Rules · Structure · Materials · Roofs
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)
A timber beam is light and strong in tension along the grain, so its own weight costs it little. This is why the widest columned halls of antiquity (the Persian apadanas, whose columns stand almost nine metres apart, and the Mycenaean megarons) were roofed with cedar or other timber, while Egyptian halls roofed entirely in stone needed their columns close together.
The difference also explains the proportions of columns. Where columns carry timber, they can be slender and widely spaced, as at Persepolis; where they carry stone architraves and stone roof slabs, they must be massive and close, as at Karnak.
In a corbelled vault each course may project only a little beyond the one below, and each overhanging half must have its centre of gravity behind the inner face of its wall; load the tails of the stones with heavy hearting until the capstone is set.
stable if Σ W·x (behind the springing edge) > Σ W·x (in front)
A beam is squeezed along its top and stretched along its bottom; stone resists squeezing well but stretching badly, so a stone lintel must be deep in proportion to its span and cannot be long. Doubling the span quadruples the stress from its own weight.
σ ≈ ¾ ρ g L² ⁄ d (self-weight) · + ≈ 0.43 ρ g L³ ⁄ d² (a wall above)
In a bonded masonry wall the courses above an opening corbel over it of their own accord, so the lintel carries roughly the triangle of wall with sides rising at 60° from its ends; everything above that triangle arches onto the jambs.
load ≈ equilateral triangle on the span: W ≈ 0.43 · L² · t · ρ g
The royal tomb grew in about a century from a low battered mastaba, through a stack of diminishing mastabas (the step pyramid), to a smooth-faced true pyramid; a failure of stability in between forced the change of slope of the Bent Pyramid.
When a steep pyramid shows signs of distress, flatten the slope of the upper part: Sneferu’s pyramid at Dahshur rises at about 54° for its lower part and about 43° above.
lower seked 5 palms (≈ 54.5°) → upper ≈ 7½ palms (≈ 43°)
Make the outer faces of pylons, enclosure walls and mastabas lean inward as they rise, so that the wall is thickest at its foot; mark the corners with a torus roll.
batter of pylons ≈ 1 : 8 (about 83°)
Cite this page Chris Paton, “Timber spans where stone cannot”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/stone-versus-timber. Text, drawings and models licensed under CC BY-NC 4.0.