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aLOTofImaginArches

Funicular analysis laboratory

Line of thrust and funicular analysis of masonry arches

User guide ↗

Example

Image and scale

Load an image Image width Image height locked Vertical perspective Horizontal perspective Distance

Block generation

Block properties

Unit weight kN/m³ Apply material to Thickness m Apply thickness to Group colours Clear blocks in

no groups yet

Add a block

Sides

Click the corners in turn. Useful for a pier, a fill, or anywhere the radial cut does not suit the shape. A click near a corner of a block already drawn snaps onto it — a green square shows which — so the two meet exactly and the joint between them can be recovered.

Scale

not scaled — lengths are pixels

Measurements

set the scale before measuring

Dome slice — Poleni

Treat the arch as a dome lune

A barrel vault cut into voussoirs gives blocks of constant width. A dome cut into lunes does not: each is bounded by two meridian planes, so it is broad at the major parallel and closes to nothing at the crown. The weights follow, and so does the line of thrust — this is what Poleni saw in 1748.

Slice angle ° Axis x

off — constant thickness

Points A and B

Impose both ends

not set — the ends follow the joints

With both ends imposed the thrust stays free and the other two parameters become results: the pole's ordinate is whatever carries the line from A to B. The force polygon shows the construction — a trial pole, the closing error, the corrected pole.

Applied forces

X kN Y kN

Click where it acts. Y is positive downward; X is positive to the right. The force joins the blocks in the same sequence.

Equilibrium state

Horizontal thrust

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Start on the springing joint

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Reaction at that springing

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Thickness of the line

The line of thrust is a band whose width is the force in each segment, against the largest. This says how wide the largest is drawn — at nothing it is a bare line, which is what to use when the band would cover the joints it has to be read against.

Three numbers fix the line, and these are they: the pole’s distance from the load line, which is the thrust; where the line leaves its springing joint; and how the total weight divides between the two reactions. Together they are the ∞³ the tool exists to show. The last two need a traced arch, which has joints for the ends to slide along.

Admissibility

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The thrust line must stay inside the ring. If it does, the safe theorem says the arch stands. A ring too thin at the mid-points of its end joints may still be admissible once those ends are free: the limit line runs through the extrados at both springings.

Hooke's cable

Show the hanging cable Weight circles

A circle at each vertex with its area proportional to the weight carried there: blue for a voussoir, orange for a load you applied, because the construction treats the two alike and the drawing should still say which is which. On a dome lune the springing circles dwarf the crown ones, which is the taper made visible. The cable itself is drawn like the line of thrust — its width is the force in each segment — because it carries the same forces, which is the whole of Hooke’s sentence.

Save and reopen

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Writes everything — the traced curves, the blocks, the applied forces, the scale, the background image and the equilibrium state — to one JSON file.

Horizontal thrust —

Arch and line of thrust

Groups

Showing

#	sides	G(x, y)	weight	group

Force polygon