Beam mechanics: how a smaller angle bears more weight
The narrower the angle q of triangle q f g, the more of the beam's weight it sustains
The sheet examines how the angle at which a beam is braced governs the load it carries. In the upper figure a beam runs from a graded vertical scale to a pulley at right, and the note states that the smaller the angle q of triangle q f g is compared to the right angle f, the more of the beam's weight that corner sustains. A second beam at lower left is slung by crossing cords, one of several small load-bearing sketches. Much of the middle and lower text on the sheet is faint and left untranscribed.
On this page
Angle q of triangle q f g and the weight it bears
The figure is keyed a f, b n, c n, d o, e p, f, g q, with the value 24. The note states that by as much as angle q of triangle q f g is smaller than the right angle f, by that much more of the beam's weight it sustains than the right angle f does.
The right angle f versus the lesser angle q
The reasoning turns on comparing the right angle at f with the smaller angle q within the same triangle q f g, relating the change in angle directly to the change in the load a corner supports. A boxed figure marked 3 accompanies a second sketch.
Beam slung by crossing cords
At lower left a horizontal beam is drawn held by two cords that cross at a central point, one of several small load-bearing sketches on the sheet. Further faint, untranscribed notes fill the middle and lower portions of the page.