Loads on Raised Members, an Arch's Thrust, and a Warning to Architects
Moments on a member lifted through a quarter-circle, and the force an arch exerts on its walls
The folio continues the study of loads carried by members raised through a quarter-circle, comparing two pieces a b and n b and how their bases divide the quadrant. A central passage warns the architect who lays transverse loads on walls and pillars to reckon on the weight of the members themselves and never trust iron or wooden ties, because time soon consumes them. A final note poses the geometrical problem of bending a rod f g until it loses a quarter of its length, asking the rise (saetta) of the resulting arc so as to model the thrust arches exert on their walls. Diagrams show inscribed quarter-circles and a semicircular arch loaded by weights on pulleys.
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Comparing the fall of two loaded pieces on a quadrant
It is as hard to make the piece a b fall as the piece n b, for the longer one is the heavier. If one takes half of its quarter-circle, that is its base b r, the other takes exactly the fourth, just so much less, and so on. But when testing, work each of the two pieces separately from the other.
Warning to the architect: do not trust iron or timber ties
You, architect, who give transverse loads to walls and pillars, always reckon on the heaviness of such members and do not trust in keys or chains of iron or of wood, because time in short order consumes them. The moving force l K meets its load at a right angle, and the weight is redistributed as it is raised.
Bending a rod into an arc: its rise and the thrust on walls
I have the rod f g and wish to bend it so it loses a quarter of its length; I ask exactly how much rise (saetta) the arc will have. Up to here things belonging to geometry have been said, but I wish to grasp the line by which the arc exerts its force, to reduce it to the nature of the force arches make on their walls, loading c t with 16 and v x with 12.
A semicircular arch loaded by weights on pulleys
The large figure sets a voussoir arch across the sheet, with cords running over pulleys to hanging box weights arranged along its extrados. The array tests, member by member, how load is carried around the curve and passed down to the springing, matching the text's inquiry into arch thrust.