Rules · Structure · Walls · Light
Gather the weight and thrust of the vaults onto a few points by ribs, carry them down piers and out across the aisles by flying buttresses to external buttress piers, and the wall between the supports carries almost nothing, so it can be opened into windows.
Abbot Suger’s choir at Saint-Denis (1140–44) is the usual starting point: its ambulatory of slender columns and rib vaults surrounds the altar with a continuous ring of stained glass. Over the next century the system was pushed upward and outward (at Chartres, Bourges, Reims, Amiens and Beauvais) until at the Sainte-Chapelle in Paris (consecrated 1248) the upper chapel is little more than a cage of stone and glass.
Viollet-le-Duc explained the whole style as the logical working-out of this idea, a structure in equilibrium in which every member has its task. His account is too tidy (Gothic builders also chose forms for their meaning and beauty), but it remains the best single key to how the buildings stand.
Build an arch of wedge-shaped stones (voussoirs) whose joints all point towards the centre of the curve: each stone can then fall only by forcing its neighbours apart, and so the ring holds itself up once the last stone, the keystone, is in place.
joints ⟂ intrados (radial to the centre)
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)
A chain hanging freely takes the one shape in which it is in pure tension; turn that shape upside down and it is the shape of an arch in pure compression for the same loads.
free-hanging chain (catenary) ↔ ideal arch under its own weight
Trace the path of the resultant force through the stones from crown to foundations. If a line can be found that stays everywhere within the masonry, the arch will stand; where it touches an edge, a hinge will open, and four hinges make it collapse.
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
An arch cannot support itself until it is complete. Build it on a timber centring shaped to the intrados, strike the centring only when the keystone is set and the mortar has taken, and reuse it from bay to bay, which is one reason to keep the spans of an arcade equal.
Cite this page Chris Paton, “Concentrate the loads; fill the rest with glass”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/gothic-skeleton. Text, drawings and models licensed under CC BY-NC 4.0.