Strength of a Column Divided Lengthwise and Widthwise
How splitting a bearing column into thinner or shorter parts changes the load it holds
Four diagrams demonstrate how a square support's load capacity changes when it is subdivided. A column bearing 320 pounds is split lengthwise into sixteen very thin beams, each so slender that together they hold only 60 pounds. Conversely, a nine-braccia column bearing 900 pounds, divided widthwise into nine short blocks, gains strength so that the low broad mass bears 64,800 pounds. Leonardo frames these as opposed rules: dividing a support along its length weakens it, while reducing its height strengthens it.
On this page
Lengthwise division weakens a support (320 becomes 60)
A square column ten parts high and one wide resists 320 pounds; if it is split lengthwise into sixteen equal beams, each is so thin that its diameter now enters forty times into its height rather than ten. Each beam, once separate, bears only 5 pounds instead of the 20 it shared when united. Sixteen times 5 makes 60, which is 260 pounds less than the united force.
Widthwise division strengthens a support (900 becomes 64,800)
A square column nine braccia high resists 900 pounds. Cut into nine short pieces and burdened according to their resistance, each piece, reduced in height by eight-ninths, gains power by eight-ninths. Eight times 900 makes 7,200, and nine pieces give nine times 7,200, which is 64,800 pounds.