Rules · Doors & windows · Structure · Walls
Over a large lintel leave a triangular opening by corbelling the courses on either side, so that the wall’s weight passes to the jambs; close the triangle with a thin slab.
At the Lion Gate of Mycenae (c. 1250 BC) the lintel is about 4.5 m long and weighs some twenty tonnes; above it the relieving triangle is filled with a thin limestone slab carved with two lions (their heads, once separate, are lost) flanking a Minoan column. At the Treasury of Atreus the inner lintel of the doorway is a block of about 120 tonnes, and the triangle above it was once screened by a slab of coloured stone.
The triangle makes explicit what every bonded wall does anyway: the courses above an opening arch over it and only a triangle of masonry loads the beam.
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)
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
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)
Build a round chamber of horizontal courses, each ring projecting a little beyond the one below, dress the inner face to a smooth curve, close the top with a capstone, and heap earth over the whole.
Build fortification walls of huge, roughly shaped limestone blocks, with small stones packed into the gaps between them; reserve cut ashlar for gates and façades.
Wall the whole hill; put the ruler’s megaron on its summit, reached by a ramp from the main gate; keep stores, shrines and the ancestral graves inside the walls, and bring water within reach by a hidden stair.
Cite this page Chris Paton, “Relieve the lintel with a triangle”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/relieving-triangle. Text, drawings and models licensed under CC BY-NC 4.0.