Why Supports Bend in the Middle, and Off-Center Loads Lean
The weakest part of a loaded support is its middle; an off-center weight makes it decline toward the heavier side
Leonardo examines where a loaded support gives way, concluding that the middle of a support's height is overcome by an excessive weight more than any other part. He proves it by experiment: three equal pieces of wood set as a triangle, wide at the feet and narrow at the top, bend first at the middle, because the load runs through the whole support and the weakest part, farthest from the fixed ends, is the midpoint, just as a bowstring's wood is weakest at its middle. He then treats off-center loading: a support not set on the perpendicular through the weight's center leans toward the greater part of that weight, whereas one truly centered would sooner drive its foot into the ground than bend. Sketches show a weight on a bowing tripod of thin beams, an off-center weight tilting a braced upright, an analytical curve of the bend, and a weight neatly centered on its beam.
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The middle of a support is the first to bend
The middle of a support's height is overcome by an excessive weight more than any other part. This is proved by three equal pieces of wood set as a triangle, wide at the feet and narrow at the top: loaded until they bend, the middle is the first part to give, because the load descends through the whole support and the weakest part, farthest from the fixed ends, is the midpoint.
A weight on a bowing tripod of thin beams
A heavy rectangular weight rests on a tripod of thin beams whose ends are pegged to the ground and braced by a triangular frame. Under the load the three beams bow inward, the middle of each yielding first.
An off-center load leans toward the heavier side
A support placed beneath its weight so that it is not centered on the perpendicular through the weight's center will decline toward the greater part of that weight. If instead the center of the support lies on the perpendicular below the center of the weight, it will drive in rather than bend, because all parts of the weight correspond to the parts of the resistance.
A centered support drives into the ground rather than bend
It is impossible for a support to bend when its center lies on a perpendicular beneath the center of the weight; it would sooner push its foundation under the ground. The reason is that the part of the support beneath the weight's center acts almost as a pivot, receiving nearly all the force, and because that part is not surrounded equally by the whole thickness of the support, its weakest part bends.