Cords Under Accidental Load; 'Tested' Beam Experiments
Why an angled cord breaks first, and how the load multiplies with the cord geometry
Marked 'Sperimentata' (tested by experiment), the page continues the study of how weights load suspending cords and beams. Leonardo argues that a bent cord a n m must break before a straight cord of equal thickness because it bears 'accidental' weight while the other bears only the natural weight, and that the weight of a rod n S stands to its counterweight f as line a n stands to n m. In a worked figure a weight n is multiplied sixteenfold along the cord c a b (128, split as 64 and 64), and he notes that this load-multiplication lessens as the weight itself grows.
On this page
The angled cord bears accidental weight and breaks first
The cord a n m, though of equal thickness to the cord n f, must break sooner because it is loaded, or rather forced, by the accidental weight, whereas f n is loaded only by the natural weight. The whole weight lies in the straight length of the cord that suspends it.
A rod's weight against its counterweight as a n to n m
The proportion that the line a n has with the line n m is that which the weight of the rod n S has with its counterweight f.
A weight multiplied sixteenfold along the cord c a b
As many times as line a r enters line a b, so many times does weight n enter cord c a b, here 16, giving 128, unloading 64 at c and 64 at b, so cord a b feels 64 pounds. If a r enters a b 16 times, each pound at a n loads c a b by 16; increase n so a r enters only 4 times, and each pound loads it by 4.