⛪ Timber Cupola: Membrane Hoop Force, Tie Ring and Snow Load (2D)

Cross-section of a thin timber cupola on a log drum, like one crown of a nine-domed wooden church, loaded by its own weight and snow. The shell is coloured by hoop force, blue where it is squeezed round the circumference and red where it is pulled, and the outward thrust at the rim is held by a timber tie ring. Set the radius, opening angle, roof weight, snow, ring section and joint efficiency, and see the membrane forces, the angle where the hoop turns to tension and the ring force and stress. The closed-form forces, the 51.8 degree switch, vertical equilibrium and the shallow limit are checked numerically, with four in-page numerical checks.

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install