Friction Between Bodies and the Bending of Loaded Beams
Why a loaded bracket curves, and how friction grows with surface roughness
The topmost note states that the friction produced between heavy bodies is created by as many different forces as there are degrees of roughness of their surfaces. The rest of the folio analyses how a horizontal beam or bracket, loaded with a hanging weight, turns about its fixed pole and bends, its upper fibres stretching while the lower ones are compressed. The diagrams at right show cantilever brackets, a triangular strut and a pointed arch, each carrying a suspended box weight, illustrating this bending under load.
On this page
Friction increases with the roughness of the touching surfaces
The friction generated between heavy bodies arises from as many varied forces as there are varied degrees of roughness or asperity in their surfaces. Rougher contact therefore yields a proportionally greater resistance to sliding.
A loaded beam a b turns in a circular arc and curves
The beams a b, in making their motion, make it circular; and because the motion is circular, the upper sides of the beams are longer than the lower. Being longer, they are the more pressed by the weight, so the more the beam gives way and the more its opposite side lengthens and bends.
Which side of a support shortens and which lengthens
When r is overcome by the weight it descends and rotates about the pole m; the part of the support farthest from the pole travels most, so the line f r is pressed more than n o and the support bends. Hence the side f r becomes shorter and the curved opposite side becomes longer.
Cantilever brackets and arches carrying suspended weights
The right-hand column carries a graded set of loaded supports: a straight cantilever bracket, a triangular strut, a curved corbel and a pointed arch, each hung with a small box weight. Together they visualise how the geometry of a support governs the way it deflects under the same load.