The values given in Table XXII are based on the formula:

P = Fx700+ 15c

700 + 15c + c2 in which,

P = Ultimate strength of timber in pounds per square inch; F = Ultimate crushing strength of timber; I = Length of column, in inches; d = Least diameter, in inches; c = l/ d

Example. If a column 10 feet long is required to support a load of 20,000 pounds, what would be the size of the column required if short-leaf yellow pine was used?

Solution. Dividing the length of the beam in inches by the assumed least diameter, 6 inches, we have 120 6 = 20, which gives the ratio of the length to the diameter. By the table it is shown that 2,857 pounds is the ultimate strength for a column of short-leaf pine, when I d = 20. Assuming a factor of safety of 5, and dividing 2,857 by 5, the working load is found to be 571 per square inch. Dividing 20,000 by 571, it is found that a column whose area is 35 square inches is required to support the load. The square root of 35 is 5.9. Therefore a column of short-leaf yellow pine 6 inches square will support the load.