frame a sphere by subdividing the triangular faces of an icosahedron and projecting the points onto the sphere; the triangulated net of short struts spreads loads through the whole surface and encloses the greatest volume for the least material.
full sphere of frequency ν: 30ν² struts, 20ν² triangles, 10ν² + 2 hubs
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)
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
Move ducts, pipes, lifts and escalators out of the building’s core onto its exterior, colour-code them, and let them become the architecture, leaving the interior free and making the plant easy to reach and replace.
Cite this page Chris Paton, “A membrane must be a saddle”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/tensile-saddle. Text, drawings and models licensed under CC BY-NC 4.0.