Where does the weight of a canal in the sky go? Follow the load from the water through the clay lining and masonry into the arch ring and down the piers. Drag to orbit, wheel or pinch to zoom; press Start navigating to send the narrowboat across.
Each button recomputes the statics for a range of values.
The science
Load path. Per metre of span the arch carries the water ρw g bw h, the puddled-clay lining, the trough walls, the masonry fill between the deck and the arch back, and the ring itself. The fill is far heavier over the haunches than over the crown, so the load is not uniform. The water in the trough is under 10 % of the total.
Thrust line. A masonry arch stands if some line of thrust (the funicular of the loads) lies inside the ring. We take the line that passes through chosen points of the crown and springing joints, compute the horizontal thrust from the moment about the springing, H = (1/zc) ∫0xs q(x)(xs − x) dx, and search all such lines for the one that stays closest to the ring centre line. Utilisation 1 means the best line just touches the ring surface, a hinge is about to form; below 1 the arch stands. The middle-third rule (utilisation 1/3) would keep every joint fully in compression.
The floating boat. By Archimedes a floating boat displaces its own weight of water. In a trough connected to the canal the displaced water leaves, so the load on the aqueduct is unchanged whatever the boat weighs. Only if the trough were sealed would the boat’s weight be added.
Trough walls. Water pressure on a wall gives an overturning moment ρ g h³/6 per metre against the restoring moment of the wall’s weight about its outer toe. Safety falls fast with depth, which is why flood levels matter.
Honest simplifications. The ring is treated as a semicircle of constant thickness, the loads act vertically, and the sidewalls of the trough do not stiffen the arch. Densities and the masonry strength are typical values; piers are checked only for axial stress. A real assessment uses limit-analysis software and site data. This is an educational model, not a structural assessment.
Made with Blender · Three.js. Educational only.