Loading and Strengthening Round Arches and Ogives
Filling the spandrels, the dangers of loading an ogive, testing an arch's strength, and a puzzle of the balance
A page of short prescriptions on arches with their diagrams, opening with a note on conformity—that the particles should correspond to the parts and the parts to the whole. Leonardo advises filling an arch's spandrels with good fill up to its crown to make it permanent, and gives paired headings on loading round arches and ogives correctly and on the harm an ogive suffers when loaded over its middle or at its flanks. He sketches an apparatus of cords and pulleys 'for measuring the strength of the arch,' and observes that a slightly curved arch is secure of itself while a strongly curved one is weak and breaks at o p. A closing question asks why a balance does not carry its larger weight below the pivot.
On this page
On conformity
A note headed 'On conformity' states a general design principle: make the particles correspond to the parts, and the parts to the whole.
Fill the spandrels to make the arch permanent
The way to make an arch permanent is to fill its spandrels with good fill up to its flat part, or crown.
The harm of loading an ogive over its middle or flanks
A heading treats the problem that arises from loading an ogive over its middle, paired with a note on the damage the ogive receives when loaded at its flanks; these accompany diagrams of loads placed at an ogive's peak and shoulders.
An apparatus for measuring an arch's strength
Cords tied to the springs of a loaded arch run over pulleys set in the inner corners of two blocks and down to a large weight, giving a way to measure the thrust—the strength—that the arch can bear.
Slightly vs. strongly curved arches (b n a m e; c o d p f)
An arch only slightly curved is secure of itself, but when loaded its shoulders must be well strengthened. An arch curved quite a lot is weak in itself and weaker still when loaded, deriving little support from its shoulders, and it breaks at o p.
Why a balance will not carry its larger weight below the pivot (a e; c b d)
Leonardo asks why a balance does not push the larger weight, placed at one end, below its pivot. If the pivot were centred in the widthwise direction as it is lengthwise, at b, and the weight's centre lay at the width's centre, then the larger weight d would drop below the pivot b.